学术报告

题      目：Alternating Nonnegative Least Squares for Nonnegative Matrix Factorization

报  告  人：储德林  教授  (邀请人：黎稳 )

                                  新加坡国立大学

时      间：7月25日  10：00-11：00

地     点：数科院东楼401

报告人简介:

        储德林，新加坡国立大学教授。1982年考入清华大学，获学士、硕士、博士学位。先后在香港大学，清华大学，德国TU Chemnitz（开姆尼斯工业大学）、University of Bielefeld（比勒费尔德大学）等高校工作过。主要研究领域是科学计算、数值代数及其应用，在SIAM系列杂志，Numerische Mathematik，Mathematics of Computation，IEEE, Trans.，Automatica等国际知名学术期刊发表论文一百余篇。任Automatica期刊的副主编，Journal of Computational and Applied Mathematics的顾问编委，Journal of The Franklin Institute期刊的客座编。

摘      要：

       Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction.In this talk, a framework called ARKNLS(Algernating Rank-k Nonnegativity constrained Least Squares) is proposed for computing NMF. First,a recursive formula for the solution of the rank-k nonnegativity-constrained least squares solution for the Rank-k NLS problem for any poisitive integer k. As a result, each subproblem for an alternating rank-k nonnegative least squares framework can be obtained based on this closed form solution. Assuming that all matrices involved in rank-k NLS in the context of NMF computation are of full rank, two of the currently best NMF algorithms HALS (hierarchical algernating least squares) and ANLS-BPP (Alternating NLS based on Block Principal Pivoting) can be considered as special cases of ARKNLS.
     This talk is then focused on the framework with k=3, which leads to a new algortihm for NMF via the closed-form solution of the rank-3 NLS problem. Furthermore, a new strategy that efficiently overcomes the potential singularity problem in rank-3 NLS within the context of NMF computation is also presented. Extensive numerical comparison using real and synthetic data sets demonstrate that the propsoed algorithm provides state-of-the-art performance in terms of computational accuracy and cpu time.