Self-Organizing and Adaptive Algorithms for Generalized Eigen-Decomposition

The paper is developed in two parts where we discuss a new approach to self-organization in a single-layer linear feed-forward network. First, two novel algorithms for self-organization are derived from a two-layer linear hetero-associative network performing a one-of-m classification, and trained with the constrained least-mean-squared classification error criterion. Second, two adaptive algorithms are derived from these selforganizing procedures to compute the principal generalized eigenvectors of two correlation matrices from two sequences of random vectors. These novel adaptive algorithms can be implemented in a single-layer linear feed-forward network. We give a rigorous convergence analysis of the adaptive algorithms by using stochastic approximation theory. As an example, we consider a problem of online signal detection in digital mobile communications.