Generalized 2-D Principal Component Analysis by Lp-Norm for Image Analysis

This paper proposes a generalized 2-D principal component analysis (G2DPCA) by replacing the L2-norm in conventional 2-D principal component analysis (2DPCA) with Lp-norm, both in objective and constraint functions. It is a generalization of previously proposed robust or sparse 2DPCA algorithms. Under the framework of minorization-maximization, we design an iterative algorithm to solve the optimization problem of G2DPCA. A closed-form solution could be obtained in each iteration. Then a deflating scheme is employed to generate multiple projection vectors. Our algorithm guarantees to find a locally optimal solution for G2DPCA. The effectiveness of the proposed method is experimentally verified.