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Randomized tensor wheel decomposition

李寒宇

（重庆大学）

报告时间：2024年6月27日 星期四 上午9：00-10：00

报告地点：腾讯会议：142-665-468 会议密码：0627

报告摘要：Tensor wheel (TW) decomposition is an elegant compromise of the popular tensor ring decomposition and fully-connected tensor network decomposition, and has many applications. In this work, we investigate the computation of this decomposition. Three randomized algorithms based on random sampling or random projection are proposed. Specifically, by defining a new tensor product called subwheel product, the structures of the coefficient matrices of the alternating least squares subproblems from the minimization problem of TW decomposition are first figured out. Then, using the structures and the properties of subwheel product, a random sampling algorithm based on leverage sampling and two random projection algorithms respectively based on Kronecker sub-sampled randomized Fourier transform and Tensor Sketch are derived. These algorithms can implement the sampling and projection on TW factors and hence can avoid forming the full coefficient matrices of subproblems. We present the complexity analysis and numerical performance on synthetic data, real data, and image reconstruction for our algorithms. Experimental results show that, compared with the deterministic algorithm in the literature, they need much less computing time while achieving similar accuracy and reconstruction effect. We also apply the proposed algorithms to tensor completion and find that the sampling-based algorithm always has excellent performance and the projection-based algorithms behave well when the sampling rate is higher than 50%.

报告人简介：李寒宇，博士、重庆大学教授、博士生导师，中国数学会计算数学分会理事、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、张量恢复等方面的研究。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SISC、SIMAX、NLA、BIT等国际知名杂志发表学术论文多篇。

邀请人： 谢家新