DBLOK4 Complex-Valued Neural Networks with Multi-Valued Neurons

Faculty of Informatics
Autumn 2013
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
Igor Aizenberg, Ph.D. (lecturer), doc. RNDr. Tomáš Brázdil, Ph.D. (deputy)
Guaranteed by
doc. RNDr. Tomáš Brázdil, Ph.D.
Faculty of Informatics
Contact Person: doc. RNDr. Tomáš Brázdil, Ph.D.
Supplier department: Faculty of Informatics
Prerequisites
No specific prerequisites, but students are expected to have basic knowledge of linear algebra and discrete mathematics
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
The capacity limit for the course is 20 student(s).
Current registration and enrolment status: enrolled: 0/20, only registered: 0/20, only registered with preference (fields directly associated with the programme): 0/20
fields of study / plans the course is directly associated with
Course objectives
This course is devoted to fundamentals and applications of complex-valued neural networks with multi-valued neurons. Due to the computational and theoretical advantages that processing in the complex domain offers over the real-valued domain, the area of complex-valued neural networks is one of fastest growing research areas in the neural network community. In addition, recent progress in pattern recognition, robotics, mathematical biosciences, brain-computer interface design has brought to light problems where nonlinearity, multidimensional data natures, uncertainty, and complexity play major roles – complex-valued neural networks are a natural model to account for these applications. At the end of the course students should be able to: understand and explain basic principles of complex-valued neural networks and particularly the ones based on multi-valued neurons; use a multilayer neural network with multi-valued neurons for solving classification and regression problems; design models for solving real-world problems using complex-valued neural networks with multi-valued neurons; make reasoned decisions about a certain type of machine learning tools for solving real-world problems; make deductions based on acquired knowledge of information processing and analysis using complex-valued neural networks; interpret the experimental results related to the use of complex-valued neural networks with multi-valued neurons.
Syllabus
  • Brief introduction to neural networks. Complex-valued neural networks: why we need them?
  • Multiple-valued (k-valued) logic over the field of complex numbers. k-separability of n-dimensional space. A multi-valued neuron (MVN) and its functionality. Discrete and continuous MVN.
  • Learning rules for MVN. The Hebbian rule. The "closeness" rule. The error-correction rule. Modification of the error-correction rule. MVN learning algorithm and its convergence. Choice of the best starting weights for the learning process.
  • MVN with a periodic activation function (MVN-P) and solving non-linearly separable problems using a single MVN-P (XOR, parity n, mod k addition of n inputs, various benchmark problems).
  • A multilayer feedforward neural network based on multi-valued neurons (MLMVN). The error backpropagation and its specific organization for the MLMVN. The error-correction learning rule for MLMVN.
  • A derivative-free learning MLMVN learning algorithm based on the error-correction learning rule and its convergence. Hard Margins learning and soft margins learning for MLMVN.
  • Solving some popular benchmark classification and prediction problems and comparison with the competitive solutions (standard backpropagation network, kernel-based networks, SVM).
  • Application of MLMVN for solving real-world problems: blur and blur parameters identification for image deblurring; recognition of blurred images; intelligent edge detection; classification of microarray gene expression data. Frequency domain as a natural source of the features for the classification purposes.
  • MLMVN as a signal decoder in an EEG-based brain-computer interface. Similarity of MVN and biological neurons.
  • MVN-based associative memories and their applications.
  • Utilization of MVN in cellular neural networks and their application to solving some image processing problems: precise edge detection and edged segmentation; multi-valued nonlinear filtering.
Literature
    recommended literature
  • AIZENBERG, Igor. Complex-Valued Neural Networks with Multi-Valued Neurons. Springer, 2011. ISBN 978-3-642-20353-4. info
Teaching methods
Lectures, homeworks, projects
Assessment methods
Completing assignments during the term. Practical projects followed by the detailed written reports. A final grade will be based on:
Homework assignments – 50%
Project (the experimental results and detailed report shall be provided) – 50%
Language of instruction
English
Further Comments
Study Materials
The course is taught only once.
The course is taught: every week.
The course is also listed under the following terms Autumn 2012.
  • Enrolment Statistics (recent)
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