报告题目：Alternating Nonnegative Least Squares for Nonnegative Matrix Factorization

报 告 人：储警林救授（新加坡国立大学）

报告时间：2023年7月19日  16:00-17:00

报告地点：格物楼601会议室

报告摘要：

Nonnegative matrix factorization (NMF) is a prominent technique for data dimmensionality reduction. In this talk, a famework called ARKNLS (Alternating Rank-k Nonnegativity constraimed Least Sqwares) is proposed for computing NMF. First, a recursive formula for the solution of the rank-k nonnegativity-constrained least squares(NLS) is established. This recersive 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 altermating rank-k nonnegative least squares framework can be obtained based oa this closed form solution. Assumaing 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 (hieraschical alternating least squares) and ANLS-BPP(Alternating NLS based on Block Principal Proting)can be considered as special cases of ARKNLS.

This talk is then focused on the framework with k-3, which leads to a new algorithuum for NMF via the closed-form solution of the rank-3 NLS problem. Furthermore, a new strategy that efficiently overcomes the potemnial singularity problem in rank-3 NLS within the context of NMF computation is also peasented. Extensive mamerical comparisons using real and symthetic data sets deanonstrate that the proposed algorithum provides state-of-the-art performance in terms of compatational accaracy and cpu tane.

报告人简介：

储德养，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，曾获得德国的“洪堡学者”和目本的“JSPS学者”等称号。现为SIAM Journal on Scientific Computing、SIAM Journal on Matrix Analysis and Applications、Automatica等期刊的副主编及编委，近年来已在SIAM Journal on Matrix Analysis and Applications、SIAM Journal on Scientific Computing、SIAM Journal on Control and Optimization、SIAM Journal on Applied Dynamical Systems、Mathematics of Computation、Numerische Mathematik、Journal of Scientific Computing、IEEE Transactions on Pattern Analysis and Machine lntelligence、IEEE Transactions on Neural Nerworks and Learning Systems等国际知名学术期利发表论文100余篇。