报告问题 (Title)：Efficient algorithms for Tucker decomposition via approximate matrix multiplication (通过近似矩阵乘法实现Tucker剖析的高效算法)

报告人 (Speaker)：魏益民 教授（复旦大学）

报告时间 (Time)：2024年12月15日 (周日) 10:10-11:10

报告所在 (Place)：校本部GJ303

约请人(Inviter)：王卿文 教授

主理部分：理学院数学系

报告摘要： This paper 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.