Adaptive Algorithms for Generalized Eigenvalue Decomposition with a Nonquadratic Criterion

WANG Rong; GAO Feifei; YAO Minli; ZOU Hongxing

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Article Navigation > Chinese Journal of Electronics > 2013 > 22(4): 807-812

WANG Rong, GAO Feifei, YAO Minli, et al., “Adaptive Algorithms for Generalized Eigenvalue Decomposition with a Nonquadratic Criterion,” Chinese Journal of Electronics, vol. 22, no. 4, pp. 807-812, 2013,

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WANG Rong, GAO Feifei, YAO Minli, et al., “Adaptive Algorithms for Generalized Eigenvalue Decomposition with a Nonquadratic Criterion,” Chinese Journal of Electronics, vol. 22, no. 4, pp. 807-812, 2013,

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Adaptive Algorithms for Generalized Eigenvalue Decomposition with a Nonquadratic Criterion

1.
High-Tech Institute of Xi'an, Xi'an 710025, China;
2.
Department of Automation, Tsinghua University, Beijing 100084, China;
3.
Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China

Funds: This work is supported in part by the National Basic Research Program of China (973 Program) (No.2012CB316102, No.2013CB336600), the National Natural Science Foundation of China (No.61071222, No.61179004, No.61179005, No.61201120, No.61201187), and Tsinghua University Initiative Scientific Research Program (No.20101082055, No.20121088074).

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Corresponding author: WANG Rong
Received Date: 2012-09-01
Rev Recd Date: 2012-11-01
Publish Date: 2013-09-25

Abstract

Abstract

In this paper, we propose a nonquadratic criterion to solve the Generalized eigenvalue decomposition (GED) problem. This criterion exhibits a single global maximum that is attained if and only if the weight matrix spans the principal generalized subspace. The other stationary points of this criterion are (unstable) saddle points. Since the criterion is nonquadratic, it has a steep landscape and, therefore, yields fast gradient-based algorithms. Applying the projection approximationmethod and Recursive least squares (RLS) technique, we develop an adaptive algorithm with low computational complexity to track the principal generalized subspace, as well as an adaptive algorithm to parallely estimate the principal generalized eigenvectors. Numerical results are provided to corroborate the proposed studie.

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