This paper proposes two novel methods. First we propose Locality Enhanced Spectral Embedding(LESE) which can make a locality preserving mapping from the original nearest neighbor graph to the real line. It uses a regularized non-nearest penalty based on a non-nearest neighbor graph to enhance the locality of the mapping result. Second we make an efficient method for face recognition task. Previous methods consider a p1 × p2 image as a high dimensional vector in Rp1×p2 space and the pixels of each image are considered independent. It fails to consider that a face image is intrinsically a matrix, the pixels spatially close to each other may also be correlated. To explicitly model the spatial locality, we propose a novel Spatially Smooth Spectral Regression(SSR). It is a two stage framework for subspace learning, sequentially SSR uses the LESE to generate an eigenspace, and it solves a Laplacian smoothing penalty regularized regression to construct the projective function and learn a spatially smooth subspace. The subspace forms a good representation of the original face image. Experimrntal results on face recognition demonstrate the effecttiveness of our proposed algorithm.
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