title: Discriminant projective non-negative matrix factorization.
abstract: Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers W(T) X as their coefficients, i.e., X≈WW(T) X. Since PNMF learns the natural parts-based representation Wof X, it has been widely used in many fields such as pattern recognition and computer vision. However, PNMF does not perform well in classification tasks because it completely ignores the label information of the dataset. This paper proposes a Discriminant PNMF method (DPNMF) to overcome this deficiency. In particular, DPNMF exploits Fisher's criterion to PNMF for utilizing the label information. Similar to PNMF, DPNMF learns a single non-negative basis matrix and needs less computational burden than NMF. In contrast to PNMF, DPNMF maximizes the distance between centers of any two classes of examples meanwhile minimizes the distance between any two examples of the same class in the lower-dimensional subspace and thus has more discriminant power. We develop a multiplicative update rule to solve DPNMF and prove its convergence. Experimental results on four popular face image datasets confirm its effectiveness comparing with the representative NMF and PNMF algorithms.
authors.affiliation: National Laboratory for Parallel and Distributed Processing, School of Computer Science, National University of Defense Technology, Changsha, Hunan, China.
authors.forename: Naiyang
authors.initials: N
authors.lastname: Guan
authors.affiliation: National Laboratory for Parallel and Distributed Processing, School of Computer Science, National University of Defense Technology, Changsha, Hunan, China.
authors.forename: Xiang
authors.initials: X
authors.lastname: Zhang
authors.affiliation: National Laboratory for Parallel and Distributed Processing, School of Computer Science, National University of Defense Technology, Changsha, Hunan, China.
authors.forename: Zhigang
authors.initials: Z
authors.lastname: Luo
authors.affiliation: Centre for Quantum Computation and Intelligent Systems and the Faculty of Engineering and Information Technology, University of Technology, Sydney, Sydney, New South Wales, Australia.
authors.forename: Dacheng
authors.initials: D
authors.lastname: Tao
authors.affiliation: State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha, Hunan, China.
authors.forename: Xuejun
authors.initials: X
authors.lastname: Yang
mesh_terms: D000465:Algorithms; D056667:Biometric Identification / Q000379:methods* / Q000706:statistics & numerical data; D016208:Databases, Factual; D005145:Face / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement; D007090:Image Interpretation, Computer-Assisted