Adaptive Algorithms for Generalized Eigenvalue Decomposition with a Nonquadratic Criterion

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 approximation method 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 studies.