题 目：加权张量核范数及应用

报告人：高全学 教授 博士生导师

时 间：2020年10月17日08:10-12:00

地 点：兰州财经大学段家滩校区艺术楼504室（信工学院会议室）

内 容：Recently, the t-SVD based tensor nuclear norm minimization (TNNM) problem has been attracting significant research interest in recent years, especially for multi-view and multi-modal clustering. TNNM recovers the underlying low-rank structure of clean tensor data corrupted with noise/outliers by shrinking all singular values equally. This does not make sense in real applications, where there has a salient difference between all singular values of a tensor matrix. Thus, the singular values should be treated differently. Inspired by this observation, we define the weighted tensor Schatten p-norm and study the weighted tensor nuclear norm minimization (WTNNM) problem, which explicitly considers the salient difference information by adaptively assigning different weights for different singular values. To solve WTNNM, we analyze the theoretical properties of it and find that, when singular values are sorted in a non-increasing order, while weights are sorted in a non-descending order, then a closed-form optimal solution can be easily obtained. We show that most existing nuclear norm minimization models can be viewed as a special case of WTNNM. The proposed WTNNM methods achieve state-of-the-art performance many applications, including multi-view clustering, color image denosing, background subtraction, and matrix completion.

报告人简介：

高全学，45岁，博士，西安电子科技大学教授，博士生导师。

主要从事模式识别、机器学习、图像去噪等领域的基础理论研究工作。主持包括国家自然科学基金项目3项，博士后基金、省自然基金，重点实验开放课题等多项研究课题，参与国家自然科学杰出青年基金和重点项目。在国际一流期刊TIP, IEEE Transactions on Cybernetics, TNNLS, IEEE Transaction on Infomation Forensics and Security， Pattern Recognition和国际顶级会议（CCF A类）CVPR，AAAI, IJCAI等处发表论文50余篇，并担任上述国际期刊的论文评审。担任中国第十一届、十二届中国生物特征识别大会委员，现任陕西省自动化学会会员。