报告时间：2025年5月9日下午4：00-5：00

报告地点：统计与数据科学学院106会议室

报告题目：Efficient algorithms for Tucker decomposition via approximate matrix multiplication

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.

专家简介：魏益民，复旦大学数学科学院教授、博士生导师。主要从事矩阵、张量方面的理论和应用研究，多次主持国家自然科学基金面上项目、教育部博士点基金项目和973子课题等项目，获得上海市科学技术奖二等奖。担任国际学术期刊Computational and Applied Mathematics，Journal of Applied Mathematics and Computing，FILOMAT，《高校计算数学学报》的编委。在国际学术期刊Math. Comput.，SIAM J. Sci. Comput.，SIAM J. Numer Anal.，SIAM J. Matrix Anal. Appl.，IEEE Trans. Auto. Control，IEEE Trans. Neural Network Learn. System，Neurocomputing和Neural Computation等发表论文150余篇；在Elsevier，Springer和科学出版社等出版英语专著5本。