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Dimensionality reduction is extremely important for understanding the intrinsic structure hidden in high-dimensional data. In recent years, sparse representation models have been widely used in dimensionality reduction. In this paper, a novel supervised learning method, called Sparsity Preserving Discriminant Projections (SPDP), is proposed. SPDP, which attempts to preserve the sparse representation structure of the data and maximize the between-class separability simultaneously, can be regarded as a combiner of manifold learning and sparse representation. Specifically, SPDP first creates a concatenated dictionary by classwise PCA decompositions and learns the sparse representation structure of each sample under the constructed dictionary using the least square method. Secondly, a local between-class separability function is defined to characterize the scatter of the samples in the different submanifolds. Then, SPDP integrates the learned sparse representation information with the local between-class relationship to construct a discriminant function. Finally, the proposed method is transformed into a generalized eigenvalue problem. Extensive experimental results on several popular face databases demonstrate the feasibility and effectiveness of the proposed approach

Sparsity Preserving Discriminant Projections with Applications to Face Recognition