报告题目：Coseparable Nonnegative Tensor Factorization with t-CUR Decomposition报告人：魏益民 教授

报告人单位：复旦大学数学科学学院

报告时间：2024年10月16日, 晚上 19:00-20:00

腾讯会议号：484-620-691

主办单位：曲阜师范大学数学科学学院

报告摘要：Nonnegative Matrix Factorization (NMF) is an important unsupervised learning method to extract meaningful features from data. To address the NMF problem within a polynomial time framework, researchers have introduced a separability assumption, which has recently evolved into the concept of coseparability. This advancement offers a more efficient core representation for the original data. However, in the real world, data is more naturally represented as a multi-dimensional array, such as images or videos. The NMF's application to high-dimensional data involves vectorization, which risks losing essential multi-dimensional correlations. To retain these inherent correlations, we turn to tensors (multi-dimensional arrays) and leverage the tensor t-product. This approach extends the coseparable NMF to the tensor setting, creating what we term coseparable Nonnegative Tensor Factorization (NTF). In this work, we provide an alternating index selection method to select the coseparable core. Furthermore, we validate the t-CUR sampling theory and integrate it with the tensor Discrete Empirical Interpolation Method (t-DEIM) to introduce an alternative, randomized index selection process. These methods have been tested on both synthetic and facial analysis datasets. The results demonstrate the efficiency of coseparable NTF when compared to coseparable NMF.

报告人简介： 魏益民，复旦大学数学科学学院的教授、复旦大学智能复杂体系基础理论与关键技术实验室双聘教授、计算数学专业的博士生导师，从事矩阵计算的理论和应用研究二十余年。1997年在复旦大学数学研究所获得理学博士学位，是上海市应用数学重点实验室的研究人员，曾获得上海市高校优秀青年教师和上海市“曙光”学者的称号；获得上海市自然科学三等奖。魏益民在国际学术期刊《Math. Comput.》,《SIAM J. Sci. Comput.》,《SIAM J. Numer Anal.》, 《SIAM J. Matrix Anal. Appl.》,《J. Sci. Comput.》,《IEEE Trans. Auto. Control》,《IEEE Trans.Neural Network Learn. System》, 《Neurocomputing》和《Neural Computation》 等发表论文150余篇; 在EDP Science, Elsevier, Springer, World Scientific和科学出版社等出版英语专著5本。5次入选爱思唯尔“中国高被引学者”榜单。Google学术引用8900余次，H 指数 48。魏益民曾主持国家自然科学基金、教育部博士点基金项目和973项目的子课题；目前正主持国家自然科学基金项目，担任国际学术期刊《Computational and Applied Mathematics》、《Journal of Applied Mathematics and Computing》、《FILOMAT》、《Communications in Mathematical Research》和《高校计算数学学报》的编委。