Adaptive Algorithms for Generalized Eigenvalue Decomposition with a Nonquadratic Criterion

In this papers we propose a nonquadratic criterion to solve the Generalized eigenvalue decomposi- tion （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 sta- tionary points of this crit...

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Bibliographic Details
Published in:电子学报：英文版 2013-10, Vol.22 (4), p.807-813
Main Author: WANG Rong GAO Feifei YAO Minli ZOU Hongxing
Format: Article
Language:English
Subjects:
分解程度
广义特征值
最小平方
权重矩阵
标准具
特征值分解
自适应算法
计算复杂度
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Summary:In this papers we propose a nonquadratic criterion to solve the Generalized eigenvalue decomposi- tion （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 sta- tionary points of this criterion are （unstable） saddle points. Since the criterion is nonquadratics it has a steep landscape ands therefores yields fast gradient-based algorithms. Ap- plying the projection approximation method and Recursive least squares （RLS） technique, we develop an adaptive al- gorithm with low computational complexity to track the principal generalized subspace, as well as an adaptive algo- rithm to parallely estimate the principal generalized eigen- vectors. Numerical results are provided to corroborate the proposed studies.
ISSN:1022-4653