Comparing Ranking Methods for Tensor Components in Multilinear and Concurrent Subspace Analysis with Applications in Face Images

Abstract

© 2015 World Scientific Publishing Company.In the area of multi-dimensional image databases modeling, the multilinear principal component analysis (MPCA) and concurrent subspace analysis (CSA) approaches were independently proposed and applied for mining image databases. The former follows the classical principal component analysis (PCA) paradigm that centers the sample data before subspace learning. The CSA, on the other hand, performs the learning procedure using the raw data. Besides, the corresponding tensor components have been ranked in order to identify the principal tensor subspaces for separating sample groups for face image analysis and gait recognition. In this paper, we first demonstrate that if CSA receives centered input samples and we consider full projection matrices then the obtained solution is equal to the one generated by MPCA. Then, we consider the general problem of ranking tensor components. We examine the theoretical aspects of typical solutions in this field: (a) Estimating the covariance structure of the database; (b) Computing discriminant weights through separating hyperplanes; (c) Application of Fisher criterium. We discuss these solutions for tensor subspaces learned using centered data (MPCA) and raw data (CSA). In the experimental results we focus on tensor principal components selected by the mentioned techniques for face image analysis considering gender classification as well as reconstruction problems.