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Self-organizing algorithms for generalized eigen-decomposition.

C Chatterjee¹, V P Roychowdhury, J Ramos

¹GDE Syst. Inc., San Diego, CA.

IEEE Transactions on Neural Networks

|January 1, 1997

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This study introduces new adaptive algorithms for generalized eigen-decomposition and linear discriminant analysis (LDA) using self-organization. These algorithms efficiently extract significant components and eigenvectors from data sequences.

Area of Science:

Artificial Intelligence
Machine Learning
Computational Neuroscience

Background:

Self-organization principles are crucial for developing adaptive algorithms.
Generalized eigen-decomposition and Linear Discriminant Analysis (LDA) are fundamental in data analysis and pattern recognition.

Purpose of the Study:

To develop novel adaptive algorithms for generalized eigen-decomposition and LDA.
To explore a new self-organization approach for these algorithms within a neural network framework.

Main Methods:

Derivation of iterative algorithms using a constrained least-mean-squared classification error cost function.
Utilizing a two-layer linear heteroassociative network for one-of-m classification.
Application of the deflation concept for sequential component extraction.

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Main Results:

Two novel iterative algorithms for LDA and generalized eigen-decomposition were derived.
Sequential algorithms were developed to extract components and eigenvectors in decreasing order of significance.
Two new adaptive algorithms were introduced for computing principal generalized eigenvectors from random matrix sequences.

Conclusions:

The proposed self-organization approach yields effective adaptive algorithms for generalized eigen-decomposition and LDA.
Rigorous convergence analysis using stochastic approximation theory confirms algorithm convergence with probability one.