报告题目：A Column-Wise Update Algorithm for Sparse Stochastic Matrix Factorization

报告人：白正简 教授（厦门大学）

报告时间：2022年12月15日（星期四）09:00-10:00

报告地点：腾讯会议：706-817-154   密码:1111

校内联系人：董波 教授          联系电话：84708351-8026

报告摘要：Nonnegative matrix factorization arises widely in machine learning and data analysis. In this talk, for a given factorization of rank r, we consider the sparse stochastic matrix factorization (SSMF) of decomposing a prescribed m-by-n stochastic matrix V into a product of an m-by-r stochastic matrix W and an r-by-n stochastic matrix H, where both W and H are required to be sparse. With the prescribed sparsity level, we reformulate the SSMF as an unconstrained nonconvex-nonsmooth minimization problem and introduce a column-wise update algorithm for solving the minimization problem. We show that our algorithm converges globally. The main advantage of our algorithm is that the generated sequence converges to a special critical point of the cost function, which is nearly a global minimizer over each column vector of the W-factor and is a global minimizer over the H-factor as a whole if there is no sparsity requirement on H. Numerical experiments on both synthetic and real data sets are given to demonstrate the effectiveness of our proposed algorithm.

报告人简介：白正简，厦门大学教授、博士生导师，教育部新世纪优秀人才支持计划入选者、福建省杰出青年基金获得者。2004年博士毕业于香港中文大学，曾在新加坡国立大学和意大利Insubria大学作博士后和访问学者。主要研究方向为数值代数、特征值问题及其逆问题、矩阵流形上的优化算法及其在数据科学中的应用等。曾主持国家自然科学基金面上项目和福建省自然科学基金项目。在SIAM系列, Numer. Math., Inverse Problems等本学科主流期刊上发表多篇学术论文。曾获得福建省科学技术奖二等奖。