1 Based on Jiawei Han et al. Data mining book/slides, 3rd edition
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3/22/21 2
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!  Data Preprocessing: An Overview
!  Data Cleaning
!  Data Integration
!  Data Reduction and Transformation
!  Dimensionality Reduction
!  Summary
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!  Data cleaning
!  Handle missing data, smooth noisy data, identify or remove outliers, and
resolve inconsistencies
!  Data integration
!  Integration of multiple databases, data cubes, or files
!  Data reduction
!  Dimensionality reduction
!  Numerosity reduction
!  Data compression
!  Data transformation and data discretization
!  Normalization
!  Concept hierarchy generation
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!  Data Preprocessing: An Overview
!  Data Cleaning
!  Data Integration
!  Data Reduction and Transformation
!  Dimensionality Reduction
!  Summary
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!  Data in the Real World Is Dirty: Lots of potentially incorrect data, e.g., instrument
faulty, human or computer error, and transmission error
!  Incomplete: lacking attribute values, lacking certain attributes of interest, or
containing only aggregate data
!  e.g., Occupation = “ ” (missing data)
!  Noisy: containing noise, errors, or outliers
!  e.g., Salary = “−10” (an error)
!  Inconsistent: containing discrepancies in codes or names, e.g.,
!  Age = “42”, Birthday = “03/07/2010”
!  Was rating “1, 2, 3”, now rating “A, B, C”
!  discrepancy between duplicate records
!  Intentional (e.g., disguised missing data)
!  Jan. 1 as everyone’s birthday?
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!  Data is not always available
!  E.g., many tuples have no recorded value for several attributes, such as
customer income in sales data
!  Missing data may be due to
!  Equipment malfunction
!  Inconsistent with other recorded data and thus deleted
!  Data were not entered due to misunderstanding
!  Certain data may not be considered important at the time of entry
!  Did not register history or changes of the data
!  Missing data may need to be inferred
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!  Ignore the tuple: usually done when class label is missing (when doing
classification)—not effective when the % of missing values per attribute
varies considerably
!  Fill in the missing value manually: tedious + infeasible?
!  Fill in it automatically with
!  a global constant : e.g., “unknown”, a new class?!
!  the attribute mean
!  the attribute mean for all samples belonging to the same class: smarter
!  the most probable value: inference-based such as Bayesian formula
or decision tree
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!  Noise: random error or variance in a measured variable
!  Incorrect attribute values may be due to
!  Faulty data collection instruments
!  Data entry problems
!  Data transmission problems
!  Technology limitation
!  Inconsistency in naming convention
!  Other data problems
!  Duplicate records
!  Incomplete data
!  Inconsistent data
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!  Binning
!  First sort data and partition into (equal-frequency) bins
!  Then one can smooth by bin means, smooth by bin median, smooth
by bin boundaries, etc.
!  Regression
!  Smooth by fitting the data into regression functions
!  Clustering
!  Detect and remove outliers
!  Semi-supervised: Combined computer and human inspection
!  Detect suspicious values and check by human (e.g., deal with possible
outliers)
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!  Data Preprocessing: An Overview
!  Data Cleaning
!  Data Integration
!  Data Reduction and Transformation
!  Dimensionality Reduction
!  Summary
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!  Χ2 (chi-square) test:
!  Null hypothesis: The two distributions are independent
!  The cells that contribute the most to the Χ2 value are those whose actual
count is very different from the expected count
!  The larger the Χ2 value, the more likely the variables are related
!  Note: Correlation does not imply causality
!  # of hospitals and # of car-theft in a city are correlated
!  Both are causally linked to the third variable: population
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!  Χ2 (chi-square) calculation (numbers in parenthesis are expected
counts calculated based on the data distribution in the two
categories)
!  It shows that like_science_fiction and play_chess are correlated
in the group
Play chess Not play chess Sum (row)
Like science fiction 250 (90) 200 (360) 450
Not like science fiction 50 (210) 1000 (840) 1050
Sum(col.) 300 1200 1500
We can reject the
null hypothesis of
independence at a
confidence level of
0.001
How to derive 90?
450/1500 * 300 =
90
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!  Data Preprocessing: An Overview
!  Data Cleaning
!  Data Integration
!  Data Reduction and Transformation
!  Dimensionality Reduction
!  Summary
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!  Data reduction:
!  Obtain a reduced representation of the data set
!  much smaller in volume but yet produces almost the same analytical
results
!  Why data reduction?—A database/data warehouse may store terabytes of
data
!  Complex analysis may take a very long time to run on the complete data
set
!  Select/create features that are important for e.g. classification
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!  Divide data into buckets (bins) and
store average (sum) for each bucket
!  Partitioning rules:
!  Equal-width
!  Equal-frequency
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!  Partition data set into clusters based on similarity,
and store cluster representation (e.g., centroid and
diameter) only
!  Can be very effective if data is clustered but not if
data is “smeared” (fuzzy)
!  Can have hierarchical clustering and be stored in
multi-dimensional index tree structures
!  There are many choices of clustering definitions
and clustering algorithms
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!  Sampling: obtaining a small sample s to represent the whole data set N
!  Allow a mining algorithm to run in complexity that is potentially sub-linear
to the size of the data
!  Key principle: Choose a representative subset of the data
!  Simple random sampling may have very poor performance in the
presence of skew
!  Develop adaptive sampling methods, e.g., stratified sampling
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SRSWOR
(simple random
sample without
replacement)
SRSWR
Raw Data
!  Simple random sampling: equal
probability of selecting any particular
item
!  Sampling without replacement
!  Once an object is selected, it is
removed from the population
!  Sampling with replacement
!  A selected object is not removed from
the population
!  Stratified sampling
!  Partition (or cluster) the data set, and
draw samples from each partition
(proportionally, i.e., approximately the
same percentage of the data)
Stratified sampling
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!  Wavelet Transform
!  Decomposes a signal into different
frequency subbands
!  Applicable to n-dimensional signals
!  Data are transformed to preserve relative
distance between objects at different
levels of resolution
!  Allow natural clusters to become more
distinguishable
!  Used for image compression
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!  Discrete wavelet transform (DWT) for linear signal processing, multiresolution
analysis
!  Compressed approximation: Store only a small fraction of the strongest of
the wavelet coefficients
!  Similar to discrete Fourier transform (DFT), but better lossy compression,
localized in space
!  Method:
!  Length, L, must be an integer power of 2 (padding with 0’s, when
necessary)
!  Each transform has 2 functions: smoothing, difference
!  Applies to pairs of data, resulting in two set of data of length L/2
!  Applies two functions recursively, until reaches the desired length
Haar2 Daubechie4
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!  Wavelets: A math tool for space-efficient hierarchical decomposition of
functions
!  S = [2, 2, 0, 2, 3, 5, 4, 4] can be transformed to S^ = [23/4, -11/4, 1/2, 0, 0, -1, -1,
0]
!  Compression: many small detail coefficients can be replaced by 0’s, and only
the significant coefficients are retained
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!  Use hat-shape filters
!  Emphasize region where points cluster
!  Suppress weaker information in their boundaries
!  Effective removal of outliers
!  Insensitive to noise, insensitive to input order
!  Multi-resolution
!  Detect arbitrary shaped clusters at different scales
!  Efficient
!  Complexity O(N)
!  Only applicable to low dimensional data
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!  Maping the entire set of values of a given attribute to a new set of replacement
values s.t. each old value can be identified with one of the new values
!  Methods
!  Smoothing: Remove noise from data
!  Attribute/feature construction
!  New attributes constructed from the given ones
!  Aggregation: Summarization, data cube construction
!  Normalization: Scaled to fall within a smaller, specified range
!  min-max normalization
!  z-score normalization
!  normalization by decimal scaling
!  Discretization: Concept hierarchy climbing
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!  Min-max normalization: to [new_minA, new_maxA]
!  Ex. Let income range $12,000 to $98,000 normalized to
[0.0, 1.0]
!  Then $73,000 is mapped to
!  Z-score normalization (µ: mean, σ: standard deviation):
!  Ex. Let µ = 54,000, σ = 16,000. Then
Z-score: The
distance between
the raw score and
the population
mean in the unit of
the standard
deviation
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!  Three types of attributes
!  Nominal—values from an unordered set, e.g., color, profession
!  Ordinal—values from an ordered set, e.g., military or academic rank
!  Numeric—real numbers, e.g., integer or real numbers
!  Discretization: Divide the range of a continuous attribute into intervals
!  Interval labels can then be used to replace actual data values
!  Reduce data size by discretization
!  Supervised vs. unsupervised
!  Split (top-down) vs. merge (bottom-up)
!  Prepare for further analysis, e.g., classification
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!  Binning
!  Top-down split, unsupervised
!  Histogram analysis
!  Top-down split, unsupervised
!  Clustering analysis
!  Unsupervised, top-down split or bottom-up merge
!  Decision-tree analysis
!  Supervised, top-down split
!  Correlation (e.g., χ2) analysis
!  Unsupervised, bottom-up merge
!  Note: All the methods can be applied recursively
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!  Equal-width (distance) partitioning
!  Divides the range into N intervals of equal size: uniform grid
!  if A and B are the lowest and highest values of the attribute, the width of
intervals will be: W = (B –A)/N.
!  The most straightforward, but outliers may dominate presentation
!  Skewed data is not handled well
!  Equal-depth (frequency) partitioning
!  Divides the range into N intervals, each containing approximately same
number of samples
!  Good data scaling
!  Managing categorical attributes can be tricky
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!  Sorted data for price (in dollars): 4, 8, 9, 15, 21, 21, 24, 25, 26, 28, 29, 34
* Partition into equal-frequency (equi-depth) bins:
- Bin 1: 4, 8, 9, 15
- Bin 2: 21, 21, 24, 25
- Bin 3: 26, 28, 29, 34
* Smoothing by bin means:
- Bin 1: 9, 9, 9, 9
- Bin 2: 23, 23, 23, 23
- Bin 3: 29, 29, 29, 29
* Smoothing by bin boundaries:
- Bin 1: 4, 4, 4, 15
- Bin 2: 21, 21, 25, 25
- Bin 3: 26, 26, 26, 34
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! Classification (e.g., decision tree analysis)
!  Supervised: Given class labels, e.g., cancerous vs. benign
!  Using entropy to determine split point (discretization point)
!  Top-down, recursive split
!  See Tree learning lecture
! Correlation analysis (e.g., Chi-merge: χ2-based discretization)
!  Supervised: use class information
!  Bottom-up merge: Find the best neighboring intervals (those having
similar distributions of classes, i.e., low χ2 values) to merge
!  Merge performed recursively, until a predefined stopping condition
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!  Data Preprocessing: An Overview
!  Data Cleaning
!  Data Integration
!  Data Reduction and Transformation
!  Dimensionality Reduction
!  Summary
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!  Curse of dimensionality
!  When dimensionality increases, data becomes increasingly sparse
!  Density and distance between points, which is critical to clustering, outlier
analysis, becomes less meaningful
!  The possible combinations of subspaces will grow exponentially
!  Dimensionality reduction
!  Reducing the number of random variables under consideration, via
obtaining a set of principal variables
!  Advantages of dimensionality reduction
!  Avoid the curse of dimensionality
!  Help eliminate irrelevant features and reduce noise
!  Reduce time and space required in data mining
!  Allow easier visualization
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!  Dimensionality reduction methodologies
!  Feature selection: Find a subset of the original variables (or features,
attributes)
!  Feature extraction: Transform the data in the high-dimensional space to a
space of fewer dimensions
!  Some typical dimensionality methods
!  Principal Component Analysis
!  Supervised and nonlinear techniques
!  Feature subset selection
!  Feature creation
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!  PCA: A statistical procedure that uses an
orthogonal transformation to convert a set of
observations of possibly correlated variables
into a set of values of linearly uncorrelated
variables called principal components
!  The original data are projected onto a much
smaller space, resulting in dimensionality
reduction
!  Method: Find the eigenvectors of the
covariance matrix, and these eigenvectors
define the new space Ball travels in a straight line. Data
from three cameras contain much
redundancy
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!  Given N data vectors from n-dimensions, find k ≤ n orthogonal
vectors (principal components) best used to represent data
!  Normalize input data: Each attribute falls within the same range
!  Compute k orthonormal (unit) vectors, i.e., principal components
!  Each input data (vector) is a linear combination of the k principal
component vectors
!  The principal components are sorted in order of decreasing
“significance” or strength
!  Since the components are sorted, the size of the data can be
reduced by eliminating the weak components, i.e., those with low
variance (i.e., using the strongest principal components, to
reconstruct a good approximation of the original data)
!  Works for numeric data only
Ack. Wikipedia:
Principal Component
Analysis
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!  Another way to reduce dimensionality of data
!  Redundant attributes
!  Duplicate much or all of the information
contained in one or more other attributes
!  E.g., purchase price of a product and the
amount of sales tax paid
!  Irrelevant attributes
!  Contain no information that is useful for the
data mining task at hand
!  Ex. A student’s ID is often irrelevant to the
task of predicting his/her GPA
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!  There are 2d possible attribute combinations of d attributes
!  Typical heuristic attribute selection methods:
!  Best single attribute under the attribute independence assumption:
choose by significance tests
!  Best step-wise feature selection:
!  The best single-attribute is picked first
!  Then next best attribute condition to the first, ...
!  Step-wise attribute elimination:
!  Repeatedly eliminate the worst attribute
!  Best combined attribute selection and elimination
!  Optimal branch and bound:
!  Use attribute elimination and backtracking
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!  Create new attributes (features) that can capture the important information
in a data set more effectively than the original ones
!  Three general methodologies
!  Attribute extraction
!  Domain-specific
!  Mapping data to new space (see: data reduction)
!  E.g., Fourier transformation, wavelet transformation, manifold approaches
(not covered)
!  Attribute construction
!  Combining features (see: discriminative frequent patterns in Chapter on
“Advanced Classification”)
!  Data discretization
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!  Data quality: accuracy, completeness, consistency, timeliness,
believability, interpretability
!  Data cleaning: e.g. missing/noisy values, outliers
!  Data integration from multiple sources:
!  Entity identification problem; Remove redundancies; Detect
inconsistencies
!  Data reduction, data transformation and data discretization
!  Numerosity reduction; Data compression
!  Normalization; Concept hierarchy generation
!  Dimensionality reduction
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!  D. P. Ballou and G. K. Tayi. Enhancing data quality in data warehouse environments.
Comm. of ACM, 42:73-78, 1999
!  T. Dasu and T. Johnson. Exploratory Data Mining and Data Cleaning. John Wiley, 2003
!  T. Dasu, T. Johnson, S. Muthukrishnan, V. Shkapenyuk.
Mining Database Structure; Or, How to Build a Data Quality Browser. SIGMOD’02
!  H. V. Jagadish et al., Special Issue on Data Reduction Techniques. Bulletin of the
Technical Committee on Data Engineering, 20(4), Dec. 1997
!  D. Pyle. Data Preparation for Data Mining. Morgan Kaufmann, 1999
!  E. Rahm and H. H. Do. Data Cleaning: Problems and Current Approaches. IEEE Bulletin of
the Technical Committee on Data Engineering. Vol.23, No.4
!  V. Raman and J. Hellerstein. Potters Wheel: An Interactive Framework for Data Cleaning
and Transformation, VLDB’2001
!  T. Redman. Data Quality: Management and Technology. Bantam Books, 1992
!  R. Wang, V. Storey, and C. Firth. A framework for analysis of data quality research. IEEE
Trans. Knowledge and Data Engineering, 7:623-640, 1995
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