A Generalized Information Criterion for Generalized Minor Component Extraction
Yingbin Gao, Kong Xiangyu, Changhua Hu, Li Hongzeng, Hou Li'an · IEEE Transactions on Signal Processing · 2016
Generalized minor component analysis (GMCA) is an essential technique in data classification and signal processing. In this paper, we propose an information criterion for GMCA and derive a fast GMCA algorithm for extracting the first generalized minor component (GMC) by using quasi-Newton method to this information criterion. In order to extract multiple GMCs, through the weighed matrix method, this information criterion is extended into a weighted one, which has a unique global maximum attained if and only if its state matrices converge to the GMCs of the matrix pencil composed of the autocorrelation matrices of two stochastic processes. A gradient algorithm is also derived based on this weighted information criterion. Theoretical analysis shows that the gradient algorithm has self-stabilizing property and does not need the normalization operation required in other algorithms. The global convergence analysis of the proposed algorithm is accomplished through the Lyapunov method. Numerical simulations and real application are carried out to further demonstrate the accuracy and speed advantages of the proposed algorithms.