报告时间：2023年1月6日（星期五）10:00-11:30

报告地点：腾讯会议：175-862-981

报 告 人：储德林 教授

工作单位：新加坡国立大学

举办单位：数学学院

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期刊的客座编委。

报告简介： Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction that has been widely used for text mining, computer vision, pattern discovery, and bioinformatics. In this talk, a framework called ARkNLS (Alternating Rank-k Nonnegativity constrained Least Squares) is introduced for computing NMF. First, a recursive formula for the solution of the rank-k nonnegativity-constrained least squares (NLS) is established. This recursive formula can be used to derive the closed-form solution for the Rank-k NLS problem for any positive 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 alternating least squares) and ANLS-BPP (Alternating NLS based on Block Principal Pivoting) can be considered as special cases of ARkNLS with k = 1 and k = r for rank r NMF, respectively. This talk is then focused on the framework with k = 3, which leads to a new algorithm 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.