An Adaptive Self-Stabilizing Algorithm for Minor Generalized Eigenvector Extraction and Its Convergence Analysis.

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2018
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Abstract
Generalized eigendecomposition, which extracts the generalized eigenvector from a matrix pencil, is a powerful tool and has been widely used in many fields, such as data classification and blind source separation. First, to extract the minor generalized eigenvector (MGE), we propose a deterministic discrete-time (DDT) system. Unlike some existing systems, the proposed DDT system does not need to normalize the weight vector in each iteration, since the weight vectors in the proposed DDT system are self-stabilizing. Second, we propose an adaptive algorithm corresponding to the proposed DDT system. Moreover, we study the dynamic behavior and convergence properties of the proposed DDT system and prove that the weight vector must converge to the direction of the MGE of a matrix pencil under some mild conditions. Numerical simulations show that the proposed algorithm has a better performance in terms of convergence speed and estimation accuracy than some existing algorithms. Finally, we conduct two experiments on real data sets to demonstrate its practicability.
Reference Key
yingbin2018anieee Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Yingbin, Gao;Xiangyu, Kong;Zhengxin, Zhang;Li'an, Hou;
Journal IEEE Transactions on Neural Networks and Learning Systems
Year 2018
DOI
10.1109/TNNLS.2017.2783360
URL
Keywords
MRI image classification particle swarm optimization multispectral independent component analysis finite generalized gaussian mixtures

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