Convergent Projective Non-negative Matrix Factorization with Kullback-Leibler Divergence

Authors:
Lirui Hu;Liang Dai;Jianguo Wu
Affiliations:
School of Computer Science and Technology, Nantong University, Nantong 226019, China and Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Anhui University, H ...;Zhongyi Information Technology Co., Ltd., Nantong 226019, China;Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Anhui University, Hefei 230039, China and School of Computer Science and Technology, Anhui University, Hefei ...
Venue:
Pattern Recognition Letters
Year:
2014

Citing 2
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Nonnegative Matrix Factorization on Orthogonal Subspace

Pattern Recognition Letters
Projective nonnegative matrix factorization for image compression and feature extraction

SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis

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Abstract

In order to solve the problem of algorithm convergence in Projective Non-negative Matrix Factorization (P-NMF), a method, called Convergent Projective Non-negative Matrix Factorization with Kullback-Leibler Divergence (CP-NMF-DIV) is proposed. In CP-NMF-DIV, an objective function of Kullback-Leibler Divergence is considered. The Taylor series expansion and the Newton iteration formula of solving root are used. An iterative algorithm for basis matrix is derived, and a proof of algorithm convergence is provided. Experimental results show that the convergence speed of the algorithm is higher; relative to Non-negative Matrix Factorization (NMF), the orthogonality and the sparseness of the basis matrix are better, however the reconstructed results of data show that the basis matrix is still approximately orthogonal; in face recognition, there is higher recognition accuracy and it is stable in most cases which the ranks of the basis matrices are set with different values. The method for CP-NMF-DIV is effective.