WANG Rong, GAO Feifei, YAO Minli, ZOU Hongxing. Adaptive Algorithms for Generalized Eigenvalue Decomposition with a Nonquadratic Criterion[J]. Chinese Journal of Electronics, 2013, 22(4): 807-812.
Citation: WANG Rong, GAO Feifei, YAO Minli, ZOU Hongxing. Adaptive Algorithms for Generalized Eigenvalue Decomposition with a Nonquadratic Criterion[J]. Chinese Journal of Electronics, 2013, 22(4): 807-812.

Adaptive Algorithms for Generalized Eigenvalue Decomposition with a Nonquadratic Criterion

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
  • 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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