A THEORETICAL FRAMEWORK FOR MATRIX-BASED FEATURE EXTRACTION ALGORITHMS WITH ITS APPLICATION TO IMAGE RECOGNITION

Abstract

Recently proposed matrix-based methods, two-dimensional Principal Component Analysis (2DPCA), two-dimensional Linear Discriminant Analysis (2DLDA) and two-dimensional Locality Preserving Projections (2DLPP) have been shown to be effective ways to avoid the problems of high dimensionality and small sample sizes that are associated with vector-based methods. In this paper, we propose a general theoretical framework for matrix-based feature extraction algorithms from the point of view of graph embedding. Our framework can be applied to extend two recently proposed vector-based algorithms, i.e. Unsupervised Discriminant Projection (UDP) and Marginal Fisher Analysis (MFA) algorithms, to their matrix-based versions. Further, our framework can also be used as a platform to generate new matrix-based feature extraction algorithms by designing meaningful graphs, e.g. two-dimensional Discriminant Embedding Analysis (2DDEA) in this paper. It is shown that 2DLDA is actually a special case of the 2DDEA method. Experiments on three publicly available image databases demonstrate the effectiveness of the proposed algorithm. Our results fit into the scene for a better picture about the matrix-based feature extraction algorithms.