学 术 报 告
题目：Practical algorithms for tensor ring decomposition
报告人：李寒宇 教授单位：重庆大学，数学与统计学院
时 间：2022年11月19日（周六）上午 10:00-11:00
地 点：腾讯会议：839-178-071
报告人及报告内容简介：
李寒宇，博士、重庆大学教授、博士生导师，现任重庆工业与应用数学学会副理事长。主要从事随机数值代数、统计计算、张量回归等方面的研究。先后主持国家自然科学基金项目、重庆市自然科学基金项目多项，在国际知名杂志发表学术论文多篇。
Abstract:Based on sketching techniques, we first propose two randomized algorithms for tensor ring (TR) decomposition. Specifically, on the basis of defining new tensor products and investigating their properties, the two algorithms are devised by applying the sub-sampled randomized Fourier transform and TensorSketch to the alternative least squares (ALS) subproblems from the fitting problem of TR decomposition. Considering that, in all the existing algorithms and our new randomized algorithms, the ALS subproblems have to be solved directly eventually, which may suffer from the intermediate data explosion issue, we then propose two strategies to tackle the computation of the subproblems. The first one is used to simplify the calculation of the coefficient matrices of the normal equations for the ALS subproblems, and the other one is to stabilize the ALS subproblems by QR factorizations on TR-cores.They can take full advantage of the structure of the coefficient matrices of the subproblems. Three corresponding algorithms are devised. Extensive numerical experiments on synthetic and real data are presented to test our methods.