Dimensionality Reduction Using Sparse Locality Preserving Projections and Its Application in Face Recognition

In the past decade, dimensionality methods based on sparse representation (SR) have received considerable interest-. The main idea of SR is that the given sample can he represented as a linear combination of as few as others, and the coefficients reflect the correlation of the samples to the given one. Some works has been reported recently that the bigger coefficients are the more "closer" the samples to the given one. While constructing the local structure in manifold learning, such as LPP method, is to find some closest samples to the given sample to gain the locally adjacency graph matrix by k-NN or E-ball methods, which is non-parameter-free. In this paper, we propose a new dimensionality reduction method named sparse locality preserving projections (SLPP) which calculate the locality adjacency graph by SR method and in dimensionality reduction stage, the locality adjacency structure of original data is preserved in low dimensional space. Compared with the manifold matrix constructed by traditional methods, SLPP method is parameter-free and robust to data noise. Experiments on PIE and Yale face image databases demonstrate the effectiveness of the proposed approach.