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An Alternating Modulus Nonnegative Least Squares Method for Nonnegative Matrix Factorization
澳门新葡8455最新网站:2016年11月30日 13:50 点击数:

报告人:Ken Hayami

报告地点:澳门新葡8455最新网站二楼会议室

报告澳门新葡8455最新网站:2016年12月08日星期四14:30-15:20

邀请人:

报告摘要:

Consider the nonnegative matrix factorization (NMF) : min_{W,H} || V – W||_F, where V R^{m×n} is a given nonnegative matrix, W R^{m×r} and H R^{r×n} are unknown nonnegative matrices, and ||?||_F represents the Frobenius norm of the corresponding matrix. Here, r ? min(m,n) is assumed. Therefore, the NMF problem seeks a nonnegative low rank approximation of a given nonnegative matrix. NMF arises in many scienti?c computing and engineering applications, e.g., image processing, spectral data analysis, audio signal separation, text mining, document clustering, recommender system, etc. For the solution of NMF, we propose a new alternating nonnegative least squares method by utilizing the modulus method [2, 3] for solving the nonnegative constrained least squares (NNLS) problems in each iteration. The method employs the modulus transform H = Z + |Z| and W = Y + |Y| for each subproblem to transform the NNLS problem to a sequence of unconstrained least squares problems, which can be solved by a CGLS method for matrix variables. Numerical experiments on random problems and ORL face image problems show the ef?ciency of the proposed method compared to the multiplicative update method [4] and gradient-type methods.

This is joint work with Dr. Ning Zheng and Dr. Nobutaka Ono

 

主讲人概况:

Ken Hayami obtained PhD from the Wessex Institute of Technology (1991) and the University of Tokyo (1993), respectively. Currently, he is a professor in the Principles of Informatics Research Division of NII and the Department of Informatics at SOKENDAI (The Graduate University of Advanced Studies) .

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