Accelerating locality preserving nonnegative matrix factorization

Matrix factorization techniques have been frequently applied in information retrieval, computer vision and pattern recognition. Among them, Non-negative Matrix Factorization (NMF) has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts-based in the human brain. Locality Preserving Non-negative Matrix Factorization (LPNMF) is a recently proposed graph-based NMF extension which tries to preserves the intrinsic geometric structure of the data. Compared with the original NMF, LPNMF has more discriminating power on data representa- tion thanks to its geometrical interpretation and outstanding ability to discover the hidden topics. However, the computa- tional complexity of LPNMF is O(n3), where n is the number of samples. In this paper, we propose a novel approach called Accelerated LPNMF (A-LPNMF) to solve the com- putational issue of LPNMF. Specifically, A-LPNMF selects p (p j n) landmark points from the data and represents all the samples as the sparse linear combination of these landmarks. The non-negative factors which incorporates the geometric structure can then be efficiently computed. Experimental results on the real data sets demonstrate the effectiveness and efficiency of our proposed method.