DBLOK4 Complex-Valued Neural Networks with Multi-Valued Neurons

Fakulta informatiky
podzim 2013
Rozsah
2/0. 2 kr. (plus ukončení). Doporučované ukončení: zk. Jiná možná ukončení: k.
Vyučující
Igor Aizenberg, Ph.D. (přednášející), doc. RNDr. Tomáš Brázdil, Ph.D. (zástupce)
Garance
doc. RNDr. Tomáš Brázdil, Ph.D.
Fakulta informatiky
Kontaktní osoba: doc. RNDr. Tomáš Brázdil, Ph.D.
Dodavatelské pracoviště: Fakulta informatiky
Předpoklady
No specific prerequisites, but students are expected to have basic knowledge of linear algebra and discrete mathematics
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Předmět si smí zapsat nejvýše 20 stud.
Momentální stav registrace a zápisu: zapsáno: 0/20, pouze zareg.: 0/20, pouze zareg. s předností (mateřské obory): 0/20
Mateřské obory/plány
Cíle předmětu
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.
Osnova
  • 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.
Literatura
    doporučená literatura
  • AIZENBERG, Igor. Complex-Valued Neural Networks with Multi-Valued Neurons. Springer, 2011. ISBN 978-3-642-20353-4. info
Výukové metody
Lectures, homeworks, projects
Metody hodnocení
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%
Vyučovací jazyk
Angličtina
Další komentáře
Studijní materiály
Předmět je vyučován jednorázově.
Výuka probíhá každý týden.
Předmět je zařazen také v obdobích podzim 2012.
  • Statistika zápisu (nejnovější)
  • Permalink: https://is.muni.cz/predmet/fi/podzim2013/DBLOK4