NDLI: Box-constrained projective nonnegative matrix factorization via augmented Lagrangian method

Content Provider	IEEE Xplore Digital Library
Author	Xiang Zhang Naiyang Guan Long Lan Dacheng Tao Zhigang Luo
Copyright Year	2014
Description	Author affiliation: Centre for Quantum Comput. & Intell. Syst., Univ. of Technol., Sydney, NSW, Australia (Dacheng Tao) \|\| Sci. & Technol. on Parallel & Distrib. Process. Lab., Nat. Univ. of Defense Technol., Changsha, China (Xiang Zhang; Naiyang Guan; Long Lan; Zhigang Luo)
Abstract	Projective non-negative matrix factorization (P-NMF) projects a set of examples onto a subspace spanned by a non-negative basis whose transpose is regarded as the projection matrix. Since PNMF learns a natural parts-based representation, it has been successfully used in text mining and pattern recognition. However, it is non-trivial to analyze the convergence of the optimization algorithms for PNMF because its objective function is non-convex. In this paper, we propose a Box-constrained PNMF (BPNMF) method to overcome this deficiency of PNMF. In particular, BPNMF introduces an auxiliary variable, i.e., the coefficients of examples, and incorporates the following two types of constraints: 1) each entry of the basis is non-negative and upper-bounded, i.e., box-constrained, and 2) the coefficients equal to the projected points of the examples. The first box constraint makes the basis to be bound and the second equality constraint keeps its equivalence to PNMF. Similar to PNMF, BPNMF is difficult because the objective function is non-convex. To solve BPNMF, we developed an efficient algorithm in the frame of augmented Lagrangian multiplier (ALM) method and proved that the ALM-based algorithm converges to local minima. Experimental results on two face image datasets demonstrate the effectiveness of BPNMF compared with the representative methods.
Starting Page	1900
Ending Page	1906
File Size	892077
Page Count	7
File Format	PDF
ISSN	21614407
e-ISBN	9781479914845
DOI	10.1109/IJCNN.2014.6889928
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-07-06
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Accuracy Linear programming Training Convergence Optimization Face Educational institutions
Content Type	Text
Resource Type	Article

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