Learning from Imbalanced Data
Haibo He, Member, IEEE, and Edwardo A. Garcia
Abstract—With the continuous expansion of data availability in many large-scale, complex, and networked systems, such as
surveillance, security, Internet, and finance, it becomes critical to advance the fundamental understanding of knowledge discovery and
analysis from raw data to support decision-making processes. Although existing knowledge discovery and data engineering techniques
have shown great success in many real-world applications, the problem of learning from imbalanced data (the imbalanced learning
problem) is a relatively new challenge that has attracted growing attention from both academia and industry. The imbalanced learning
problem is concerned with the performance of learning algorithms in the presence of underrepresented data and severe class
distribution skews. Due to the inherent complex characteristics of imbalanced data sets, learning from such data requires new
understandings, principles, algorithms, and tools to transform vast amounts of raw data efficiently into information and knowledge
representation. In this paper, we provide a comprehensive review of the development of research in learning from imbalanced data.
Our focus is to provide a critical review of the nature of the problem, the state-of-the-art technologies, and the current assessment
metrics used to evaluate learning performance under the imbalanced learning scenario. Furthermore, in order to stimulate future
research in this field, we also highlight the major opportunities and challenges, as well as potential important research directions for
learning from imbalanced data.
Index Terms—Imbalanced learning, classification, sampling methods, cost-sensitive learning, kernel-based learning, active learning,
assessment metrics.
Ç
1 INTRODUCTION
RECENT developments in science and technology have
enabled the growth and availability of raw data to
occur at an explosive rate. This has created an immense
opportunity for knowledge discovery and data engineering
research to play an essential role in a wide range of
applications from daily civilian life to national security,
from enterprise information processing to governmental
decision-making support systems, from microscale data
analysis to macroscale knowledge discovery. In recent
years, the imbalanced learning problem has drawn a
significant amount of interest from academia, industry,
and government funding agencies. The fundamental issue
with the imbalanced learning problem is the ability of
imbalanced data to significantly compromise the performance
of most standard learning algorithms. Most standard
algorithms assume or expect balanced class distributions or
equal misclassification costs. Therefore, when presented
with complex imbalanced data sets, these algorithms fail to
properly represent the distributive characteristics of the
data and resultantly provide unfavorable accuracies across
the classes of the data. When translated to real-world
domains, the imbalanced learning problem represents a
recurring problem of high importance with wide-ranging
implications, warranting increasing exploration. This increased
interest is reflected in the recent installment of
several major workshops, conferences, and special issues
including the American Association for Artificial Intelligence
(now the Association for the Advancement of
Artificial Intelligence) workshop on Learning from Imbalanced
Data Sets (AAAI ’00) [1], the International Conference
on Machine Learning workshop on Learning from Imbalanced
Data Sets (ICML’03) [2], and the Association for
Computing Machinery Special Interest Group on Knowledge
Discovery and Data Mining Explorations (ACM
SIGKDD Explorations ’04) [3].
With the great influx of attention devoted to the
imbalanced learning problem and the high activity of
advancement in this field, remaining knowledgeable of all
current developments can be an overwhelming task. Fig. 1
shows an estimation of the number of publications on the
imbalanced learning problem over the past decade based on
the Institute of Electrical and Electronics Engineers (IEEE)
and Association for Computing Machinery (ACM) databases.
As can be seen, the activity of publications in this
field is growing at an explosive rate. Due to the relatively
young age of this field and because of its rapid expansion,
consistent assessments of past and current works in the
field in addition to projections for future research are
essential for long-term development. In this paper, we seek
to provide a survey of the current understanding of the
imbalanced learning problem and the state-of-the-art solutions
created to address this problem. Furthermore, in order
to stimulate future research in this field, we also highlight
the major opportunities and challenges for learning from
imbalanced data.
In particular, we first describe the nature of the imbalanced
learning problem in Section 2, which provides the
foundation for our review of imbalanced learning solutions.
In Section 3, we provide a critical review of the innovative
research developments targeting the imbalanced learning
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009 1263
. The authors are with the Department of Electrical and Computer
Engineering, Stevens Institute of Technology, Hoboken, NJ 07030.
E-mail: hhe@stevens.edu, edwardo.garcia@nyu.edu.
Manuscript received 1 May 2008; revised 6 Oct. 2008; accepted 1 Dec. 2008;
published online 19 Dec. 2008.
Recommended for acceptance by C. Clifton.
For information on obtaining reprints of this article, please send e-mail to:
tkde@computer.org, and reference IEEECS Log Number
TKDE-2008-05-0233.
Digital Object Identifier no. 10.1109/TKDE.2008.239.
1041-4347/09/$25.00 ß 2009 IEEE Published by the IEEE Computer Society
problem, including sampling methods, cost-sensitive learning
methods, kernel-based learning methods, and active
learning methods. Assessment metrics for imbalanced
learning are reviewed in Section 4, which provides various
suggested methods that are used to compare and evaluate
the performance of different imbalanced learning algorithms.
Considering how learning from imbalanced data
is a relatively new topic in the research community, in
Section 5, we present a detailed discussion on the opportunities
and challenges for research development in this field.
We hope that this section will provide some useful
suggestions to promote and guide the long-term advancement
of research in this area. Finally, a conclusion is
provided in Section 6.
2 NATURE OF THE PROBLEM
Technically speaking, any data set that exhibits an unequal
distribution between its classes can be considered imbalanced.
However, the common understanding in the
community is that imbalanced data correspond to data
sets exhibiting significant, and in some cases extreme,
imbalances. Specifically, this form of imbalance is referred
to as a between-class imbalance; not uncommon are betweenclass
imbalances on the order of 100:1, 1,000:1, and 10,000:1,
where in each case, one class severely outrepresents
another [4], [5], [6]. Although this description would seem
to imply that all between-class imbalances are innately
binary (or two-class), we note that there are multiclass data
in which imbalances exist between the various classes [7],
[8], [9], [10], [11], [12]. In this paper, we only briefly touch
upon the multiclass imbalanced learning problem, focusing
instead on the two-class imbalanced learning problem for
space considerations.
In order to highlight the implications of the imbalanced
learning problem in the real world, we present an example
from biomedical applications. Consider the “Mammography
Data Set,” a collection of images acquired from a series
of mammography exams performed on a set of distinct
patients, which has been widely used in the analysis of
algorithms addressing the imbalanced learning problem
[13], [14], [15]. Analyzing the images in a binary sense, the
natural classes (labels) that arise are “Positive” or “Negative”
for an image representative of a “cancerous” or
“healthy” patient, respectively. From experience, one would
expect the number of noncancerous patients to exceed
greatly the number of cancerous patients; indeed, this data
set contains 10,923 “Negative” (majority class) samples and
260 “Positive” (minority class) samples. Preferably, we
require a classifier that provides a balanced degree of
predictive accuracy (ideally 100 percent) for both the
minority and majority classes on the data set. In reality,
we find that classifiers tend to provide a severely imbalanced
degree of accuracy, with the majority class having
close to 100 percent accuracy and the minority class having
accuracies of 0-10 percent, for instance [13], [15]. Suppose a
classifier achieves 10 percent accuracy on the minority class
of the mammography data set. Analytically, this would
suggest that 234 minority samples are misclassified as
majority samples. The consequence of this is equivalent to
234 cancerous patients classified (diagnosed) as noncancerous.
In the medical industry, the ramifications of such a
consequence can be overwhelmingly costly, more so than
classifying a noncancerous patient as cancerous [16]. Therefore,
it is evident that for this domain, we require a classifier
that will provide high accuracy for the minority class
without severely jeopardizing the accuracy of the majority
class. Furthermore, this also suggests that the conventional
evaluation practice of using singular assessment criteria,
such as the overall accuracy or error rate, does not provide
adequate information in the case of imbalanced learning.
Therefore, more informative assessment metrics, such as the
receiver operating characteristics curves, precision-recall
curves, and cost curves, are necessary for conclusive
evaluations of performance in the presence of imbalanced
data. These topics will be discussed in detail in Section 4 of
this paper. In addition to biomedical applications, further
speculation will yield similar consequences for domains
such as fraud detection, network intrusion, and oil-spill
detection, to name a few [5], [16], [17], [18], [19].
Imbalances of this form are commonly referred to as
intrinsic, i.e., the imbalance is a direct result of the nature of
the dataspace. However, imbalanced data are not solely
restricted to the intrinsic variety. Variable factors such as
time and storage also give rise to data sets that are
imbalanced. Imbalances of this type are considered extrinsic,
i.e., the imbalance is not directly related to the nature of the
dataspace. Extrinsic imbalances are equally as interesting as
their intrinsic counterparts since it may very well occur that
the dataspace from which an extrinsic imbalanced data set
is attained may not be imbalanced at all. For instance,
suppose a data set is procured from a continuous data
stream of balanced data over a specific interval of time, and
if during this interval, the transmission has sporadic
interruptions where data are not transmitted, then it is
possible that the acquired data set can be imbalanced in
which case the data set would be an extrinsic imbalanced
data set attained from a balanced dataspace.
In addition to intrinsic and extrinsic imbalance, it is
important to understand the difference between relative
imbalance and imbalance due to rare instances (or “absolute
rarity”) [20], [21]. Consider a mammography data set with
100,000 examples and a 100:1 between-class imbalance. We
would expect this data set to contain 1,000 minority class
examples; clearly, the majority class dominates the minority
class. Suppose we then double the sample space by testing
more patients, and suppose further that the distribution
1264 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
Fig. 1. Number of publications on imbalanced learning.
does not change, i.e., the minority class now contains
2,000 examples. Clearly, the minority class is still outnumbered;
however, with 2,000 examples, the minority class
is not necessarily rare in its own right but rather relative to
the majority class. This example is representative of a
relative imbalance. Relative imbalances arise frequently in
real-world applications and are often the focus of many
knowledge discovery and data engineering research efforts.
Some studies have shown that for certain relative imbalanced
data sets, the minority concept is accurately learned
with little disturbance from the imbalance [22], [23], [24].
These results are particularly suggestive because they show
that the degree of imbalance is not the only factor that
hinders learning. As it turns out, data set complexity is the
primary determining factor of classification deterioration,
which, in turn, is amplified by the addition of a relative
imbalance.
Data complexity is a broad term that comprises issues
such as overlapping, lack of representative data, small
disjuncts, and others. In a simple example, consider the
depicted distributions in Fig. 2. In this figure, the stars and
circles represent the minority and majority classes, respectively.
By inspection, we see that both distributions in
Figs. 2a and 2b exhibit relative imbalances. However, notice
how Fig. 2a has no overlapping examples between its classes
and has only one concept pertaining to each class, whereas
Fig. 2b has both multiple concepts and severe overlapping.
Also of interest is subconcept C in the distribution of Fig. 2b.
This concept might go unlearned by some inducers due to its
lack of representative data; this issue embodies imbalances
due to rare instances, which we proceed to explore.
Imbalance due to rare instances is representative of
domains where minority class examples are very limited,
i.e., where the target concept is rare. In this situation, the
lack of representative data will make learning difficult
regardless of the between-class imbalance [20]. Furthermore,
the minority concept may additionally contain a
subconcept with limited instances, amounting to diverging
degrees of classification difficulty [25], [26]. This, in fact, is
the result of another form of imbalance, a within-class
imbalance, which concerns itself with the distribution of
representative data for subconcepts within a class [27], [28],
[29]. These ideas are again highlighted in our simplified
example in Fig. 2. In Fig. 2b, cluster B represents the
dominant minority class concept and cluster C represents a
subconcept of the minority class. Cluster D represents two
subconcepts of the majority class and cluster A (anything
not enclosed) represents the dominant majority class
concept. For both classes, the number of examples in the
dominant clusters significantly outnumber the examples in
their respective subconcept clusters, so that this dataspace
exhibits both within-class and between-class imbalances.
Moreover, if we completely remove the examples in cluster
B, the dataspace would then have a homogeneous minority
class concept that is easily identified (cluster C), but can go
unlearned due to its severe underrepresentation.
The existence of within-class imbalances is closely
intertwined with the problem of small disjuncts, which has
been shown to greatly depreciate classification performance
[23], [27], [28], [29]. Briefly, the problem of small disjuncts
can be understood as follows: A classifier will attempt to
learn a concept by creating multiple disjunct rules that
describe the main concept [20], [25], [26]. In the case of
homogeneous concepts, the classifier will generally create
large disjuncts, i.e., rules that cover a large portion (cluster)
of examples pertaining to the main concept. However, in
the case of heterogeneous concepts, small disjuncts, i.e.,
rules that cover a small cluster of examples pertaining to
the main concept, arise as a direct result of underrepresented
subconcepts [20], [25], [26]. Moreover, since classifiers
attempt to learn both majority and minority concepts,
the problem of small disjuncts is not only restricted to the
minority concept. On the contrary, small disjuncts of the
majority class can arise from noisy misclassified minority
class examples or underrepresented subconcepts. However,
because of the vast representation of majority class data,
this occurrence is infrequent. A more common scenario is
that noise may influence disjuncts in the minority class. In
this case, the validity of the clusters corresponding to the
small disjuncts becomes an important issue, i.e., whether
these examples represent an actual subconcept or are
merely attributed to noise. For example, in Fig. 2b, suppose
a classifier generates disjuncts for each of the two noisy
minority samples in cluster A, then these would be
illegitimate disjuncts attributed to noise compared to
cluster C, for example, which is a legitimate cluster formed
from a severely underrepresented subconcept.
The last issue we would like to discuss is the
combination of imbalanced data and the small sample size
problem [30], [31]. In many of today’s data analysis and
knowledge discovery applications, it is often unavoidable
to have data with high dimensionality and small sample
size; some specific examples include face recognition and
gene expression data analysis, among others. Traditionally,
the small sample size problem has been studied extensively
in the pattern recognition community [30]. Dimensionality
reduction methods have been widely adopted to
handle this issue, e.g., principal component analysis (PCA)
and various extension methods [32]. However, when the
representative data sets’ concepts exhibit imbalances of the
forms described earlier, the combination of imbalanced
data and small sample size presents a new challenge to the
community [31]. In this situation, there are two critical
issues that arise simultaneously [31]. First, since the
sample size is small, all of the issues related to absolute
rarity and within-class imbalances are applicable. Second
and more importantly, learning algorithms often fail to
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1265
Fig. 2. (a) A data set with a between-class imbalance. (b) A highcomplexity
data set with both between-class and within-class imbalances,
multiple concepts, overlapping, noise, and lack of representative
data.
generalize inductive rules over the sample space when
presented with this form of imbalance. In this case, the
combination of small sample size and high dimensionality
hinders learning because of difficultly involved in forming
conjunctions over the high degree of features with limited
samples. If the sample space is sufficiently large enough, a
set of general (albeit complex) inductive rules can be
defined for the dataspace. However, when samples are
limited, the rules formed can become too specific, leading
to overfitting. In regards to learning from such data sets,
this is a relatively new research topic that requires much
needed attention in the community. As a result, we will
touch upon this topic again later in our discussions.
3 THE STATE-OF-THE-ART SOLUTIONS
FOR IMBALANCED LEARNING
The topics discussed in Section 2 provide the foundation for
most of the current research activities on imbalanced
learning. In particular, the immense hindering effects that
these problems have on standard learning algorithms are
the focus of most of the existing solutions. When standard
learning algorithms are applied to imbalanced data, the
induction rules that describe the minority concepts are often
fewer and weaker than those of majority concepts, since the
minority class is often both outnumbered and underrepresented.
To provide a concrete understanding of the
direct effects of the imbalanced learning problem on
standard learning algorithms, we observe a case study of
the popular decision tree learning algorithm.
In this case, imbalanced data sets exploit inadequacies in
the splitting criterion at each node of the decision tree [23],
[24], [33]. Decision trees use a recursive, top-down greedy
search algorithm that uses a feature selection scheme (e.g.,
information gain) to select the best feature as the split
criterion at each node of the tree; a successor (leaf) is then
created for each of the possible values corresponding to the
split feature [26], [34]. As a result, the training set is
successively partitioned into smaller subsets that are
ultimately used to form disjoint rules pertaining to class
concepts. These rules are finally combined so that the final
hypothesis minimizes the total error rate across each class.
The problem with this procedure in the presence of
imbalanced data is two-fold. First, successive partitioning
of the dataspace results in fewer and fewer observations of
minority class examples resulting in fewer leaves describing
minority concepts and successively weaker confidences
estimates. Second, concepts that have dependencies on
different feature space conjunctions can go unlearned by the
sparseness introduced through partitioning. Here, the first
issue correlates with the problems of relative and absolute
imbalances, while the second issue best correlates with the
between-class imbalance and the problem of high dimensionality.
In both cases, the effects of imbalanced data on
decision tree classification performance are detrimental. In
the following sections, we evaluate the solutions proposed
to overcome the effects of imbalanced data.
For clear presentation, we establish here some of the
notations used in this section. Considering a given training
data set S with m examples (i.e., jSj ¼ m), we define:
S ¼ fðxixi; yiÞg; i ¼ 1; . . . ; m, where xixi 2 X is an instance in
the n-dimensional feature space X ¼ f1; f2; . . . ; fnf g, and
yi 2 Y ¼ 1; . . . ; Cf g is a class identity label associated with
instance xixi. In particular, C ¼ 2 represents the two-class
classification problem. Furthermore, we define subsets
Smin & S and Smaj & S, where Smin is the set of minority
class examples in S, and Smaj is the set of majority class
examples in S, so that Smin \ Smaj ¼ Èf g and Smin[
Smaj ¼ Sf g. Lastly, any sets generated from sampling
procedures on S are labeled E, with disjoint subsets Emin
and Emaj representing the minority and majority samples of
E, respectively, whenever they apply.
3.1 Sampling Methods for Imbalanced Learning
Typically, the use of sampling methods in imbalanced
learning applications consists of the modification of an
imbalanced data set by some mechanisms in order to
provide a balanced distribution. Studies have shown that
for several base classifiers, a balanced data set provides
improved overall classification performance compared to
an imbalanced data set [35], [36], [37]. These results justify
the use of sampling methods for imbalanced learning.
However, they do not imply that classifiers cannot learn
from imbalanced data sets; on the contrary, studies have
also shown that classifiers induced from certain imbalanced
data sets are comparable to classifiers induced from the
same data set balanced by sampling techniques [22], [23].
This phenomenon has been directly linked to the problem
of rare cases and its corresponding consequences, as
described in Section 2. Nevertheless, for most imbalanced
data sets, the application of sampling techniques does
indeed aid in improved classifier accuracy.
3.1.1 Random Oversampling and Undersampling
The mechanics of random oversampling follow naturally from
its description by adding a set E sampled from the minority
class: for a set of randomly selected minority examples in
Smin, augment the original set S by replicating the selected
examples and adding them to S. In this way, the number of
total examples in Smin is increased by jEj and the class
distribution balance of S is adjusted accordingly. This
provides a mechanism for varying the degree of class
distribution balance to any desired level. The oversampling
method is simple to both understand and visualize, thus we
refrain from providing any specific examples of its
functionality.
While oversampling appends data to the original data
set, random undersampling removes data from the original
data set. In particular, we randomly select a set of majority
class examples in Smaj and remove these samples from S so
that jSj ¼ jSminj þ jSmajj À jEj. Consequently, undersampling
readily gives us a simple method for adjusting the
balance of the original data set S.
At first glance, the oversampling and undersampling
methods appear to be functionally equivalent since they
both alter the size of the original data set and can actually
provide the same proportion of balance. However, this
commonality is only superficial, each method introduces its
own set of problematic consequences that can potentially
hinder learning [25], [38], [39]. In the case of undersampling,
the problem is relatively obvious: removing
1266 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
examples from the majority class may cause the classifier to
miss important concepts pertaining to the majority class. In
regards to oversampling, the problem is a little more
opaque: since oversampling simply appends replicated data
to the original data set, multiple instances of certain
examples become “tied,” leading to overfitting [38]. In
particular, overfitting in oversampling occurs when classifiers
produce multiple clauses in a rule for multiple copies
of the same example which causes the rule to become too
specific; although the training accuracy will be high in this
scenario, the classification performance on the unseen
testing data is generally far worse [25].
3.1.2 Informed Undersampling
Two examples of informed undersampling that have shown
good results are presented in [40], the EasyEnsemble and
BalanceCascade algorithms. The objective of these two
methods is to overcome the deficiency of information loss
introduced in the traditional random undersampling
method. The implementation of EasyEnsemble is very
straightforward: it develops an ensemble learning system
by independently sampling several subsets from the
majority class and developing multiple classifiers based
on the combination of each subset with the minority class
data. In this way, EasyEnsemble can be considered as an
unsupervised learning algorithm that explores the majority
class data by using independent random sampling with
replacement. On the other hand, the BalanceCascade
algorithm takes a supervised learning approach that
develops an ensemble of classifiers to systematically select
which majority class examples to undersample. Specifically,
for the first hypothesis of the ensemble, Hð1Þ, consider a
sampled set of majority class examples, E, such that Ej j ¼
Sminj j and subject the ensemble to set N ¼ E [ Sminf g to
induce Hð1Þ. Observing the results of Hð1Þ, identify all xixi 2
N that are correctly classified as belonging to Smaj, call this
collection NÃ
maj. Then, since we already have Hð1Þ, it is
reasonable to assume that NÃ
maj is somewhat redundant in
Smaj given that Hð1Þ is already trained. Based on this, we
remove set NÃ
maj from Smaj and generate a new sampled set
of majority class samples, E, with Ej j ¼ Sminj j and again
subject the ensemble to set N ¼ E [ Sminf g to derive Hð2Þ.
This procedure is iterated to a stopping criteria at which
point a cascading combination scheme is used to form a
final hypothesis [40].
Another example of informed undersampling uses the
K-nearest neighbor (KNN) classifier to achieve undersampling.
Based on the characteristics of the given data
distribution, four KNN undersampling methods were
proposed in [41], namely, NearMiss-1, NearMiss-2, NearMiss-3,
and the “most distant” method. The NearMiss-1
method selects those majority examples whose average
distance to the three closest minority class examples is the
smallest, while the NearMiss-2 method selects the majority
class examples whose average distance to the three farthest
minority class examples is the smallest. NearMiss-3 selects
a given number of the closest majority examples for each
minority example to guarantee that every minority example
is surrounded by some majority examples. Finally, the
“most distance” method selects the majority class examples
whose average distance to the three closest minority class
examples is the largest. Experimental results suggested that
the NearMiss-2 method can provide competitive results for
imbalanced learning.
There are also other types of informed undersampling
methods. For instance, the one-sided selection (OSS)
method [42] selects a representative subset of the majority
class E and combines it with the set of all minority
examples Smin to form a preliminary set N; N ¼ E [ Sminf g.
This set N is further refined by using a data cleaning
technique. We will return to the discussion of this method
in Section 3.1.5, now turning our attention to synthetic
sampling methods.
3.1.3 Synthetic Sampling with Data Generation
In regards to synthetic sampling, the synthetic minority
oversampling technique (SMOTE) is a powerful method that
has shown a great deal of success in various applications [13].
The SMOTE algorithm creates artificial data based on the
feature space similarities between existing minority examples.
Specifically, for subset Smin 2 S, consider the K-nearest
neighbors for each example xixi 2 Smin, for some specified
integer K; the K-nearest neighbors are defined as the
K elements of Smin whose euclidian distance between itself
and xixi under consideration exhibits the smallest magnitude
along the n-dimensions of feature space X. To create a
synthetic sample, randomly select one of the K-nearest
neighbors, then multiply the corresponding feature vector
difference with a random number between ½0; 1Š, and finally,
add this vector to xixi
xnewxnew ¼ xixi þ ^xi^xi À xixið Þ Â ; ð1Þ
where xixi 2 Smin is the minority instance under consideration,
^xi^xi is one of the K-nearest neighbors for xixi: ^xi^xi 2 Smin,
and  2 ½0; 1Š is a random number. Therefore, the resulting
synthetic instance according to (1) is a point along the line
segment joining xixi under consideration and the randomly
selected K-nearest neighbor ^xi^xi.
Fig. 3 shows an example of the SMOTE procedure. Fig. 3a
shows a typical imbalanced data distribution, where the stars
and circles represent examples of the minority and majority
class, respectively. The number of K-nearest neighbors is set
to K ¼ 6. Fig. 3b shows a created sample along the line
between xixi and ^xixi, highlighted by the diamond shape. These
synthetic samples help break the ties introduced by simple
oversampling, and furthermore, augment the original data
set in a manner that generally significantly improves
learning. Though it has shown many promising benefits,
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1267
Fig. 3. (a) Example of the K-nearest neighbors for the xixi example under
consideration (K ¼ 6). (b) Data creation based on euclidian distance.
the SMOTE algorithm also has its drawbacks, including over
generalization and variance [43]. We will further analyze
these limitations in the following discussion.
3.1.4 Adaptive Synthetic Sampling
In the SMOTE algorithm, the problem of over generalization
is largely attributed to the way in which it creates
synthetic samples. Specifically, SMOTE generates the same
number of synthetic data samples for each original minority
example and does so without consideration to neighboring
examples, which increases the occurrence of overlapping
between classes [43]. To this end, various adaptive
sampling methods have been proposed to overcome this
limitation; some representative work includes the Borderline-SMOTE
[44] and Adaptive Synthetic Sampling (ADASYN)
[45] algorithms.
Of particular interest with these adaptive algorithms are
the techniques used to identify minority seed samples. In
the case of Borderline-SMOTE, this is achieved as follows:
First, determine the set of nearest neighbors for each
xixi 2 Smin; call this set Si:mÀNN ; Si:mÀNN & S. Next, for each
xixi, identify the number of nearest neighbors that belongs to
the majority class, i.e., jSi:mÀNN \ Smajj. Finally, select those
xixi that satisfy:
m
2
jSi:mÀNN \ Smajj < m: ð2Þ
Equation (2) suggests that only those xixi that have more
majority class neighbors than minority class neighbors are
selected to form the set “DANGER” [44]. Therefore, the
examples in DANGER represent the borderline minority
class examples (the examples that are most likely to be
misclassified). The DANGER set is then fed to the SMOTE
algorithm to generate synthetic minority samples in the
neighborhood of the borders. One should note that if
jSi:mÀNN \ Smajj ¼ m, i.e., if all of the m nearest neighbors of
xixi are majority examples, such as the instance C in Fig. 4,
then this xixi is considered as noise and no synthetic
examples are generated for it. Fig. 4 illustrates an example
of the Borderline-SMOTE procedure. Comparing Fig. 4 and
Fig. 3, we see that the major difference between BorderlineSMOTE
and SMOTE is that SMOTE generates synthetic
instances for each minority instance, while BorderlineSMOTE
only generates synthetic instances for those
minority examples “closer” to the border.
ADASYN, on the other hand, uses a systematic method to
adaptively create different amounts of synthetic data according
to their distributions [45]. This is achieved as follows:
First, calculate the number of synthetic data examples that
need to be generated for the entire minority class:
G ¼ jSmajj À jSminj
À Á
 ; ð3Þ
where  2 ½0; 1Š is a parameter used to specify the desired
balance level after the synthetic data generation process.
Next, for each example xixi 2 Smin, find the K-nearest
neighbors according to the euclidean distance and calculate
the ratio Ài defined as:
Ài ¼
Ái=K
Z
; i ¼ 1; . . . ; jSminj; ð4Þ
where Ái is the number of examples in the K-nearest
neighbors of xixi that belong to Smaj, and Z is a normalization
constant so that Ài is a distribution function (
P
Ài ¼ 1).
Then, determine the number of synthetic data samples that
need to be generated for each xixi 2 Smin:
gi ¼ Ài  G: ð5Þ
Finally, for each xixi 2 Smin, generate gi synthetic data
samples according to (1). The key idea of the ADASYN
algorithm is to use a density distribution À as a criterion to
automatically decide the number of synthetic samples that
need to be generated for each minority example by
adaptively changing the weights of different minority
examples to compensate for the skewed distributions.
3.1.5 Sampling with Data Cleaning Techniques
Data cleaning techniques, such as Tomek links, have been
effectively applied to remove the overlapping that is
introduced from sampling methods. Generally speaking,
Tomek links [46] can be defined as a pair of minimally
distanced nearest neighbors of opposite classes. Given an
instance pair: ðxixi; xxjÞ, where xixi 2 Smin; xxj 2 Smaj, and
dðxixi; xxjÞ is the distance between xixi and xxj, then the ðxixi; xxjÞ
pair is called a Tomek link if there is no instance xxk, such
that dðxixi; xxkÞ < dðxixi; xxjÞ or dðxxj; xxkÞ < dðxixi; xxjÞ. In this way,
if two instances form a Tomek link then either one of these
instances is noise or both are near a border. Therefore, one
can use Tomek links to “cleanup” unwanted overlapping
between classes after synthetic sampling where all Tomek
links are removed until all minimally distanced nearest
neighbor pairs are of the same class. By removing overlapping
examples, one can establish well-defined class
clusters in the training set, which can, in turn, lead to welldefined
classification rules for improved classification
performance. Some representative work in this area
includes the OSS method [42], the condensed nearest
neighbor rule and Tomek Links ðCNNþTomek LinksÞ
integration method [22], the neighborhood cleaning rule
(NCL) [36] based on the edited nearest neighbor (ENN)
rule—which removes examples that differ from two of its
three nearest neighbors, and the integrations of SMOTE
with ENN ðSMOTEþENNÞ and SMOTE with Tomek links
ðSMOTEþTomekÞ [22].
Fig. 5 shows a typical procedure of using SMOTE and
Tomek to clean the overlapping data points.
Fig. 5a shows the original data set distribution for an
artificial imbalanced data set; note the inherent overlapping
that exists between the minority and majority examples.
1268 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
Fig. 4. Data creation based on Borderline instance.
Fig. 5b shows the data set distribution after synthetic
sampling by SMOTE. As can be seen, there is an increased
amount of overlapping introduced by SMOTE. In Fig. 5c,
the Tomek links are identified, which are represented by the
dashed boxes. Last, Fig. 5d shows the data set after cleanup
is performed. We can see that the algorithm produces more
well-defined class clusters, which potentially contributes to
improved classification performance. Furthermore, the idea
illustrated in Fig. 5 is important since it introduces a
consideration for class clusters; we further investigate class
clusters in the following discussion of the cluster-based
sampling algorithm.
3.1.6 Cluster-Based Sampling Method
Cluster-based sampling algorithms are particularly interesting
because they provide an added element of flexibility
that is not available in most simple and synthetic sampling
algorithms, and accordingly can be tailored to target very
specific problems. In [27], the cluster-based oversampling
(CBO) algorithm is proposed to effectively deal with the
within-class imbalance problem in tandem with the
between-class imbalance problem.
The CBO algorithm makes use of the K-means clustering
technique. This procedure takes a random set of K examples
from each cluster (for both classes) and computes the mean
feature vector of these examples, which is designated as the
cluster center. Next, the remaining training examples are
presented one at a time and for each example, the euclidean
distance vector between it and each cluster center is
computed. Each training example is then assigned to the
cluster that exhibits the smallest distance vector magnitude.
Lastly, all cluster means are updated and the process is
repeated until all examples are exhausted (i.e., only one
cluster mean is essentially updated for each example).
Fig. 6 illustrates these steps. Fig. 6a shows the original
distribution. Here, the majority class has three clusters A,
B, and C (mmaj ¼ 3), and each of the clusters has 20, 10,
and 8 examples, respectively. The minority class has two
clusters, D and E (mmin ¼ 2), each with eight and five
examples, respectively. Fig. 6b shows the cluster means
(represented by triangles) for three random examples of
each cluster, i.e., k ¼ 3. Fig. 6b also shows the distance
vectors for the five individually introduced examples
xx1; xx2; xx3; xx4, and xx5. Fig. 6c shows the updated cluster
means and cluster borders as a result of the five
introduced examples. Once all examples are exhausted,
the CBO algorithm inflates all majority class clusters other
than the largest by oversampling so that all majority class
clusters are of the same size as the largest (i.e., clusters B
and C will each have 20 examples). We denote the total
number of majority class examples after the oversampling
process as NCBO; NCBO ¼ jSmajj þ jEmajj (e.g., NCBO ¼ 60
in our example). Then, we oversample the minority
clusters so that each cluster contains NCBO=mmin total
examples (i.e., each minority clusters D and E will have a
total number of 60=2 ¼ 30 examples after the oversampling
procedure). Fig. 6d shows the final data set after
applying the CBO method. Compared to Fig. 6a, we can
see that the final data set has a stronger representation of
rare concepts. We would also like to note that different
oversampling methods can be integrated into the CBO
algorithm. For instance, Jo and Japkowicz [27] used the
random oversampling method discussed in Section 3.1.1,
while our example in Fig. 6 uses synthetic sampling.
Empirical results of CBO are very suggestive into the
nature of the imbalanced learning problem; namely, that
targeting within-class imbalance in tandem with the
between-class imbalance is an effective strategy for imbalanced
data sets.
3.1.7 Integration of Sampling and Boosting
The integration of sampling strategies with ensemble
learning techniques has also been studied in the community.
For instance, the SMOTEBoost [47] algorithm is based
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1269
Fig. 5. (a) Original data set distribution. (b) Post-SMOTE data set.
(c) The identified Tomek Links. (d) The data set after removing Tomek
links.
Fig. 6. (a) Original data set distribution. (b) Distance vectors of examples
and cluster means. (c) Newly defined cluster means and cluster borders.
(d) The data set after cluster-based oversampling method.
on the idea of integrating SMOTE with Adaboost.M2.
Specifically, SMOTEBoost introduces synthetic sampling at
each boosting iteration. In this way, each successive
classifier ensemble focuses more on the minority class.
Since each classifier ensemble is built on a different
sampling of data, the final voted classifier is expected to
have a broadened and well-defined decision region for the
minority class.
Another integrated approach, the DataBoost-IM [14]
method, combines the data generation techniques introduced
in [48] with AdaBoost.M1 to achieve high predictive
accuracy for the minority class without sacrificing accuracy
on the majority class. Briefly, DataBoost-IM generates
synthetic samples according to the ratio of difficult-to-learn
samples between classes. Concretely, for a data set S with
corresponding subsets Smin & S and Smaj & S, and weighted
distribution Dt representing the relative difficulty of learning
for each example xixi 2 S, we rank xixi in descending order
according to their respective weight. We then select the top
jSj  errorðtÞ examples to populate set E; E & S, where
errorðtÞ is the error rate of the current learned classifier.
Thus, E is a collection of the hard-to-learn (hard) samples
from both classes and has subsets Emin & E and Emaj & E.
Moreover, since minority class samples are generally more
difficult to learn than majority class samples, it is expected
that jEmajj jEminj.
Once the difficult examples are identified, DataBoost-IM
proceeds to create synthetic samples according to a twotier
process: first, identify the “seeds” of E from which
synthetic samples are formed, and then, generate synthetic
data based on these samples. The seed identification
procedure is based on the ratio of class representation in
E and S. The number of majority class seeds ML is defined
as ML ¼ minð
jSmajj
jSminj ; jEmajjÞ, and the number of minority
seeds MS is defined as MS ¼ minð
jSmajjÂML
jSminj ; jEminjÞ. We
then proceed to generate synthetic set Esyn, with subsets
Esmin & Esyn and Esmaj & Esyn, such that jEsminj ¼ MS Â
jSminj and jEsmajj ¼ ML Â jSmajj . Set S is then augmented
by Esyn to provide a more balanced class distribution with
more new instances of the minority class. Lastly, the
weighted distribution Dt is updated with consideration to
the newly added synthetic samples.
Evidence that synthetic sampling methods are effective
in dealing with learning from imbalanced data is quite
strong. However, the data generation methods discussed
thus far are complex and computationally expensive.
Noting the essential problem of “ties” in random oversampling
as discussed in Section 3.1.1, Mease et al. [38]
propose a much simpler technique for breaking these ties:
instead of generating new data from computational
methods, use the duplicate data obtained from random
oversampling and introduce perturbations (“jittering”) to
this data to break ties. The resulting algorithm, over/
undersampling with jittering (JOUS-Boost), introduces
independently and identically distributed (iid) noise at
each iteration of boosting to minority examples for which
oversampling creates replicates [38]. This idea is relatively
simple compared to its synthetic sampling counterparts and
also incorporates the benefits of boosted ensembles to
improve performance. It was shown to provide very
efficient results in empirical studies, which suggests that
synthetic procedures can be successful without jeopardizing
runtime costs.
3.2 Cost-Sensitive Methods\for Imbalanced
Learning
While sampling methods attempt to balance distributions
by considering the representative proportions of class
examples in the distribution, cost-sensitive learning methods
consider the costs associated with misclassifying
examples [49], [50]. Instead of creating balanced data
distributions through different sampling strategies, costsensitive
learning targets the imbalanced learning problem
by using different cost matrices that describe the costs for
misclassifying any particular data example. Recent research
indicates that there is a strong connection between costsensitive
learning and learning from imbalanced data;
therefore, the theoretical foundations and algorithms of
cost-sensitive methods can be naturally applied to imbalanced
learning problems [3], [20], [51]. Moreover, various
empirical studies have shown that in some application
domains, including certain specific imbalanced learning
domains [11], [52], [53], cost-sensitive learning is superior to
sampling methods. Therefore, cost-sensitive techniques
provide a viable alternative to sampling methods for
imbalanced learning domains.
3.2.1 Cost-Sensitive Learning Framework
Fundamental to the cost-sensitive learning methodology is
the concept of the cost matrix. The cost matrix can be
considered as a numerical representation of the penalty of
classifying examples from one class to another. For
example, in a binary classification scenario, we define
CðMin; MajÞ as the cost of misclassifying a majority class
example as a minority class example and let CðMaj; MinÞ
represents the cost of the contrary case. Typically, there is
no cost for correct classification of either class and the cost
of misclassifying minority examples is higher than the
contrary case, i.e., CðMaj; MinÞ > CðMin; MajÞ. The objective
of cost-sensitive learning then is to develop a hypothesis
that minimizes the overall cost on the training data set,
which is usually the Bayes conditional risk. These concepts
are easily extended to multiclass data by considering Cði; jÞ
which represents the cost of predicting class i when the true
class is j, where i; j 2 Y ¼ 1; . . . ; Cf g. Fig. 7 shows a typical
cost matrix for a multiclass problem. In this case, the
conditional risk is defined as R ijxxð Þ ¼
P
j P jjxxð ÞC i; jð Þ,
1270 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
Fig. 7. Multiclass cost matrix.
where P jjxxð Þ represents the probability of each class j for a
given example xx [49], [54].
There are many different ways of implementing costsensitive
learning, but, in general, the majority of techniques
fall under three categories. The first class of techniques apply
misclassification costs to the data set as a form of dataspace
weighting; these techniques are essentially cost-sensitive
bootstrap sampling approaches where misclassification
costs are used to select the best training distribution for
induction. The second class applies cost-minimizing techniques
to the combination schemes of ensemble methods; this
class consists of various Metatechniques where standard
learning algorithms are integrated with ensemble methods
to develop cost-sensitive classifiers. Both of these classes
have rich theoretical foundations that justify their approaches,
with cost-sensitive dataspace weighting methods
building on the translation theorem [55], and cost-sensitive
Metatechniques building on the Metacost framework [54]. In
fact, many of the existing research works often integrate the
Metacost framework with dataspace weighting and adaptive
boosting to achieve stronger classification results. To
this end, we consider both of these classes of algorithms as
one in the following section. The last class of techniques
incorporates cost-sensitive functions or features directly into
classification paradigms to essentially “fit” the cost-sensitive
framework into these classifiers. Because many of these
techniques are specific to a particular paradigm, there is no
unifying framework for this class of cost-sensitive learning,
but in many cases, solutions that work for one paradigm can
often be abstracted to work for others. As such, in our
discussion of these types of techniques, we consider a few
methods on a case-specific basis.
3.2.2 Cost-Sensitive Dataspace Weighting
with Adaptive Boosting
Motivated by the pioneering work of the AdaBoost
algorithms [56], [57], several cost-sensitive boosting methods
for imbalanced learning have been proposed. Three
cost-sensitive boosting methods, AdaC1, AdaC2, and
AdaC3, were proposed in [58] which introduce cost items
into the weight updating strategy of AdaBoost. The key idea
of the AdaBoost.M1 method is to iteratively update the
distribution function over the training data. In this way, on
each iteration t :¼ 1; . . . ; T, where T is a preset number of
the total number of iterations, the distribution function Dt is
updated sequentially and used to train a new hypothesis:
Dtþ1ðiÞ ¼ DtðiÞ expðÀthtðxixiÞyiÞ=Zt; ð6Þ
where t ¼ 1
2 lnð1À"t
"t
Þ is the weight updating parameter,
htðxixiÞ is the prediction output of hypothesis ht on the
instance xixi; "t is the error of hypothesis ht over the training
data "t ¼
P
i:htðxixiÞ6¼yi
DtðiÞ, and Zt is a normalization factor
so that Dtþ1 is a distribution function, i.e.,
Pm
i¼1 Dtþ1ðiÞ ¼ 1.
With this description in mind, a cost factor can be applied in
three ways, inside of the exponential, outside of the
exponential, and both inside and outside the exponential.
Analytically, this translates to
Dtþ1ðiÞ ¼ DtðiÞ expðÀtCihtðxixiÞyiÞ=Zt; ð7Þ
Dtþ1ðiÞ ¼ CiDtðiÞ expðÀthtðxixiÞyiÞ=Zt; ð8Þ
Dtþ1ðiÞ ¼ CiDtðiÞ expðÀtCihtðxixiÞyiÞ=Zt: ð9Þ
Equations (7), (8), and (9) corresponds to the AdaC1,
AdaC2,andAdaC3methods,respectively.Here,thecostitem
Ci is the associated cost for each xixi and Cis of higher value
correspond to examples with higher misclassification costs.
In essence, these algorithms increase the probability of
sampling a costly example at each iteration, giving the
classifier more instances of costly examples for a more
targeted approach of induction. In general, it was observed
that the inclusion of cost factors into the weighting scheme of
Adaboost imposes a bias toward the minority concepts and
also increases the use of more relevant data samples in each
hypothesis,providingforamorerobustformofclassification.
Another cost-sensitive boosting algorithm that follows a
similar methodology is AdaCost [59]. AdaCost, like AdaC1,
introduces cost sensitivity inside the exponent of the weight
updating formula of Adaboost. However, instead of applying
the cost items directly, AdaCost uses a cost-adjustment
function that aggressively increases the weights of costly
misclassifications and conservatively decreases the weights
of high-cost examples that are correctly classified. This
modification becomes:
Dtþ1ðiÞ ¼ DtðiÞ expðÀthtðxixiÞyiiÞ=Zt; ð10Þ
with the cost-adjustment function i, defined as i ¼
 sign yi; htðxixiÞð Þ; Cið Þ, where signðyi; htðxixiÞÞ is positive for
correct classification and negative for misclassification. For
clear presentation, one can use þ when signðyi; htðxixiÞÞ ¼ 1
and À when signðyi; htðxixiÞÞ ¼ À1. This method also allows
some flexibility in the amount of emphasis given to the
importance of an example. For instance, Fan et al. [59]
suggest þ ¼ À0:5Ci þ 0:5 and À ¼ 0:5Ci þ 0:5 for good
results in most applications, but these coefficients can be
adjusted according to specific needs. An empirical comparison
over four imbalanced data sets of AdaC1, AdaC2,
AdaC3, and AdaCost and two other similar algorithms,
CSB1 and CSB2 [60], was performed in [58] using decision
trees and a rule association system as the base classifiers. It
was noted that in all cases, a boosted ensemble performed
better than the stand-alone base classifiers using F-measure
(see Section 4.1) as the evaluation metric, and in nearly all
cases, the cost-sensitive boosted ensembles performed
better than plain boosting.
Though these cost-sensitive algorithms can significantly
improve classification performance, they take for granted the
availability of a cost matrix and its associated cost items. In
many situations, an explicit description of misclassification
costs is unknown, i.e., only an informal assertion is known,
such as misclassifications on the positive class are more expensive
than the negative class [51]. Moreover, determining a cost
representation of a given domain can be particularly
challenging and in some cases impossible [61]. As a result,
the techniques discussed in this section are not applicable in
these situations and other solutions must be established. This
is the prime motivation for the cost-sensitive fitting techniques
mentioned earlier. In the following sections, we provide
an overview of these methods for two popular learning
paradigms, namely, decision trees and neural networks.
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1271
3.2.3 Cost-Sensitive Decision Trees
In regards to decision trees, cost-sensitive fitting can take
three forms: first, cost-sensitive adjustments can be applied
to the decision threshold; second, cost-sensitive considerations
can be given to the split criteria at each node; and lastly,
cost-sensitive pruning schemes can be applied to the tree.
A decision tree threshold moving scheme for imbalanced
data with unknown misclassification costs was observed in
[51]. The relationships between the misclassification costs of
each class, the distribution of training examples, and the
placement of the decision threshold have been established in
[62]. However, Maloof [51] notes that the precise definition
of these relationships can be task-specific, rendering a
systematic approach for threshold selection based on these
relationships unfeasible. Therefore, instead of relying on the
training distribution or exact misclassification costs, the
proposed technique uses the ROC evaluation procedure (see
Section 4.2) to plot the range of performance values as the
decision threshold is moved from the point where the total
misclassifications on the positive class are maximally costly
to the point where total misclassifications on the negative
class are maximally costly. The decision threshold that
yields the most dominant point on the ROC curve is then
used as the final decision threshold.
When considering cost sensitivity in the split criterion, the
task at hand is to fit an impurity function that is insensitive
to unequal costs. For instance, traditionally accuracy is used
as the impurity function for decision trees, which chooses
the split with minimal error at each node. However, this
metric is sensitive to changes in sample distributions (see
Section 4.1), and thus, inherently sensitive to unequal costs.
In [63], three specific impurity functions, Gini, Entropy, and
DKM, were shown to have improved cost insensitivity
compared with the accuracy/error rate baseline. Moreover,
these empirical experiments also showed that using the
DKM function generally produced smaller unpruned
decision trees that at worse provided accuracies comparable
to Gini and Entropy. A detailed theoretical basis explaining
the conclusions of these empirical results was later established
in [49], which generalizes the effects of decision tree
growth for any choice of spit criteria.
The final case of cost-sensitive decision tree fitting
applies to pruning. Pruning is beneficial for decision trees
because it improves generalization by removing leaves with
class probability estimates below a specified threshold.
However, in the presence of imbalanced data, pruning
procedures tend to remove leaves describing the minority
concept. It has been shown that though pruning trees
induced from imbalanced data can hinder performance,
using unpruned trees in such cases does not improve
performance [23]. As a result, attention has been given to
improving the class probability estimate at each node to
develop more representative decision tree structures such
that pruning can be applied with positive effects. Some
representative works include the Laplace smoothing method
of the probability estimate and the Laplace pruning
technique [49].
3.2.4 Cost-Sensitive Neural Networks
Cost-sensitive neural networks have also been widely
studied in the community for imbalanced learning. The
neural network is generally represented by a densely
interconnected set of simple neurons. Most practical
applications of the neural network classifier involve a
multilayer structure, such as the popular multilayer
perceptron (MLP) model [64], and learning is facilitated
by using the back propagation algorithm in tandem with
the gradient descent rule. Concretely, assume that one
defines an error function as
Eð!Þ ¼
1
2
X
ðtk À okÞ2
; ð11Þ
where ! is a set of weights that require training, and tk and ok
are the target value and network output value for a neuron k,
respectively. The gradient descent rule aims to find the
steepest descent to modify the weights at each iteration:
Á!n ¼ Àr!Eð!nÞ; ð12Þ
where  is the specified neural network learning rate and
r! represents the gradient operator with respect to
weights !. Moreover, a probabilistic estimate for the
output can be defined by normalizing the output values
of all output neurons.
With this framework at hand, cost sensitivity can be
introduced to neural networks in four ways [65]: first, costsensitive
modifications can be applied to the probabilistic
estimate; second, the neural network outputs (i,e., each ok)
can be made cost-sensitive; third, cost-sensitive modifications
can be applied to the learning rate ; and fourth, the
error minimization function can be adapted to account for
expected costs.
In regards to the probability estimate, Kukar and
Kononenko [65] integrate cost factors into the testing stage
of classification to adaptively modify the probability
estimate of the neural network output. This has the benefit
of maintaining the original structure (and outputs) of the
neural network while strengthening the original estimates
on the more expensive class through cost consideration.
Empirical results in [65] showed that this technique
improves the performance over the original neural network,
although the improvement is not drastic. However, we note
that a more significant performance increase can be
achieved by applying this estimate to ensemble methods
by using cross-validation techniques on a given set; a
similar approach is considered in [11], however using a
slightly different estimate.
The second class of neural network cost-sensitive fitting
techniques directly changes the outputs of the neural
network. In [65], the outputs of the neural network are
altered during training to bias the neural network to focus
more on the expensive class. Empirical results on this
method showed an improvement in classification performance
on average, but also showed a high degree of
variance in the performance measures compared to the least
expected cost over the evaluated data sets. We speculate
that ensemble methods can be applied to alleviate this
problem, but to our knowledge, such experiments have not
been performed to date.
1272 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
The learning rate  can also influence the weight
adjustment (see (12)). As a result, cost-sensitive factors can
be applied to the learning rate to change the impact that the
modification procedure has on the weights, where costly
examples will have a greater impact on weight changes. The
key idea of this approach is to put more attention on costly
examples during learning by effectively decreasing the
learning rate for each corresponding costly example. This
also suggests that low-cost examples will train at a faster
rate than costly examples, so this method also strikes a
balance in training time. Experiments on this technique have
shown it to be very effective for training neural networks
with significant improvements over the base classifier [65].
The final adaptation of cost-sensitive neural networks
replaces the error-minimizing function shown in (11) by an
expected cost minimization function. This form of costsensitive
fitting was shown to be the most dominant of the
methods discussed in this section [65]. It also is in line with
the back propagation methodology and theoretic foundations
established on the transitivity between error-minimizing
and cost-minimizing classifiers.
Though we only provide a treatment for decision trees
and neural networks, many cost-sensitive fitting techniques
exist for other types of learning paradigms as well. For
instance, a great deal of works have focused on costsensitive
Bayesian Classifiers [66], [67], [68], [69] and some
works exist which integrate cost functions with support
vector machines [70], [71], [72]. Interested readers can refer
to these works for a broader overview.
3.3 Kernel-Based Methods and Active Learning
Methods for Imbalanced Learning
Although sampling methods and cost-sensitive learning
methods seem to dominate the current research efforts in
imbalanced learning, numerous other approaches have also
been pursued in the community. In this section, we briefly
review kernel-based learning methods and active learning
methods for imbalanced learning. Since kernel-based
learning methods provide state-of-the-art techniques for
many of today’s data engineering applications, the use of
kernel-based methods to understand imbalanced learning
has naturally attracted growing attention recently.
3.3.1 Kernel-Based Learning Framework
The principles of kernel-based learning are centered on the
theories of statistical learning and Vapnik-Chervonenkis
(VC) dimensions [73]. The representative kernel-based
learning paradigm, support vector machines (SVMs), can
provide relatively robust classification results when applied
to imbalanced data sets [23]. SVMs facilitate learning by
using specific examples near concept boundaries (support
vectors) to maximize the separation margin (soft-margin
maximization) between the support vectors and the
hypothesized concept boundary (hyperplane), meanwhile
minimizing the total classification error [73].
The effects of imbalanced data on SVMs exploit
inadequacies of the soft-margin maximization paradigm
[74], [75]. Since SVMs try to minimize total error, they are
inherently biased toward the majority concept. In the
simplest case, a two-class space is linearly separated by an
“ideal” separation line in the neighborhood of the majority
concept. In this case, it might occur that the support vectors
representing the minority concept are “far away” from this
“ideal” line, and as a result, will contribute less to the final
hypothesis [74], [75], [76]. Moreover, if there is a lack of data
representing the minority concept, there could be an
imbalance of representative support vectors that can also
degrade performance. These same characteristics are also
readily evident in linear nonseparable spaces. In this case, a
kernel function is used to map the linear nonseparable
space into a higher dimensional space where separation is
achievable. However, in this case, the optimal hyperplane
separating the classes will be biased toward the majority
class in order to minimize the high error rates of
misclassifying the more prevalent majority class. In the
worst case, SVMs will learn to classify all examples as
pertaining to the majority class—a tactic that, if the
imbalance is severe, can provide the minimal error rate
across the dataspace.
3.3.2 Integration of Kernel Methods
with Sampling Methods
There have been many works in the community that apply
general sampling and ensemble techniques to the SVM
framework. Some examples include the SMOTE with
Different Costs (SDCs) method [75] and the ensembles of
over/undersampled SVMs [77], [78], [79], [80]. For example,
the SDC algorithm uses different error costs [75] for different
classes to bias the SVM in order to shift the decision boundary
away from positive instances and make positive instances
more densely distributed in an attempt to guarantee a more
well-defined boundary. Meanwhile, the methods proposed
in [78], [79] develop ensemble systems by modifying the data
distributions without modifying the underlying SVM classifier.
Lastly, Wang and Japkowicz [80] proposed to modify the
SVMs with asymmetric misclassification costs in order to
boost performance. This idea is similar to the AdaBoost.M1
[56], [57] algorithm in that it uses an iterative procedure to
effectively modify the weights of the training observations. In
this way, one can build a modified version of the training
data based on such sequential learning procedures to
improve classification performance.
The Granular Support Vector Machines—Repetitive Undersampling
algorithm (GSVM-RU) was proposed in [81] to
integrate SVM learning with undersampling methods. This
method is based on granular support vector machines
(GSVMs) which were developed in a series of papers
according to the principles from statistical learning theory
and granular computing theory [82], [83], [84]. The major
characteristics of GSVMs are two-fold. First, GSVMs can
effectively analyze the inherent data distribution by obser-
vingthetrade-offsbetweenthelocalsignificanceofasubsetof
data and its global correlation. Second, GSVMs improve the
computational efficiency of SVMs through use of parallel
computation. In the context of imbalanced learning, the
GSVM-RU method takes advantage of the GSVM by using an
iterative learning procedure that uses the SVM itself for
undersampling [81]. Concretely, since all minority (positive)
examples are considered to be informative, a positive
information granule is formed from these examples. Then, a
linear SVM is developed using the positive granule and the
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1273
remaining examples in the data set (i.e., Smaj); the negative
examples that are identified as support vectors by this SVM,
the so-called “negative local support vectors” (NLSVs), are
formed into a negative information granule and are removed
from the original training data to obtain a smaller training
data set. Based on this reduced training data set, a new linear
SVM is developed, and again, the new set of NLSVs is formed
into a negative granule and removed from the data set. This
procedure is repeated multiple times to obtain multiple
negative information granules. Finally, an aggregation
operation that considers global correlation is used to select
specific sample sets from those iteratively developed negative
information granules, which are then combined with all
positive samples to develop a final SVM model. In this way,
the GSVM-RU method uses the SVM itself as a mechanism for
undersampling to sequentially develop multiple information
granules with different informative samples, which are later
combined to develop a final SVM for classification.
3.3.3 Kernel Modification Methods
for Imbalanced Learning
In addition to the aforementioned sampling and ensemble
kernel-based learning methods, another major category of
kernel-based learning research efforts focuses more concretely
on the mechanics of the SVM itself; this group of
methods is often called kernel modification method.
One example of kernel modification is the kernel
classifier construction algorithm proposed in [85] based
on orthogonal forward selection (OFS) and the regularized
orthogonal weighted least squares (ROWLSs) estimator.
This algorithm optimizes generalization in the kernel-based
learning model by introducing two major components that
deal with imbalanced data distributions for two-class data
sets. The first component integrates the concepts of leaveone-out
(LOO) cross validation and the area under curve
(AUC) evaluation metric (see Section 4.2) to develop an
LOO-AUC objective function as a selection mechanism of
the most optimal kernel model. The second component
takes advantage of the cost sensitivity of the parameter
estimation cost function in the ROWLS algorithm to assign
greater weight to erroneous data examples in the minority
class than those in the majority class.
Other examples of kernel modification are the various
techniques for adjusting the SVM class boundary. These
methods apply boundary alignment techniques to improve
SVM classification [76], [86], [87]. For instance, in [76],
three algorithmic approaches for adjusting boundary
skews were presented: the boundary movement (BM)
approach, the biased penalties (BPs) approach, and the
class-boundary alignment (CBA) approach. Additionally,
in [86] and [87], the kernel-boundary alignment (KBA)
algorithm was proposed which is based on the idea of
modifying the kernel matrix generated by a kernel function
according to the imbalanced data distribution. The underlying
theoretical foundation of the KBA method builds on
the adaptive conformal transformation (ACT) methodology,
where the conformal transformation on a kernel
function is based on the consideration of the feature-space
distance and the class-imbalance ratio [88]. By generalizing
the foundation of ACT, the KBA method tackles the
imbalanced learning problem by modifying the kernel
matrix in the feature space. Theoretical analyses and
empirical studies showed that this method not only
provides competitive accuracy, but it can also be applied
to both vector data and sequence data by modifying the
kernel matrix.
In a more integrated approach of kernel based learning,
Liu and Chen [89] and [90] propose the total margin-based
adaptive fuzzy SVM kernel method (TAF-SVM) to improve
SVM robustness. The major beneficial characteristics of
TAF-SVM are three-fold. First, TAF-SVM can handle overfitting
by “fuzzifying” the training data, where certain
training examples are treated differently according to their
relative importance. Second, different cost algorithms are
embedded into TAF-SVM, which allows this algorithm to
self-adapt to different data distribution skews. Last, the
conventional soft-margin maximization paradigm is replaced
by the total margin paradigm, which considers both
the misclassified and correctly classified data examples in
the construction of the optimal separating hyperplane.
A particularly interesting kernel modification method for
imbalanced learning is the k-category proximal support
vector machine (PSVM) with Newton refinement [91]. This
method essentially transforms the soft-margin maximization
paradigm into a simple system of k linear equations for
either linear or nonlinear classifiers, where k is the number
of classes. One of the major advantages of this method is that
it can perform the learning procedure very fast because this
method requires nothing more sophisticated than solving
this simple system of linear equations. Lastly, in the presence
of extremely imbalanced data sets, Raskutti and Kowalcyzk
[74] consider both sampling and dataspace weighting
compensation techniques in cases where SVMs completely
ignore one of the classes. In this procedure, two balancing
modes are used in order to balance the data: a similarity
detector is used to learn a discriminator based predominantly
on positive examples, and a novelty detector is used to learn a
discriminator using primarily negative examples.
Several other kernel modification methods exist in the
community including the support cluster machines (SCMs)
for large-scale imbalanced data sets [92], the kernel neural
gas (KNG) algorithm for imbalanced clustering [93], the
P2PKNNC algorithm based on the k-nearest neighbors
classifier and the P2P communication paradigm [94], the
hybrid kernel machine ensemble (HKME) algorithm including
a binary support vector classifier (BSVC) and a one-class
support vector classifier (ÀSV C) with Gaussian radial basis
kernel function [95], and the Adaboost relevance vector
machine (RVM) [96], amongst others. Furthermore, we
would like to note that for many kernel-based learning
methods, there is no strict distinction between the aforementioned
two major categories of Sections 3.3.2 and 3.3.3. In
many situations, learning methods take a hybrid approach
where sampling and ensemble techniques are integrated
with kernel modification methods for improved performance.
For instance, [75] and [76] are good examples of
hybrid solutions for imbalanced learning. In this section, we
categorize kernel-based learning in two sections for better
presentation and organization.
1274 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
3.3.4 Active Learning Methods for Imbalanced Learning
Active learning methods have also been investigated in the
community for imbalanced learning problems. Traditionally,
active learning methods are used to solve problems
related to unlabeled training data. Recently, however,
various issues on active learning from imbalanced data
sets have been discussed in literature [97], [98], [99], [100].
Moreover, we point out that active learning approaches for
imbalanced learning are often integrated into kernel-based
learning methods; as a result, we discuss both methods in
the same light.
SVM-based active learning aims to select the most
informative instances from the unseen training data in
order to retrain the kernel-based model [99], i.e., those
instances that are closest to the current hyperplane. Fig. 8
illustrates the motivation for the selection procedure for
imbalanced data sets [98]. Assume that Fig. 8 represents the
class distribution of an imbalanced data set, where the
shaded region corresponds to the class distribution within
the margin. In this case, the imbalance ratio of data within
the margin is much smaller than the imbalance ratio of the
entire data set. Motivated by this observation, Ertekin et al.
[98] and [99] proposed an efficient SVM-based active
learning method which queries a small pool of data at each
iterative step of active learning instead of querying the
entire data set. In this procedure, an SVM is trained on the
given training data, after which the most informative
instances are extracted and formed into a new training set
according to the developed hyperplane. Finally, the
procedure uses this new training set and all unseen training
data to actively retrain the SVM using the LASVM online
SVM learning algorithm [101] to facilitate the active
learning procedure.
Ertekin et al. [98] and [99] also point out that the search
process for the most informative instances can be computationally
expensive because, for each instance of unseen
data, the algorithm needs to recalculate the distance
between each instance and the current hyperplane. To
solve this problem, they proposed a method to effectively
select such informative instances from a random set of
training populations to reduce the computational cost for
large-scale imbalanced data sets [98], [99]. Additionally,
early stopping criteria for active learning are also discussed
in this work which can be used to achieve faster convergence
of the active learning process as compared to the
random sample selection solution.
In addition to kernel-based integrations, active learning
integrations with sampling techniques have also been
investigated in the community. For instance, Zhu and Hovy
[102] analyzed the effect of undersampling and oversampling
techniques with active learning for the word
sense disambiguation (WSD) imbalanced learning problem.
The active learning method studied in this work is based on
the uncertainty sampling methodology; here, the challenge
is how to measure the uncertainty of an unlabeled instance
in order to select the maximally uncertain instance to
augment the training data. In this case, Entropy was used as
a metric for determining uncertainty. Additionally, two
stopping mechanisms based on maximum confidence and
minimal error were investigated in [102]. Simulation results
concluded that one can use max-confidence as the upper
bound and min-error as the lower bound of the stopping
conditions for active learning in this case. Another active
learning sampling method is the simple active learning
heuristic (SALH) approach proposed in [103]. The key idea
of this method is to provide a generic model for the
evolution of genetic programming (GP) classifiers by
integrating the stochastic subsampling method and a
modified Wilcoxon-Mann-Whitney (WMW) cost function
[103]. The major advantages of the SALH method include
the ability to actively bias the data distribution for learning,
the existence of a robust cost function, and the improvement
of the computational cost related to the fitness
evaluation. Simulation results over six data sets were used
to illustrate the effectiveness of this method.
3.4 Additional Methods for Imbalanced Learning
In closing our review of the state-of-the-art solutions for
imbalanced learning, we would like to note that community
solutions to handle the imbalanced learning problem are
not solely in the form of sampling methods, cost-sensitive
methods, kernel-based methods, and active learning methods.
For instance, the one-class learning or novelty detection
methods have also attracted much attention in the community
[3]. Generally speaking, this category of approaches
aims to recognize instances of a concept by using mainly, or
only, a single class of examples (i.e., recognition-based
methodology) rather than differentiating between instances
of both positive and negative classes as in the conventional
learning approaches (i.e., discrimination-based inductive
methodology). Representative works in this area include the
one-class SVMs [74], [104], [105], [106], [107], [108] and the
autoassociator (or autoencoder) method [109], [110], [111],
[112]. Specifically, Raskutti and Kowalcyzk [74] suggested
that one-class learning is particularly useful in dealing with
extremely imbalanced data sets with high feature space
dimensionality. Additionally, Japkowicz [109] proposed an
approach to train an autoassociator to reconstruct the
positive class at the output layer, and it was suggested that
under certain conditions, such as in multimodal domains,
the one-class learning approach may be superior to the
discrimination-based approaches. Meanwhile, Manevitz
and Yousef [105] and [110] presented the successful
applications of the one-class learning approach to the
document classification domain based on SVMs and
autoencoder, respectively. In [111], a comparison of
different sampling methods and the one-class autoassociator
method was presented, which provides useful suggestions
about the advantages and limitations of both methods.
The novelty detection approach based on redundancy
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1275
Fig. 8. Data imbalance ratio within and outside the margin [98].
compression and nonredundancy differentiation techniques
was investigated in [112]. Recently, Lee and Cho [107]
suggested that novelty detection methods are particularly
useful for extremely imbalanced data sets, while regular
discrimination-based inductive classifiers are suitable for a
relatively moderate imbalanced data sets.
Recently, the Mahalanobis-Taguchi System (MTS) has also
been used for imbalanced learning [113]. The MTS was
originally developed as a diagnostic and forecasting technique
for multivariate data [114], [115]. Unlike most of the
classification paradigms, learning in the MTS is performed by
developing a continuous measurement scale using singleclass
examples instead of the entire training data. Because of
its characteristics, it is expected that the MTS model will not
be influenced by the skewed data distribution, therefore
providing robust classification performance. Motivated by
these observations, Su and Hsiao [113] presented an evaluation
of the MTS model for imbalanced learning with
comparisons to stepwise discriminate analysis (SDA), backpropagation
neural networks, decision trees, and SVMs. This
work showed the effectiveness of the MTS in the presence of
imbalanced data. Moreover, Su and Hsiao [113] also present a
probabilistic thresholding method based on the Chebyshev’s
theorem to systematically determine an appropriate threshold
for MTS classification.
Another important example relates to the combination of
imbalanced data and the small sample size problem, as
discussed in Section 2. Two major approaches were
proposed in [31] to address this issue. First, rank metrics
were proposed as the training and model selection criteria
instead of the traditional accuracy metric. Rank metrics
helps facilitate learning from imbalanced data with small
sample sizes and high dimensionality by placing a greater
emphasis on learning to distinguish classes themselves
instead of the internal structure (feature space conjunctions)
of classes. The second approach is based on the multitask
learning methodology. The idea here is to use a shared
representation of the data to train extra task models related
to the main task, therefore amplifying the effective size of
the underrepresented class by adding extra training
information to the data [31].
Finally, we would also like to note that although the
current efforts in the community are focused on two-class
imbalanced problems, multiclass imbalanced learning problems
exist and are of equal importance. For instance, in [7], a
cost-sensitive boosting algorithm AdaC2.M1 was proposed
to tackle the class imbalance problem with multiple classes.
In this paper, a genetic algorithm was used to search the
optimum cost setup for each class. In [8], an iterative method
for multiclass cost-sensitive learning was proposed based on
three key ideas: iterative cost weighting, dataspace expansion,
and gradient boosting with stochastic ensembles. In [9],
a min-max modular network was proposed to decompose a
multiclass imbalanced learning problem into a series of small
two-class subproblems. Other works of multiclass imbalanced
learning include the rescaling approach for multiclass
cost-sensitive neural networks [10], [11], the ensemble
knowledge for imbalance sample sets (eKISS) method [12],
and others.
As is evident, the range of existing solutions to the
imbalanced learning problem is both multifaceted and well
associated. Consequently, the assessment techniques used
to evaluate these solutions share similar characteristics. We
now turn our attention to these techniques.
4 ASSESSMENT METRICS
FOR IMBALANCED LEARNING
As the research community continues to develop a greater
number of intricate and promising imbalanced learning
algorithms, it becomes paramount to have standardized
evaluation metrics to properly assess the effectiveness of
such algorithms. In this section, we provide a critical review
of the major assessment metrics for imbalanced learning.
4.1 Singular Assessment Metrics
Traditionally, the most frequently used metrics are accuracy
and error rate. Considering a basic two-class classification
problem, let p; nf g be the true positive and negative class
label and Y ; Nf g be the predicted positive and negative
class labels. Then, a representation of classification performance
can be formulated by a confusion matrix (contingency
table), as illustrated in Fig. 9.
In this paper, we use the minority class as the positive
class and the majority class as the negative class. Following
this convention, accuracy and error rate are defined as
Accuracy ¼
TP þ TN
PC þ NC
; ErrorRate ¼ 1 À accuracy: ð13Þ
These metrics provide a simple way of describing a
classifier’s performance on a given data set. However, they
can be deceiving in certain situations and are highly
sensitive to changes in data. In the simplest situation, if a
given data set includes 5 percent of minority class examples
and 95 percent of majority examples, a naive approach of
classifying every example to be a majority class example
would provide an accuracy of 95 percent. Taken at face
value, 95 percent accuracy across the entire data set appears
superb; however, on the same token, this description fails to
reflect the fact that 0 percent of minority examples are
identified. That is to say, the accuracy metric in this case does
not provide adequate information on a classifier’s functionality
with respect to the type of classification required.
Many representative works on the ineffectiveness of
accuracy in the imbalanced learning scenario exist in the
community [14], [20], [47], [51], [58], [116], [117], [118].
The fundamental issue can be explained by evaluating the
1276 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
Fig. 9. Confusion matrix for performance evaluation.
confusion matrix in Fig. 9: The left column represents
positive instances of the data set and the right column
represents the negative instances. Therefore, the proportion
of the two columns is representative of the class
distribution of the data set, and any metric that uses
values from both columns will be inherently sensitive to
imbalances. As we can see from (13), accuracy uses both
columns’ information; therefore, as class distribution
varies, measures of the performance will change even
though the underlying fundamental performance of the
classifier does not. As one can imagine, this can be very
problematic when comparing the performance of different
learning algorithms over different data sets because of the
inconsistency of performance representation. In other
words, in the presence of imbalanced data, it becomes
difficult to make relative analysis when the evaluation
metrics are sensitive to data distributions.
In lieu of accuracy, other evaluation metrics are frequently
adopted in the research community to provide comprehensive
assessments of imbalanced learning problems, namely,
precision; recall; F-measure, and G-mean. These metrics are
defined as:
Precision ¼
TP
TP þ FP
; ð14Þ
Recall ¼
TP
TP þ FN
; ð15Þ
F-Measure ¼
ð1 þ Þ2
Á Recall Á Precision
2 Á Recall þ Precision
; ð16Þ
where  is a coefficient to adjust the relative importance of
precision versus recall (usually,  ¼ 1):
G-mean ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
TP
TP þ FN
Â
TN
TN þ FP
r
: ð17Þ
Intuitively, precision is a measure of exactness (i.e., of the
examples labeled as positive, how many are actually labeled
correctly), whereas recall is a measure of completeness (i.e.,
how many examples of the positive class were labeled
correctly). These two metrics, much like accuracy and error,
share an inverse relationship between each other. However,
unlike accuracy and error, precision and recall are not both
sensitive to changes in data distributions. A quick inspection
on the precision and recall formulas readily yields that
precision (14) is sensitive to data distributions, while recall
(15) is not. On the other hand, that recall is not distribution
dependent is almost superfluous because an assertion based
solely on recall is equivocal, since recall provides no insight
to how many examples are incorrectly labeled as positive.
Similarly, precision cannot assert how many positive
examples are labeled incorrectly. Nevertheless, when used
properly, precision and recall can effectively evaluate
classification performance in imbalanced learning scenarios.
Specifically, the F-Measure metric (16) combines precision
and recall as a measure of the effectiveness of classification
in terms of a ratio of the weighted importance on either recall
or precision as determined by the  coefficient set by the
user. As a result, F-Measure provides more insight into the
functionality of a classifier than the accuracy metric,
however remaining sensitive to data distributions. Another
metric, the G-Mean metric (17), evaluates the degree of
inductive bias in terms of a ratio of positive accuracy and
negative accuracy. Though F-Measure and G-Mean are great
improvements over accuracy, they are still ineffective in
answering more generic questions about classification
evaluations. For instance, how can we compare the performance
of different classifiers over a range sample distributions?
4.2 Receiver Operating Characteristics
(ROC) Curves
In order to overcome such issues, the ROC assessment
technique [119], [120] makes use of the proportion of two
single-column-based evaluation metrics, namely, true positives
rate (TP rate) and false positives rate (FP rate),
which are defined as:
TP rate ¼
TP
PC
; FP rate ¼
FP
NC
: ð18Þ
The ROC graph is formed by plotting TP rate over
FP rate, and any point in ROC space corresponds to the
performance of a single classifier on a given distribution.
The ROC curve is useful because it provides a visual
representation of the relative trade-offs between the benefits
(reflected by true positives) and costs (reflected by false
positives) of classification in regards to data distributions.
For hard-type classifiers that output only discrete class
labels, each classifier will produce a (TP rate; FP rate) pair
that corresponds to a single point in the ROC space. Fig. 10
illustrates a typical ROC graph with points A, B, C, D, E, F,
and G representing ROC points and curves L1 and L2
representing ROC curves. According to the structure of the
ROC graph, point A ð0; 1Þ represents a perfect classification.
Generally speaking, one classifier is better than another if its
corresponding point in ROC space closer to point A (upper
left hand in the ROC space) than the other. Any classifier
whose corresponding ROC point is located on the diagonal,
such as point E in Fig. 10, is representative of a classifier
that will provide a random guess of the class labels (i.e., a
random classifier). Therefore, any classifier that appears in
the lower right triangle of ROC space performs worse than
random guessing, such as the classifier associated with
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1277
Fig. 10. ROC curve representation.
point F in the shaded area in Fig. 10. Nevertheless, a
classifier that performs worse than random guessing does
not mean that the classifier cannot provide useful information.
On the contrary, the classifier is informative; however,
the information is incorrectly applied. For instance, if one
negates the classification results of classifier F, i.e., reverse
its classification decision on each instance, then this will
produce point G in Fig. 10, the symmetric classification
point of F.
In the case of soft-type classifiers, i.e., classifiers that
output a continuous numeric value to represent the
confidence of an instance belonging to the predicted class,
a threshold can be used to produce a series of points in ROC
space. This technique can generate an ROC curve instead of
a single ROC point, as illustrated by curves L1 and L2 in
Fig. 10. In order to assess different classifiers’ performance
in this case, one generally uses the area under the curve
(AUC) as an evaluation criterion [119], [120]. For instance,
in Fig. 10, the L2 ROC curve provides a larger AUC
measure compared to that of L1; therefore, the corresponding
classifier associated with curve L2 can provide better
average performance compared to the classifier associated
with curve L1. Of course, one should also note that it is
possible for a high AUC classifier to perform worse in a
specific region in ROC space than a low AUC classifier
[119], [120]. We additionally note that it is generally very
straightforward to make hard-type classifiers provide softtype
outputs based on the observations of the intrinsic
characteristics of those classifiers [54], [56], [121], [122].
4.3 Precision-Recall (PR) Curves
Although ROC curves provide powerful methods to
visualize performance evaluation, they also have their
own limitations. In the case of highly skewed data sets, it
is observed that the ROC curve may provide an overly
optimistic view of an algorithm’s performance. Under such
situations, the PR curves can provide a more informative
representation of performance assessment [123].
Given a confusion matrix as in Fig. 9 and the definition of
precision (14) and recall (15), the PR curve is defined by
plotting precision rate over the recall rate. PR curves exhibit
a strong correspondence to ROC curves: A curve dominates
in ROC space if and only if it dominates in PR space [123].
However, an algorithm that optimizes the AUC in the ROC
space is not guaranteed to optimize the AUC in PR space
[123]. Moreover, while the objective of ROC curves is to be
in the upper left hand of the ROC space, a dominant PR
curve resides in the upper right hand of the PR space. PR
space also characterizes curves analogous to the convex hull
in the ROC space, namely, the achievable PR curve [123].
Hence, PR space has all the analogous benefits of ROC
space, making it an effective evaluation technique. For
space considerations, we refrain from providing a representative
figure of PR space and instead direct interested
readers to [123].
To see why the PR curve can provide more informative
representations of performance assessment under highly
imbalanced data, we consider a distribution where negative
examples significantly exceed the number of positive
examples (i.e., Nc > Pc). In this case, if a classifier’s
performance has a large change in the number of false
positives, it will not significantly change the FP_rate since the
denominator (Nc) is very large (see (18)). Hence, the ROC
graph will fail to capture this phenomenon. The precision
metric, on the other hand, considers the ratio of TP with
respect to TPþFP (see Fig. 9 and (14)); hence, it can correctly
capture the classifier’s performance when the number of
false positives drastically change [123]. Hence, as evident by
this example, the PR curve is an advantageous technique for
performance assessment in the presence of highly skewed
data. As a result, many of the current research work in the
community use PR curves for performance evaluations and
comparisons [124], [125], [126], [127].
4.4 Cost Curves
Another shortcoming of ROC curves is that they lack the
ability to provide confidence intervals on a classifier’s
performance and are unable to infer the statistical
significance of different classifiers’ performance [128],
[129]. They also have difficulties providing insights on a
classifier’s performance over varying class probabilities or
misclassification costs [128], [129]. In order to provide a
more comprehensive evaluation metric to address these
issues, cost curves were proposed in [128], [129], [130]. A
cost curve is a cost-sensitive evaluation technique that
provides the ability to explicitly express a classifier’s
performance over varying misclassification costs and class
distributions in a visual format. Thus, the cost curve
method retains the attractive visual representation features
of ROC analysis and further provides a technique
that yields a broadened range of information regarding
classification performance.
Generally speaking, the cost curve method plots performance
(i.e., normalized expected cost) over operation
points, which are represented by a probability cost function
that is based on the probability of correctly classifying a
positive sample. The cost space exhibits a duality with ROC
space where each point in ROC space is represented by a
line in cost space, and vice versa [128]. Any (FP, TP)
classification pair in ROC space is related to a line in cost
space by
E½CŠ ¼ ð1 À TP À FPÞ Â PCFðþÞ þ FP; ð19Þ
where E[C] is the expected cost and PCF ðþÞ is the
probability of an example being from the positive class.
Fig. 11 provides an example of cost space; here, we
highlight the correspondence between the ROC points of
1278 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
Fig. 11. Cost curve representation.
Fig. 10 and their lines in cost space. For instance, the bottom
axis represents perfect classification, while the top axis
represents the contrary case; these lines correspond to ROC
points A and B, respectively.
With a collection of cost lines at hand, a cost curve is then
created by selecting a classification line for each possible
operation point. For example, a cost curve can be created
that minimizes the normalized expected cost across all
possible operation points. In particular, this technique
allows for a clearer visual representation of classification
performance compared to ROC curves, as well as more
direct assessments between classifiers as they range over
operation points.
4.5 Assessment Metrics for Multiclass
Imbalanced Learning
While all of the assessment metrics discussed so far in this
section are appropriate for two-class imbalanced learning
problems, some of them can be modified to accommodate
the multiclass imbalanced learning problems. For instance,
Fawcett [119] and [120] discussed multiclass ROC graphs.
For an n classes problem, the confusion matrix presented in
Fig. 9 becomes an n  n matrix, with n correct classifications
(the major diagonal elements) and n2
À n errors (the offdiagonal
elements). Therefore, instead of representing the
trade-offs between a single benefit (TP) and cost (FP), we
have to manage n benefits and n2
À n costs. A straightforward
way of doing this is to generate n different ROC
graphs, one for each class [119], [120]. For instance,
considering a problem with a total of W classes, the ROC
graph i; ROCi, plots classification performance using class
wi as the positive class and all other classes as the negative
class. However, this approach compromises one of the
major advantages of using ROC analysis for imbalanced
learning problems: It becomes sensitive to the class skew
because the negative class in this situation is the combination
of n À 1 classes (see Sections 4.1 and 4.2).
Similarly, under the multiclass imbalanced learning
scenario, the AUC values for two-class problems become
multiple pairwise discriminability values [131]. To calculate
such multiclass AUCs, Provost and Domingos [121]
proposed a probability estimation-based approach: First,
the ROC curve for each reference class wi is generated and
their respective AUCs are measured. Second, all of the
AUCs are combined by a weight coefficient according to the
reference class’s prevalence in the data. Although this
approach is quite simple in calculation, it is sensitive to the
class skews for the same reason as mentioned before. To
eliminate this constraint, Hand and Till [131] proposed the
M measure, a generalization approach that aggregates all
pairs of classes based on the inherent characteristics of the
AUC. The major advantage of this method is that it is
insensitive to class distribution and error costs. Interested
readers can refer to [131] for a more detailed overview of
this technique.
In addition to multiclass ROC analysis, the community
has also adopted other assessment metrics for multiclass
imbalanced learning problems. For instance, in cost-sensitive
learning, it is natural to use misclassification costs for
performance evaluation for multiclass imbalanced problems
[8], [10], [11]. Also, Sun et al. [7] extend the G-mean
definition (see (17)) to the geometric means of recall values
of every class for multiclass imbalanced learning.
5 OPPORTUNITIES AND CHALLENGES
The availability of vast amounts of raw data in many of
today’s real-world applications enriches the opportunities
of learning from imbalanced data to play a critical role
across different domains. However, new challenges arise at
the same time. Here, we briefly discuss several aspects for
the future research directions in this domain.
5.1 Understanding the Fundamental Problems
Currently, most of the research efforts in imbalanced
learning focus on specific algorithms and/or case studies;
only a very limited amount of theoretical understanding
on the principles and consequences of this problem have
been addressed. For example, although almost every
algorithm presented in literature claims to be able to
improve classification accuracy over certain benchmarks,
there exist certain situations in which learning from the
original data sets may provide better performance. This
raises an important question: to what extent do imbalanced
learning methods help with learning capabilities? This is a
fundamental and critical question in this field for the
following reasons. First, suppose there are specific (existing
or future) techniques or methodologies that significantly
outperform others across most (or, ideally, all)
applicable domains, then rigorous studies of the underlying
effects of such methods would yield fundamental
understandings of the problem at hand. Second, as data
engineering research methodologies materialize into realworld
solutions, questions such as “how will this solution
help” or “can this solution efficiently handle various types
of data,” become the basis on which economic and
administrative decisions are made. Thus, the consequences
of this critical question have wide-ranging effects in the
advancement of this field and data engineering at large.
This important question follows directly from a previous
proposition addressed by Provost in the invited paper for
the AAAI 2000 Workshop on Imbalanced Data Sets [100]:
“[In regards to imbalanced learning,]. . . isn’t the best research
strategy to concentrate on how machine learning algorithms can
deal most effectively with whatever data they are given?”
We believe that this fundamental question should be
investigated with greater intensity both theoretically and
empirically in order to thoroughly understand the essence
of imbalanced learning problems. More specifically, we
believe that the following questions require careful and
thorough investigation:
1. What kind of assumptions will make imbalanced
learning algorithms work better compared to learning
from the original distributions?
2. To what degree should one balance the original
data set?
3. How do imbalanced data distributions affect the
computational complexity of learning algorithms?
4. What is the general error bound given an imbalanced
data distribution?
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1279
5. Is there a general theoretical methodology that can
alleviate the impediment of learning from imbalanced
data sets for specific algorithms and application
domains?
Fortunately, we have noticed that these critical fundamental
problems have attracted growing attention in the
community. For instance, important works are presented in
[37] and [24] that directly relate to the aforementioned
question 2 regarding the “level of the desired degree of
balance.” In [37], the rate of oversampling and undersampling
was discussed as a possible aid for imbalanced
learning. Generally speaking, though the resampling paradigm
has had successful cases in the community, tuning
these algorithms effectively is a challenging task. To
alleviate this challenge, Estabrooks et al. [37] suggested
that a combination of different expressions of resampling
methods may be an effective solution to the tuning problem.
Weiss and Provost [24] have analyzed, for a fixed training
set size, the relationship between the class distribution of
training data (expressed as the percentage of minority class
examples) and classifier performance in terms of accuracy
and AUC. This work provided important suggestions
regarding “how do different training data class distributions
affect classification performance” and “which class
distribution provides the best classifier” [24]. Based on a
thorough analysis of 26 data sets, it was suggested that if
accuracy is selected as the performance criterion, the best
class distribution tends to be near the naturally occurring
class distribution. However, if the AUC is selected as the
assessment metric, then the best class distribution tends to
be near the balanced class distribution. Based on these
observations, a “budget-sensitive” progressive sampling
strategy was proposed to efficiently sample the minority
and majority class examples such that the resulting training
class distribution can provide the best performance.
In summary, the understanding of all these questions will
not only provide fundamental insights to the imbalanced
learning issue, but also provide an added level of comparative
assessment between existing and future methodologies.
It is essential for the community to investigate all of these
questions in order for research developments to focus on the
fundamental issues regarding imbalanced learning.
5.2 Need of a Uniform Benchmark Platform
Data resources are critical for research development in the
knowledge discovery and data engineering field. Although
there are currently many publicly available benchmarks for
assessing the effectiveness of different data engineering
algorithm/tools, such as the UCI Repository [132] and the
NIST Scientific and Technical Databases [133], there are a
very limited number of benchmarks, if any, that are solely
dedicated to imbalanced learning problems. For instance,
many of the existing benchmarks do not clearly identify
imbalanced data sets and their suggested evaluation use in
an organized manner. Therefore, many data sets require
additional manipulation before they can be applied to
imbalanced learning scenarios. This limitation can create a
bottleneck for the long-term development of research in
imbalanced learning in the following aspects:
1. lack of a uniform benchmark for standardized
performance assessments;
2. lack of data sharing and data interoperability across
different disciplinary domains;
3. increased procurement costs, such as time and labor,
for the research community as a whole group since
each research group is required to collect and
prepare their own data sets.
With these factors in mind, we believe that a wellorganized,
publicly available benchmark specifically dedicated
to imbalanced learning will significantly benefit the
long-term research development of this field. Furthermore,
as a required component, an effective mechanism to promote
the interoperability and communication across various
disciplines should be incorporated into such a benchmark
to ultimately uphold a healthy, diversified community.
5.3 Need of Standardized Evaluation Practices
As discussed in Section 4, the traditional technique of
using a singular evaluation metric is not sufficient when
handling imbalanced learning problems. Although most
publications use a broad assortment of singular assessment
metrics to evaluate the performance and potential
trade-offs of their algorithms, without an accompanied
curve-based analysis, it becomes very difficult to provide
any concrete relative evaluations between different algorithms,
or answer the more rigorous questions of
functionality. Therefore, it is necessary for the community
to establish—as a standard—the practice of using the
curve-based evaluation techniques described in Sections
4.2, 4.3, and 4.4 in their analysis. Not only because
each technique provides its own set of answers to
different fundamental questions, but also because an
analysis in the evaluation space of one technique can be
correlated to the evaluation space of another, leading to
increased transitivity and a broader understanding of the
functional abilities of existing and future works. We hope
that a standardized set of evaluation practices for proper
comparisons in the community will provide useful guides
for the development and evaluation of future algorithms
and tools.
5.4 Incremental Learning from Imbalanced
Data Streams
Traditional static learning methods require representative
data sets to be available at training time in order to develop
decision boundaries. However, in many realistic application
environments, such as Web mining, sensor networks,
multimedia systems, and others, raw data become available
continuously over an indefinite (possibly infinite) learning
lifetime [134]. Therefore, new understandings, principles,
methodologies, algorithms, and tools are needed for such
stream data learning scenarios to efficiently transform raw
data into useful information and knowledge representation
to support the decision-making processes. Although the
importance of stream data mining has attracted increasing
attention recently, the attention given to imbalanced data
streams has been rather limited. Moreover, in regards to
incremental learning from imbalanced data streams, many
important questions need to be addressed, such as:
1280 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
1. How can we autonomously adjust the learning
algorithm if an imbalance is introduced in the
middle of the learning period?
2. Should we consider rebalancing the data set during
the incremental learning period? If so, how can we
accomplish this?
3. How can we accumulate previous experience and
use this knowledge to adaptively improve learning
from new data?
4. How do we handle the situation when newly
introduced concepts are also imbalanced (i.e., the
imbalanced concept drifting issue)?
A concrete understanding and active exploration in these
areas can significantly advance the development of technology
for real-world incremental learning scenarios.
5.5 Semisupervised Learning from Imbalanced Data
The semisupervised learning problem concerns itself with
learning when data sets are a combination of labeled and
unlabeled data, as opposed to fully supervised learning
where all training data are labeled. The key idea of
semisupervised learning is to exploit the unlabeled examples
by using the labeled examples to modify, refine, or
reprioritize the hypothesis obtained from the labeled data
alone [135]. For instance, cotraining works under the
assumption of two-viewed sets of feature spaces. Initially,
two separate classifiers are trained with the labeled
examples on two sufficient and conditionally independent
feature subsets. Then, each classifier is used to predict the
unlabeled data and recover their labels according to their
respective confidence levels [136], [137]. Other representative
works for semisupervised learning include the selftraining
methods [138], [139], semisupervised support
vector machines [140], [141], graph-based methods [142],
[143], and Expectation-Maximization (EM) algorithm with
generative mixture models [144], [145]. Although all of
these methods have illustrated great success in many
machine learning and data engineering applications, the
issue of semisupervised learning under the condition of
imbalanced data sets has received very limited attention in
the community. Some important questions include:
1. How can we identify whether an unlabeled data
example came from a balanced or imbalanced
underlying distribution?
2. Given an imbalanced training data with labels, what
are the effective and efficient methods for recovering
the unlabeled data examples?
3. What kind of biases may be introduced in the
recovery process (through the conventional semisupervised
learning techniques) given imbalanced,
labeled data?
We believe that all of these questions are important not
only for theoretical research development, but also for
many practical application scenarios.
6 CONCLUSIONS
In this paper, we discussed a challenging and critical
problem in the knowledge discovery and data engineering
field, the imbalanced learning problem. We hope that our
discussions of the fundamental nature of the imbalanced
learning problem, the state-of-the-art solutions used to
address this problem, and the several major assessment
techniques used to evaluate this problem will serve as a
comprehensive resource for existing and future knowledge
discovery and data engineering researchers and practitioners.
Additionally, we hope that our insights on the many
opportunities and challenges available in this relatively new
research area will help guide the potential research directions
for the future development of this field.
REFERENCES
[1] “Learning from Imbalanced Data Sets,” Proc. Am. Assoc. for
Artificial Intelligence (AAAI) Workshop, N. Japkowicz, ed., 2000,
(Technical Report WS-00-05).
[2] “Workshop Learning from Imbalanced Data Sets II,” Proc. Int’l
Conf. Machine Learning, N.V. Chawla, N. Japkowicz, and A. Kolcz,
eds., 2003.
[3] N.V. Chawla, N. Japkowicz, and A. Kolcz, “Editorial: Special Issue
on Learning from Imbalanced Data Sets,” ACM SIGKDD Explorations
Newsletter, vol. 6, no. 1, pp. 1-6, 2004.
[4] H. He and X. Shen, “A Ranked Subspace Learning Method for
Gene Expression Data Classification,” Proc. Int’l Conf. Artificial
Intelligence, pp. 358-364, 2007.
[5] M. Kubat, R.C. Holte, and S. Matwin, “Machine Learning for the
Detection of Oil Spills in Satellite Radar Images,” Machine
Learning, vol. 30, nos. 2/3, pp. 195-215, 1998.
[6] R. Pearson, G. Goney, and J. Shwaber, “Imbalanced Clustering for
Microarray Time-Series,” Proc. Int’l Conf. Machine Learning, Workshop
Learning from Imbalanced Data Sets II, 2003.
[7] Y. Sun, M.S. Kamel, and Y. Wang, “Boosting for Learning Multiple
Classes with Imbalanced Class Distribution,” Proc. Int’l Conf. Data
Mining, pp. 592-602, 2006.
[8] N. Abe, B. Zadrozny, and J. Langford, “An Iterative Method for
Multi-Class Cost-Sensitive Learning,” Proc. ACM SIGKDD Int’l
Conf. Knowledge Discovery and Data Mining, pp. 3-11, 2004.
[9] K. Chen, B.L. Lu, and J. Kwok, “Efficient Classification of MultiLabel
and Imbalanced Data Using Min-Max Modular Classifiers,”
Proc. World Congress on Computation Intelligence—Int’l Joint Conf.
Neural Networks, pp. 1770-1775, 2006.
[10] Z.H. Zhou and X.Y. Liu, “On Multi-Class Cost-Sensitive Learning,”
Proc. Nat’l Conf. Artificial Intelligence, pp. 567-572, 2006.
[11] X.Y. Liu and Z.H. Zhou, “Training Cost-Sensitive Neural Networks
with Methods Addressing the Class Imbalance Problem,”
IEEE Trans. Knowledge and Data Eng., vol. 18, no. 1, pp. 63-77, Jan.
2006.
[12] C. Tan, D. Gilbert, and Y. Deville, “Multi-Class Protein Fold
Classification Using a New Ensemble Machine Learning Approach,”
Genome Informatics, vol. 14, pp. 206-217, 2003.
[13] N.V. Chawla, K.W. Bowyer, L.O. Hall, and W.P. Kegelmeyer,
“SMOTE: Synthetic Minority Over-Sampling Technique,”
J. Artificial Intelligence Research, vol. 16, pp. 321-357, 2002.
[14] H. Guo and H.L. Viktor, “Learning from Imbalanced Data Sets
with Boosting and Data Generation: The DataBoost IM Approach,”
ACM SIGKDD Explorations Newsletter, vol. 6, no. 1,
pp. 30-39, 2004.
[15] K. Woods, C. Doss, K. Bowyer, J. Solka, C. Priebe, and W.
Kegelmeyer, “Comparative Evaluation of Pattern Recognition
Techniques for Detection of Microcalcifications in Mammography,”
Int’l J. Pattern Recognition and Artificial Intelligence, vol. 7,
no. 6, pp. 1417-1436, 1993.
[16] R.B. Rao, S. Krishnan, and R.S. Niculescu, “Data Mining for
Improved Cardiac Care,” ACM SIGKDD Explorations Newsletter,
vol. 8, no. 1, pp. 3-10, 2006.
[17] P.K. Chan, W. Fan, A.L. Prodromidis, and S.J. Stolfo, “Distributed
Data Mining in Credit Card Fraud Detection,” IEEE Intelligent
Systems, vol. 14, no. 6, pp. 67-74, Nov./Dec. 1999.
[18] P. Clifton, A. Damminda, and L. Vincent, “Minority Report in
Fraud Detection: Classification of Skewed Data,” ACM SIGKDD
Explorations Newsletter, vol. 6, no. 1, pp. 50-59, 2004.
[19] P. Chan and S. Stolfo, “Toward Scalable Learning with NonUniform
Class and Cost Distributions,” Proc. Int’l Conf. Knowledge
Discovery and Data Mining, pp. 164-168, 1998.
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1281
[20] G.M. Weiss, “Mining with Rarity: A Unifying Framework,” ACM
SIGKDD Explorations Newsletter, vol. 6, no. 1, pp. 7-19, 2004.
[21] G.M. Weiss, “Mining Rare Cases,” Data Mining and Knowledge
Discovery Handbook: A Complete Guide for Practitioners and
Researchers, pp. 765-776, Springer, 2005.
[22] G.E.A.P.A. Batista, R.C. Prati, and M.C. Monard, “A Study of the
Behavior of Several Methods for Balancing Machine Learning
Training Data,” ACM SIGKDD Explorations Newsletter, vol. 6, no. 1,
pp. 20-29, 2004.
[23] N. Japkowicz and S. Stephen, “The Class Imbalance Problem: A
Systematic Study,” Intelligent Data Analysis, vol. 6, no. 5, pp. 429-
449, 2002.
[24] G.M. Weiss and F. Provost, “Learning When Training Data Are
Costly: The Effect of Class Distribution on Tree Induction,”
J. Artificial Intelligence Research, vol. 19, pp. 315-354, 2003.
[25] R.C. Holte, L. Acker, and B.W. Porter, “Concept Learning and the
Problem of Small Disjuncts,” Proc. Int’l J. Conf. Artificial
Intelligence, pp. 813-818, 1989.
[26] J.R. Quinlan, “Induction of Decision Trees,” Machine Learning,
vol. 1, no. 1, pp. 81-106, 1986.
[27] T. Jo and N. Japkowicz, “Class Imbalances versus Small
Disjuncts,” ACM SIGKDD Explorations Newsletter, vol. 6, no. 1,
pp. 40-49, 2004.
[28] N. Japkowicz, “Class Imbalances: Are We Focusing on the Right
Issue?” Proc. Int’l Conf. Machine Learning, Workshop Learning from
Imbalanced Data Sets II, 2003.
[29] R.C. Prati, G.E.A.P.A. Batista, and M.C. Monard, “Class Imbalances
versus Class Overlapping: An Analysis of a Learning
System Behavior,” Proc. Mexican Int’l Conf. Artificial Intelligence,
pp. 312-321, 2004.
[30] S.J. Raudys and A.K. Jain, “Small Sample Size Effects in Statistical
Pattern Recognition: Recommendations for Practitioners,” IEEE
Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 3,
pp. 252-264, Mar. 1991.
[31] R. Caruana, “Learning from Imbalanced Data: Rank Metrics and
Extra Tasks,” Proc. Am. Assoc. for Artificial Intelligence (AAAI) Conf.,
pp. 51-57, 2000 (AAAI Technical Report WS-00-05).
[32] W.H. Yang, D.Q. Dai, and H. Yan, “Feature Extraction Uncorrelated
Discriminant Analysis for High-Dimensional Data,” IEEE
Trans. Knowledge and Data Eng., vol. 20, no. 5, pp. 601-614, May
2008.
[33] N.V. Chawla, “C4.5 and Imbalanced Data Sets: Investigating the
Effect of Sampling Method, Probabilistic Estimate, and Decision
Tree Structure,” Proc. Int’l Conf. Machine Learning, Workshop
Learning from Imbalanced Data Sets II, 2003.
[34] T.M. Mitchell, Machine Learning. McGraw Hill, 1997.
[35] G.M. Weiss and F. Provost, “The Effect of Class Distribution on
Classifier Learning: An Empirical Study,” Technical Report MLTR-43,
Dept. of Computer Science, Rutgers Univ., 2001.
[36] J. Laurikkala, “Improving Identification of Difficult Small Classes
by Balancing Class Distribution,” Proc. Conf. AI in Medicine in
Europe: Artificial Intelligence Medicine, pp. 63-66, 2001.
[37] A. Estabrooks, T. Jo, and N. Japkowicz, “A Multiple Resampling
Method for Learning from Imbalanced Data Sets,” Computational
Intelligence, vol. 20, pp. 18-36, 2004.
[38] D. Mease, A.J. Wyner, and A. Buja, “Boosted Classification Trees
and Class Probability/Quantile Estimation,” J. Machine Learning
Research, vol. 8, pp. 409-439, 2007.
[39] C. Drummond and R.C. Holte, “C4.5, Class Imbalance, and Cost
Sensitivity: Why Under Sampling Beats Over-Sampling,” Proc.
Int’l Conf. Machine Learning, Workshop Learning from Imbalanced
Data Sets II, 2003.
[40] X.Y. Liu, J. Wu, and Z.H. Zhou, “Exploratory Under Sampling for
Class Imbalance Learning,” Proc. Int’l Conf. Data Mining, pp. 965-
969, 2006.
[41] J. Zhang and I. Mani, “KNN Approach to Unbalanced Data
Distributions: A Case Study Involving Information Extraction,”
Proc. Int’l Conf. Machine Learning (ICML ’2003), Workshop Learning
from Imbalanced Data Sets, 2003.
[42] M. Kubat and S. Matwin, “Addressing the Curse of Imbalanced
Training Sets: One-Sided Selection,” Proc. Int’l Conf. Machine
Learning, pp. 179-186, 1997.
[43] B.X. Wang and N. Japkowicz, “Imbalanced Data Set Learning with
Synthetic Samples,” Proc. IRIS Machine Learning Workshop, 2004.
[44] H. Han, W.Y. Wang, and B.H. Mao, “Borderline-SMOTE: A New
Over-Sampling Method in Imbalanced Data Sets Learning,” Proc.
Int’l Conf. Intelligent Computing, pp. 878-887, 2005.
[45] H. He, Y. Bai, E.A. Garcia, and S. Li, “ADASYN: Adaptive
Synthetic Sampling Approach for Imbalanced Learning,” Proc.
Int’l J. Conf. Neural Networks, pp. 1322-1328, 2008.
[46] I. Tomek, “Two Modifications of CNN,” IEEE Trans. System, Man,
Cybernetics, vol. 6, no. 11, pp. 769-772, Nov. 1976.
[47] N.V. Chawla, A. Lazarevic, L.O. Hall, and K.W. Bowyer,
“SMOTEBoost: Improving Prediction of the Minority Class in
Boosting,” Proc. Seventh European Conf. Principles and Practice of
Knowledge Discovery in Databases, pp. 107-119, 2003.
[48] H. Guo and H.L. Viktor, “Boosting with Data Generation:
Improving the Classification of Hard to Learn Examples,” Proc.
Int’l Conf. Innovations Applied Artificial Intelligence, pp. 1082-1091,
2004.
[49] C. Elkan, “The Foundations of Cost-Sensitive Learning,” Proc. Int’l
Joint Conf. Artificial Intelligence, pp. 973-978, 2001.
[50] K.M. Ting, “An Instance-Weighting Method to Induce CostSensitive
Trees,” IEEE Trans. Knowledge and Data Eng., vol. 14,
no. 3, pp. 659-665, May/June 2002.
[51] M.A. Maloof, “Learning When Data Sets Are Imbalanced and
When Costs Are Unequal and Unknown,” Proc. Int’l Conf. Machine
Learning, Workshop Learning from Imbalanced Data Sets II, 2003.
[52] K. McCarthy, B. Zabar, and G.M. Weiss, “Does Cost-Sensitive
Learning Beat Sampling for Classifying Rare Classes?” Proc. Int’l
Workshop Utility-Based Data Mining, pp. 69-77, 2005.
[53] X.Y. Liu and Z.H. Zhou, “The Influence of Class Imbalance on
Cost-Sensitive Learning: An Empirical Study,” Proc. Int’l Conf.
Data Mining, pp. 970-974, 2006.
[54] P. Domingos, “MetaCost: A General Method for Making
Classifiers Cost-Sensitive,” Proc. Int’l Conf. Knowledge Discovery
and Data Mining, pp. 155-164, 1999.
[55] B. Zadrozny, J. Langford, and N. Abe, “Cost-Sensitive Learning by
Cost-Proportionate Example Weighting,” Proc. Int’l Conf. Data
Mining, pp. 435-442, 2003.
[56] Y. Freund and R.E. Schapire, “Experiments with a New Boosting
Algorithm,” Proc. Int’l Conf. Machine Learning, pp. 148-156, 1996.
[57] Y. Freund and R.E. Schapire, “A Decision-Theoretic Generalization
of On-Line Learning and an Application to Boosting,”
J. Computer and System Sciences, vol. 55, no. 1, pp. 119-139, 1997.
[58] Y. Sun, M.S. Kamel, A.K.C. Wong, and Y. Wang, “Cost-Sensitive
Boosting for Classification of Imbalanced Data,” Pattern Recognition,
vol. 40, no. 12, pp. 3358-3378, 2007.
[59] W. Fan, S.J. Stolfo, J. Zhang, and P.K. Chan, “AdaCost:
Misclassification Cost-Sensitive Boosting,” Proc. Int’l Conf. Machine
Learning, pp. 97-105, 1999.
[60] K.M. Ting, “A Comparative Study of Cost-Sensitive Boosting
Algorithms,” Proc. Int’l Conf. Machine Learning, pp. 983-990, 2000.
[61] M. Maloof, P. Langley, S. Sage, and T. Binford, “Learning to Detect
Rooftops in Aerial Images,” Proc. Image Understanding Workshop,
pp. 835-845, 1997.
[62] L. Breiman, J. Friedman, R. Olshen, and C. Stone, Classification and
Regression Trees. Chapman & Hall/CRC Press, 1984.
[63] C. Drummond and R.C. Holte, “Exploiting the Cost (In)Sensitivity
of Decision Tree Splitting Criteria,” Proc. Int’l Conf. Machine
Learning, pp. 239-246, 2000.
[64] S. Haykin, Neural Networks: A Comprehensive Foundation, second
ed. Prentice-Hall, 1999.
[65] M.Z. Kukar and I. Kononenko, “Cost-Sensitive Learning with
Neural Networks,” Proc. European Conf. Artificial Intelligence,
pp. 445-449, 1998.
[66] P. Domingos and M. Pazzani, “Beyond Independence: Conditions
for the Optimality of the Simple Bayesian Classifier,” Proc. Int’l
Conf. Machine Learning, pp. 105-112, 1996.
[67] G.R.I. Webb and M.J. Pazzani, “Adjusted Probability Naive
Bayesian Induction,” Proc. Australian Joint Conf. Artificial Intelligence,
pp. 285-295, 1998.
[68] R. Kohavi and D. Wolpert, “Bias Plus Variance Decomposition for
Zero-One Loss Functions,” Proc. Int’l Conf. Machine Learning, 1996.
[69] J. Gama, “Iterative Bayes,” Theoretical Computer Science, vol. 292,
no. 2, pp. 417-430, 2003.
[70] G. Fumera and F. Roli, “Support Vector Machines with Embedded
Reject Option,” Proc. Int’l Workshop Pattern Recognition with Support
Vector Machines, pp. 68-82, 2002.
[71] J.C. Platt, “Fast Training of Support Vector Machines Using
Sequential Minimal Optimization,” Advances in Kernel Methods:
Support Vector Learning, pp. 185-208, MIT Press, 1999.
1282 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009
[72] J.T. Kwok, “Moderating the Outputs of Support Vector Machine
Classifiers,” IEEE Trans. Neural Networks, vol. 10, no. 5, pp. 1018-
1031, Sept. 1999.
[73] V.N. Vapnik, The Nature of Statistical Learning Theory. Springer,
1995.
[74] B. Raskutti and A. Kowalczyk, “Extreme Re-Balancing for SVMs:
A Case Study,” ACM SIGKDD Explorations Newsletter, vol. 6, no. 1,
pp. 60-69, 2004.
[75] R. Akbani, S. Kwek, and N. Japkowicz, “Applying Support Vector
Machines to Imbalanced Data Sets,” Lecture Notes in Computer
Science, vol. 3201, pp. 39-50, 2004.
[76] G. Wu and E. Chang, “Class-Boundary Alignment for Imbalanced
Data Set Learning,” Proc. Int’l Conf. Data Mining (ICDM ’03),
Workshop Learning from Imbalanced Data Sets II, 2003.
[77] F. Vilarino, P. Spyridonos, P. Radeva, and J. Vitria, “Experiments
with SVM and Stratified Sampling with an Imbalanced Problem:
Detection of Intestinal Contractions,” Lecture Notes in Computer
Science, vol. 3687, pp. 783-791, 2005.
[78] P. Kang and S. Cho, “EUS SVMs: Ensemble of Under sampled
SVMs for Data Imbalance Problems,” Lecture Notes in Computer
Science, vol. 4232, pp. 837-846, 2006.
[79] Y. Liu, A. An, and X. Huang, “Boosting Prediction Accuracy on
Imbalanced Data Sets with SVM Ensembles,” Lecture Notes in
Artificial Intelligence, vol. 3918, pp. 107-118, 2006.
[80] B.X. Wang and N. Japkowicz, “Boosting Support Vector Machines
for Imbalanced Data Sets,” Lecture Notes in Artificial Intelligence,
vol. 4994, pp. 38-47, 2008.
[81] Y. Tang and Y.Q. Zhang, “Granular SVM with Repetitive
Undersampling for Highly Imbalanced Protein Homology Prediction,”
Proc. Int’l Conf. Granular Computing, pp. 457- 460, 2006.
[82] Y.C. Tang, B. Jin, and Y.-Q. Zhang, “Granular Support Vector
Machines with Association Rules Mining for Protein Homology
Prediction,” Artificial Intelligence in Medicine, special issue on
computational intelligence techniques in bioinformatics, vol. 35,
nos. 1/2, pp. 121-134, 2005.
[83] Y.C. Tang, B. Jin, Y.-Q. Zhang, H. Fang, and B. Wang, “Granular
Support Vector Machines Using Linear Decision Hyperplanes for
Fast Medical Binary Classification,” Proc. Int’l Conf. Fuzzy Systems,
pp. 138-142, 2005.
[84] Y.C. Tang, Y.Q. Zhang, Z. Huang, X.T. Hu, and Y. Zhao,
“Granular SVM-RFE Feature Selection Algorithm for Reliable
Cancer-Related Gene Subsets Extraction on Microarray Gene
Expression Data,” Proc. IEEE Symp. Bioinformatics and Bioeng.,
pp. 290-293, 2005.
[85] X. Hong, S. Chen, and C.J. Harris, “A Kernel-Based Two-Class
Classifier for Imbalanced Data Sets,” IEEE Trans. Neural Networks,
vol. 18, no. 1, pp. 28-41, Jan. 2007.
[86] G. Wu and E.Y. Chang, “Aligning Boundary in Kernel Space for
Learning Imbalanced Data Set,” Proc. Int’l Conf. Data Mining,
pp. 265-272, 2004.
[87] G. Wu and E.Y. Chang, “KBA: Kernel Boundary Alignment
Considering Imbalanced Data Distribution,” IEEE Trans. Knowledge
and Data Eng., vol. 17, no. 6, pp. 786-795, June 2005.
[88] G. Wu and E.Y. Chang, “Adaptive Feature-Space Conformal
Transformation for Imbalanced-Data Learning,” Proc. Int’l Conf.
Machine Learning, pp. 816-823, 2003.
[89] Y.H. Liu and Y.T. Chen, “Face Recognition Using Total MarginBased
Adaptive Fuzzy Support Vector Machines,” IEEE Trans.
Neural Networks, vol. 18, no. 1, pp. 178-192, Jan. 2007.
[90] Y.H. Liu and Y.T. Chen, “Total Margin Based Adaptive Fuzzy
Support Vector Machines for Multiview Face Recognition,” Proc.
Int’l Conf. Systems, Man and Cybernetics, pp. 1704-1711, 2005.
[91] G. Fung and O.L. Mangasarian, “Multicategory Proximal Support
Vector Machine Classifiers,” Machine Learning, vol. 59, nos. 1/2,
pp. 77-97, 2005.
[92] J. Yuan, J. Li, and B. Zhang, “Learning Concepts from Large Scale
Imbalanced Data Sets Using Support Cluster Machines,” Proc. Int’l
Conf. Multimedia, pp. 441-450, 2006.
[93] A.K. Qin and P.N. Suganthan, “Kernel Neural Gas Algorithms
with Application to Cluster Analysis,” Proc. Int’l Conf. Pattern
Recognition, 2004.
[94] X.P. Yu and X.G. Yu, “Novel Text Classification Based on KNearest
Neighbor,” Proc. Int’l Conf. Machine Learning Cybernetics,
pp. 3425-3430, 2007.
[95] P. Li, K.L. Chan, and W. Fang, “Hybrid Kernel Machine Ensemble
for Imbalanced Data Sets,” Proc. Int’l Conf. Pattern Recognition,
pp. 1108-1111, 2006.
[96] A. Tashk, R. Bayesteh, and K. Faez, “Boosted Bayesian Kernel
Classifier Method for Face Detection,” Proc. Int’l Conf. Natural
Computation, pp. 533-537, 2007.
[97] N. Abe, “Invited Talk: Sampling Approaches to Learning from
Imbalanced Data Sets: Active Learning, Cost Sensitive Learning
and Deyond,” Proc. Int’l Conf. Machine Learning, Workshop Learning
from Imbalanced Data Sets II, 2003.
[98] S. Ertekin, J. Huang, L. Bottou, and L. Giles, “Learning on the
Border: Active Learning in Imbalanced Data Classification,” Proc.
ACM Conf. Information and Knowledge Management, pp. 127-136,
2007.
[99] S. Ertekin, J. Huang, and C.L. Giles, “Active Learning for Class
Imbalance Problem,” Proc. Int’l SIGIR Conf. Research and Development
in Information Retrieval, pp. 823-824, 2007.
[100] F. Provost, “Machine Learning from Imbalanced Data Sets 101,”
Proc. Learning from Imbalanced Data Sets: Papers from the Am.
Assoc. for Artificial Intelligence Workshop, 2000 (Technical Report
WS-00-05).
[101] Bordes, S. Ertekin, J. Weston, and L. Bottou, “Fast Kernel
Classifiers with Online and Active Learning,” J. Machine Learning
Research, vol. 6, pp. 1579-1619, 2005.
[102] J. Zhu and E. Hovy, “Active Learning for Word Sense Disambiguation
with Methods for Addressing the Class Imbalance
Problem,” Proc. Joint Conf. Empirical Methods in Natural Language
Processing and Computational Natural Language Learning, pp. 783-
790, 2007.
[103] J. Doucette and M.I. Heywood, “GP Classification under
Imbalanced Data Sets: Active Sub-Sampling AUC Approximation,”
Lecture Notes in Computer Science, vol. 4971, pp. 266-277,
2008.
[104] B. Scholkopt, J.C. Platt, J. Shawe-Taylor, A.J. Smola, and R.C.
Williamson, “Estimating the Support of a High-Dimensional
Distribution,” Neural Computation, vol. 13, pp. 1443-1471, 2001.
[105] L.M. Manevitz and M. Yousef, “One-Class SVMs for Document
Classification,” J. Machine Learning Research, vol. 2, pp. 139-154,
2001.
[106] L. Zhuang and H. Dai, “Parameter Estimation of One-Class SVM
on Imbalance Text Classification,” Lecture Notes in Artificial
Intelligence, vol. 4013, pp. 538-549, 2006.
[107] H.J. Lee and S. Cho, “The Novelty Detection Approach for
Difference Degrees of Class Imbalance,” Lecture Notes in Computer
Science, vol. 4233, pp. 21-30, 2006.
[108] L. Zhuang and H. Dai, “Parameter Optimization of Kernel-Based
One-Class Classifier on Imbalance Text Learning,” Lecture Notes in
Artificial Intelligence, vol. 4099, pp. 434-443, 2006.
[109] N. Japkowicz, “Supervised versus Unsupervised Binary-Learning
by Feedforward Neural Networks,” Machine Learning, vol. 42,
pp. 97-122, 2001.
[110] L. Manevitz and M. Yousef, “One-Class Document Classification
via Neural Networks,” Neurocomputing, vol. 70, pp. 1466-1481,
2007.
[111] N. Japkowicz, “Learning from Imbalanced Data Sets: A Comparison
of Various Strategies,” Proc. Am. Assoc. for Artificial Intelligence
(AAAI) Workshop Learning from Imbalanced Data Sets, pp. 10-15,
2000 (Technical Report WS-00-05).
[112] N. Japkowicz, C. Myers, and M. Gluck, “A Novelty Detection
Approach to Classification,” Proc. Joint Conf. Artificial Intelligence,
pp. 518-523, 1995.
[113] C.T. Su and Y.H. Hsiao, “An Evaluation of the Robustness of MTS
for Imbalanced Data,” IEEE Trans. Knowledge and Data Eng.,
vol. 19, no. 10, pp. 1321-1332, Oct. 2007.
[114] G. Taguchi, S. Chowdhury, and Y. Wu, The Mahalanobis-Taguchi
System. McGraw-Hill, 2001.
[115] G. Taguchi and R. Jugulum, The Mahalanobis-Taguchi Strategy. John
Wiley & Sons, 2002.
[116] M.V. Joshi, V. Kumar, and R.C. Agarwal, “Evaluating Boosting
Algorithms to Classify Rare Classes: Comparison and Improvements,”
Proc. Int’l Conf. Data Mining, pp. 257-264, 2001.
[117] F.J. Provost and T. Fawcett, “Analysis and Visualization of
Classifier Performance: Comparison under Imprecise Class and
Cost Distributions,” Proc. Int’l Conf. Knowledge Discovery and Data
Mining, pp. 43-48, 1997.
[118] F.J. Provost, T. Fawcett, and R. Kohavi, “The Case against
Accuracy Estimation for Comparing Induction Algorithms,” Proc.
Int’l Conf. Machine Learning, pp. 445-453, 1998.
HE AND GARCIA: LEARNING FROM IMBALANCED DATA 1283
[119] T. Fawcett, “ROC Graphs: Notes and Practical Considerations for
Data Mining Researchers,” Technical Report HPL-2003-4, HP
Labs, 2003.
[120] T. Fawcett, “An Introduction to ROC Analysis,” Pattern Recognition
Letters, vol. 27, no. 8, pp. 861-874, 2006.
[121] F. Provost and P. Domingos, “Well-Trained Pets: Improving
Probability Estimation Trees,” CeDER Working Paper: IS-00-04,
Stern School of Business, New York Univ., 2000.
[122] T. Fawcett, “Using Rule Sets to Maximize ROC Performance,”
Proc. Int’l Conf. Data Mining, pp. 131-138, 2001.
[123] J. Davis and M. Goadrich, “The Relationship between PrecisionRecall
and ROC Curves,” Proc. Int’l Conf. Machine Learning,
pp. 233-240, 2006.
[124] R. Bunescu, R. Ge, R. Kate, E. Marcotte, R. Mooney, A. Ramani,
and Y. Wong, “Comparative Experiments on Learning Information
Extractors for Proteins and Their Interactions,” Artificial
Intelligence in Medicine, vol. 33, pp. 139-155, 2005.
[125] J. Davis, E. Burnside, I. Dutra, D. Page, R. Ramakrishnan, V.S.
Costa, and J. Shavlik, “View Learning for Statistical Relational
Learning: With an Application to Mammography,” Proc. Int’l Joint
Conf. Artificial Intelligence, pp. 677-683, 2005.
[126] P. Singla and P. Domingos, “Discriminative Training of Markov
Logic Networks,” Proc. Nat’l Conf. Artificial Intelligence, pp. 868-
873, 2005.
[127] T. Landgrebe, P. Paclik, R. Duin, and A.P. Bradley, “PrecisionRecall
Operating Characteristic (P-ROC) Curves in Imprecise
Environments,” Proc. Int’l Conf. Pattern Recognition, pp. 123-127,
2006.
[128] R.C. Holte and C. Drummond, “Cost Curves: An Improved
Method for Visualizing Classifier Performance,” Machine Learning,
vol. 65, no. 1, pp. 95-130, 2006.
[129] R.C. Holte and C. Drummond, “Cost-Sensitive Classifier Evaluation,”
Proc. Int’l Workshop Utility-Based Data Mining, pp. 3-9, 2005.
[130] R.C. Holte and C. Drummond, “Explicitly Representing Expected
Cost: An Alternative to ROC Representation,” Proc. Int’l Conf.
Knowledge Discovery and Data Mining, pp. 198-207, 2000.
[131] D.J. Hand and R.J. Till, “A Simple Generalization of the Area
under the ROC Curve to Multiple Class Classification Problems,”
Machine Learning, vol. 45, no. 2, pp. 171-186, 2001.
[132] UC Irvine Machine Learning Repository, http://archive.ics.uci.
edu/ml/, 2009.
[133] NIST Scientific and Technical Databases, http://nist.gov/srd/
online.htm, 2009.
[134] H. He and S. Chen, “IMORL: Incremental Multiple Objects
Recognition Localization,” IEEE Trans. Neural Networks, vol. 19,
no. 10, pp. 1727-1738, Oct. 2008.
[135] X. Zhu, “Semi-Supervised Learning Literature Survey,” Technical
Report TR-1530, Univ. of Wisconsin-Madson, 2007.
[136] A. Blum and T. Mitchell, “Combining Labeled and Unlabeled
Data with Co-Training,” Proc. Workshop Computational Learning
Theory, pp. 92-100, 1998.
[137] T.M. Mitchell, “The Role of Unlabeled Data in Supervised
Learning,” Proc. Int’l Colloquium on Cognitive Science, 1999.
[138] C. Rosenberg, M. Hebert, and H. Schneiderman, “Semi-Supervised
Self-Training of Object Detection Models,” Proc. IEEE
Workshops Application of Computer Vision, pp. 29-36, 2005.
[139] M. Wang, X.S. Hua, L.R. Dai, and Y. Song, “Enhanced SemiSupervised
Learning for Automatic Video Annotation,” Proc. Int’l
Conf. Multimedia and Expo, pp. 1485-1488, 2006.
[140] K.P. Bennett and A. Demiriz, “Semi-Supervised Support Vector
Machines,” Proc. Conf. Neural Information Processing Systems,
pp. 368-374, 1998.
[141] V. Sindhwani and S.S. Keerthi, “Large Scale Semi-Supervised
Linear SVMs,” Proc. Int’l SIGIR Conf. Research and Development in
Information Retrieval, pp. 477-484, 2006.
[142] A. Blum and S. Chawla, “Learning from Labeled and Unlabeled
Data Using Graph Mincuts,” Proc. Int’l Conf. Machine Learning,
pp. 19-26, 2001.
[143] D. Zhou, B. Scholkopf, and T. Hofmann, “Semi-Supervised
Learning on Directed Graphs,” Proc. Conf. Neural Information
Processing Systems, pp. 1633-1640, 2004.
[144] A. Fujino, N. Ueda, and K. Saito, “A Hybrid Generative/
Discriminative Approach to Semi-Supervised Classifier Design,”
Proc. Nat’l Conf. Artificial Intelligence, pp. 764-769, 2005.
[145] D.J. Miller and H.S. Uyar, “A Mixture of Experts Classifier with
Learning Based on Both Labeled and Unlabelled Data,” Proc. Ann.
Conf. Neural Information Processing Systems, pp. 571-577, 1996.
Haibo He received the BS and MS degrees in
electrical engineering from Huazhong University
of Science and Technology (HUST), Wuhan,
China, in 1999 and 2002, respectively, and the
PhD degree in electrical engineering from Ohio
University, Athens, in 2006. He is currently an
assistant professor in the Department of Electrical
and Computer Engineering, Stevens Institute
of Technology, Hoboken, New Jersey.
His research interests include machine learning,
data mining, computational intelligence, VLSI and FPGA design, and
embedded intelligent systems design. He has served regularly on the
organization committees and the program committees of many
international conferences and has also been a reviewer for the leading
academic journals in his fields, including the IEEE Transactions on
Knowledge and Data Engineering, the IEEE Transactions on Neural
Networks, the IEEE Transactions on Systems, Man and Cybernetics
(part A and part B), and others. He has also served as a guest editor for
several international journals, such as Soft Computing (Springer) and
Applied Mathematics and Computation (Elsevier), among others. He
has delivered several invited talks including the IEEE North Jersey
Section Systems, Man & Cybernetics invited talk on “Self-Adaptive
Learning for Machine Intelligence.” He was the recipient of the
Outstanding Master Thesis Award of Hubei Province, China, in 2002.
Currently, he is the editor of the IEEE Computational Intelligence
Society (CIS) Electronic Letter (E-letter), and a committee member of
the IEEE Systems, Man, and Cybernetic (SMC) Technical Committee
on Computational Intelligence. He is a member of the IEEE, the ACM,
and the AAAI.
Edwardo A. Garcia received the BS degree in
mathematics from New York University, New
York, and the BE degree in computer engineering
from Stevens Institute of Technology, Hoboken,
New Jersey, both in 2008. He currently
holds research appointments with the Department
of Electrical and Computer Engineering at
Stevens Institute of Technology and with the
Department of Anesthesiology at New York
University School of Medicine. His research
interests include machine learning, biologically inspired intelligence,
cognitive neuroscience, data mining for medical diagnostics, and
mathematical methods for f-MRI.
. For more information on this or any other computing topic,
please visit our Digital Library at www.computer.org/publications/dlib.
1284 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 21, NO. 9, SEPTEMBER 2009