报告题目：Numerical Computation for Nonnegative Matrix Factorization

报 告 人：Chu Delin (NUS, Singapore)

报告时间：2025年6月27日  11:00-12:00

报告地点：格物楼528

报告摘要：

Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction. 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 integer k. As a result, each subproblem for an alternating rank-k nonnegative least squares framework can be obtained based on this closed forin solution.This talk is then focused on the framework with=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. Extensive numerical comparisons using real and synthetic data sets demonstrate that the proposed algorithm provides state-of-the-art performance in terms of computational accuracy and cpu time.

报告人简介：

储德林，新加坡国立大学教授，德国“洪堡学者”和日本“JSPS学者”。先后任职于香港大学，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)等国内外知名高校。主要研究领域是科学计算、数值代数及其应用。现为国际顶级期刊SIAM Journal on Scientific Computing副主编、SIAM Journal on Matrix Analysis and Applications副主编、Automatica副主编、Journal of Computational and Applied Mathematics编委、Journal of the Franklin Institute客座编委。已在Mathematics of Computation、Numerische Mathematik、SIAM Journal on Matrix Analysis and Applications、SIAM Journal on Scientific Computing、SIAM Journal on Control and Optimization、SIAM Journal on Applied Dynamical Svstems、Journal of Scientific Computing、IEEE Transactions on Pattern Analysis and Machine Intelligence、IEEE Transactions on Neural Networks and Learning Systems等国际知名学术期刊发表论文100余篇。