Coupled Subspaces Analysis

Subspace learning is a fundamental approach for face recognition and facial expression analysis. In this paper, we propose a novel subspace analysis scheme for the two applications. Unlike the traditional subspace algorithms, such as PCA and LDA, in which an image is treated as a vector; in our scheme, an image is directly treated as a 2D matrix, and a new criterion is proposed to infer two low dimensional coupled subspaces that optimally reconstruct the original matrices from row and column directions collaboratively. An efficient approach, namely Coupled Subspace Analysis (CSA), is applied to learn these two subspaces in an iterative manner. Then we reveal the essence of each step in CSA and propose an approach to select the dimension numbers for these two subspaces with the given rate of information lost. Moreover, we prove that PCA and the recently proposed 2DPCA are just simplified special cases of CSA and answer the unsolved theoretical problems in 2DPCA. The main contributions of this paper include: 1) for both face recognition and facial expression analysis, we propose a novel image matrix based scheme, and obtain a much lower dimensional face representation for subsequent discriminant analysis; 2) CSA effectively alleviates the curse of dimensionality dilemma and small sample size problem existed in face recognition problem; and 3) CSA clarifies the essence of 2DPCA and explains the superiority of 2DPCA compared with PCA. The extensive experiments on both face recognition and facial expression analysis demonstrate that CSA is superior to the classical algorithms.