学术报告

题      目： LOW-RANK MODELS FOR TENSORIAL DATA IN VISUAL ANALYSIS

报  告  人：杨明   博士  (邀请人：黎稳 )

                                埃文斯维尔大学

时      间：2022-11-10 20:30-21:30

腾 讯 会 议：869 329 948

报告人简介:

       杨明，2007年获得中国长春吉林大学数学学士学位，2012年在美国德克萨斯 A&M 大学学院站获得数学博士学位，曾为韦斯特菲尔德州立大学数学与计算机与信息科学系的数据科学助理教授，现为埃文斯维尔大学数学系助理教授。研究兴趣是机器学习、图像处理和张量分解。他在顶级期刊上发表了多篇研究论文，包括 SIAM Journal on Imaging Sciences、IEEE Signal Processing Letters、IEEE Transactions on Knowledge and Data Engineering、IEEE Transactions on Image Processing、IEEE Transactions on Signal Processing、IEEE Transactions on Multimedia、Pattern Recognition、Neural Network、Journal of Dynamics and Differential Equations，Linear and Multilinear Algebra。

摘      要：

       We study the 3D array image data completion, robust principal component analysis (PCA), and multi-view subspace clustering problems via a non-convex low-rank representation under the framework of tensors. Most of the recent studies of tensor-based linear models use the Tensor Nuclear Norm (TNN) as a convex surrogate of the tensor rank. However, since the tensor nuclear norm is linearly proportional to the sum of singular values, the tensor rank approximation by using the tensor nuclear norm may become problematic if the ratios of the nonzero singular values are far away being from 1. Some non-convex tensor-based functions are proposed as the objective function regularizer, aiming to achieve a better tensor low-rank approximation. A corresponding algorithm associated with the augmented Lagrangian multipliers is established and the constructed convergent sequence to the desirable Karush--Kuhn--Tucker (KKT)  critical point solution is mathematically validated in detail.  Extensive simulations on eight benchmark image datasets are provided, along with full comparisons with the latest existing approaches. The obtained results demonstrate that our proposed method significantly outperforms those convex approaches currently available in the literature.