报 告 人：魏益民 教授
报告题目：Efficient algorithms for Tucker decomposition via approximate matrix multiplication
报告时间：2025年5月8日（周四）下午15:30—16:30
报告地点：静远楼1506学术报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
魏益民，男，教授，博士生导师。复旦大学数学科学学院教授，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”学者称号；获得上海市自然科学二等奖、三等奖各一项。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。10次入选爱思唯尔“中国高被引学者”榜单。Google学术引用12000余次，H 指数 55。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。
报告摘要：
This talk develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated high-order singular value decomposition (T-HOSVD) and the sequentially T-HOSVD (ST-HOSVD), which are two common algorithms for approximating Tucker decomposition. To reduce the complexities of these two algorithms, fast and efficient algorithms are designed by combining two algorithms and approximate matrix multiplication. The theoretical results are also achieved based on the bounds of singular values of standard Gaussian matrices and the theoretical results for approximate matrix multiplication. Finally, the efficiency of these algorithms are illustrated via some test tensors from synthetic and real datasets.