Part of Advances in Neural Information Processing Systems 18 (NIPS 2005)
Xiaofei He, Deng Cai, Partha Niyogi
Previous work has demonstrated that the image variations of many ob- jects (human faces in particular) under variable lighting can be effec- tively modeled by low dimensional linear spaces. The typical linear sub- space learning algorithms include Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Locality Preserving Projec- tion (LPP). All of these methods consider an n1 × n2 image as a high dimensional vector in Rn1×n2, 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 sec- ond order tensor in Rn1 ⊗ Rn2, where Rn1 and Rn2 are two vector spaces. The relationship between the column vectors of the image ma- trix 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.