报告题目：Nonconvex multi-view subspace clustering via simultaneously learning

the representation tensor and affinity matrix

报告人：黎稳 华南师范大学数学科学学院

报告时间：2023 年3月3日15:00-16:00 (北京时间)

报告地点：龙洞校区行政楼 610

主持人：吴先萍

报告摘要：Multi-view subspace clustering, which aims to partition a dataset into its relevant subspaces based on their multi-view features, has been widely applied to identify various characteristics of datasets. The typical model of multi-view subspace  clustering in literature often makes use of the nuclear norm to seek the underlying low-rank representation. However, due to the sum property of the singular values defined by tensor nuclear norm, the existing multi-view subspace clustering does not well handle the noise and the illumination variations embedded in multi-view data. To address and improve the robustness and clustering performance, we propose a new nonconvex multi-view subspace clustering model via tensor minimax concave penalty (MCP) approximation associated with rank minimization, which can simultaneously construct the low-rank representation tensor and affinity matrix in a unified framework. Specifically, the nonconvex MCP approximation rank function is adopted to as a tighter tensor rank approximation to discriminate the dimension of features so that better accuracy can be achieved. In addition, we also address the local structure by including both hyper-Laplacian regularization and auto-weighting scheme into the objective function to promote the clustering performance. A corresponding iterative algorithm is then developed to solve the proposed model and the constructed iterative sequence generated by the proposed algorithm is shown to converge to the desirable KKT critical point. Extensive experiments on benchmark datasets have demonstrate the highly desirable effectiveness of the proposed method.

简介：黎稳，华南师范大学二级教授。现任中国数学会理事，广东省数学学会副理事长。曾任中国计算数学会理事、广东省工业与应用数学学会副理事长、广东省计算数学学会副理事长。研究方向：数值代数、张量分析与计算等。主持五项国家自然科学基金面上项目，参与一项广东省与国家自然科学基金集成项目。在学术刊物Numer Math、SIAM J Optim、SIAM J Matrix Anal Appl、SIAM J Imaging Sci、Inverse Problems 、IEEE Transactions on Signal Processing、IEEE Transactions on Cybernetics、J Sci Comput、Comput Optim Appl 和 Pattern Recognition 等发表学术论文多篇。研究成果《数值代数中若干问题研究》和《结构张量的理论、计算与应用》分别获 2011 年和 2020 年广东省科学技术奖二等奖（排名第一）。