A Generalized Minor Component Extraction Algorithm and Its Analysis

Generalized minor component analysis (GMCA) is of great use in modern signal processing. The GMCA algorithms can be simplified to extract the minor generalized eigenvector of the autocorrelation input matrices pencil. In contrast to batching methods, the Hebbian-rule-based algorithm can extract the minor generalized eigenvector online. Few Hebbian-rule-based GMCA algorithms have been reported in the literature, and most of them are not self-stabilizing. Thus, a novel algorithm for GMCA, which is advantageous in terms of good convergence speed, self-stabilizing property, and multiple generalized minor component extraction in sequence, is proposed in this paper. A theoretical analysis verifies these properties via matrix theory and the deterministic discrete-time method. Numerical simulations are conducted to further demonstrate the advantages of the proposed algorithm.