Document Clustering Using Locality Preserving Indexing
IEEE Transactions on Knowledge and Data Engineering
Locality preserving nonnegative matrix factorization
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Graph Regularized Nonnegative Matrix Factorization for Data Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-Negative Patch Alignment Framework
IEEE Transactions on Neural Networks
Manifold Regularized Discriminative Nonnegative Matrix Factorization With Fast Gradient Descent
IEEE Transactions on Image Processing
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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.