Matrix factorization techniques have been frequently applied in information processing tasks. Among them, Non-negative Matrix Factorization (NMF) have received considerable attentions due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts-based in human brain. On the other hand, from geometric perspective the data is usually sampled from a low dimensional manifold embedded in high dimensional ambient space. One hopes then to find a compact representation which uncovers the hidden topics and simultaneously respects the intrinsic geometric structure. In this paper, we propose a novel algorithm, called Locality Preserving Non-negative Matrix Factorization (LPNMF), for this purpose. For two data points, we use KL-divergence to evaluate their similarity on the hidden topics. The optimal maps are obtained such that the feature values on hidden topics are restricted to be non-negative and vary smoothly along the geodesics of the data manifold. Our empirical study shows the encouraging results of the proposed algorithm in comparisons to the state-ofthe-art algorithms on two large high-dimensional databases.

Authors

• Deng Cai Bytedance Seed, China
• Xiaofei He State Key Lab of CAD&CG, Zhejiang University Fabu Inc.
• Xuanhui Wang
• Hujun Bao Zhejiang University
• Jiawei Han University of Illinois Urbana-Champaign

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