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厦门大学白正简教授学术报告通知
发布时间 : 2023-06-08     点击量:

报告题目:A Columnwise Update Algorithm for Sparse Stochastic Matrix Factorization

报告人:白正简(厦门大学)

报告时间:69日(周五) 14:30

报告地点:数学楼 2-2会议室


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.


个人简介: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 J. Matrix Anal. Appl., SIAM J. Numer. Anal., 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。


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