Tensor Subspace Analysis

Previous work has demonstrated that the image variations of many objects (human faces in particular) under variable lighting can be effectively modeled by low dimensional linear spaces. The typical linear subspace learning algorithms include Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Locality Preserving Projection (LPP). All of these methods consider an n1 × n2 image as a high dimensional vector in R12 , while an image represented in the plane is intrinsically a matrix. In this paper, we propose a new algorithm called Tensor Subspace Analysis (TSA). TSA considers an image as the second order tensor in R1 ⊗ R2 , where R1 and R2 are two vector spaces. The relationship between the column vectors of the image matrix and that between the row vectors can be naturally characterized by TSA. TSA detects the intrinsic local geometrical structure of the tensor space by learning a lower dimensional tensor subspace. We compare our proposed approach with PCA, LDA and LPP methods on two standard databases. Experimental results demonstrate that TSA achieves better recognition rate, while being much more efficient.