Face Recognition by Discriminative Orthogonal Rank-one Tensor Decomposition

Discriminative subspace analysis has been a popular approach to face recognition. Most of the previous work such as Eigen-faces (Turk & Pentlend, 1991), LDA (Belhumeur et al., 1997), Laplacian faces (He et al., 2005a), as well as a variety of tensor based subspace analysis methods (He et al., 2005b; Chen et al., 2005; Xu et al., 2006; Hua et al., 2007), can all be unified in the graph embedding framework (Yan et al., 2007). In this Chapter, we investigate the effects of two types of regularizations on discriminative subspace based face recognition techniques: a new 2D tensor representation for face image, and an orthogonal constraint on the discriminative tensor projections. Given a face image, the new tensor representation firstly divides it into non-overlapping blocks. Then following the raster-scan order, the raster-scanned pixel vectors of each of the image blocks are put into the columns of a new 2D tensor. It is easy to figure out that the row vectors of the new 2D tensor are in essence different down-sampled images of the original face images. Pursuing discriminative 2D tensor projections with the new tensor representation is of special interest, because the left projection indeed functions as local filters in the original face image and the right projection reveals to us that which local block is more important for recognition. This new representation puts concrete physical meanings to the left and right projections of the discriminative tensor projections. While the 2D tensor representation using the original images does not present any meaningful physical explanations on column and row pixel vectors. We call this new tensor representation Global-Local representation (Chen et al., 2005; Hua et al., 2007). On the other hand, we reveal a very important property regarding the orthogonality between two tensor projections, and thus present a novel discriminative orthogonal tensor decomposition method for face recognition. To the best of our knowledge, this method, firstly introduced in (Hua et at., 2007), is the first discriminative orthogonal tensor decomposition method ever proposed in the literature. Both of the two regularization techniques put additional constraints on the capacity (a.k.a., the VC-dimension) of the discriminative projections and thereby improve the generalization ability of the learned projections. We perform empirical analysis and comparative study on widely adopted face recognition bench-mark such as Yale, ORL, YaleB and PIE databased to O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg