Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting, gross corruptions and computational efficiency. To address these problems, we first propose a parallel trace norm regularized tensor decomposition method, and formulate it as a convex optimization problem. This method does not require the rank of each mode to be specified beforehand, and can automatically determine the number of factors in each mode through our optimization scheme. By considering the low-rank structure of the observed tensor, we analyze the equivalent relationship of the trace norm between a low-rank tensor and its core tensor. Then, we cast a non-convex tensor decomposition model into a weighted combination of multiple much smaller-scale matrix trace norm minimization. Finally, we develop two parallel alternating direction methods of multipliers (ADMM) to solve our problems. Experimental results verify that our regularized formulation is effective, and our methods are robust to noise or outliers.
Asynchronous Distributed ADMM for Large-Scale Optimization- Part I: Algorithm and Convergence Analysis
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Iowa State University（爱荷华州立大学）；University of Minnesota（明尼苏达大学）；East China Normal University（华东师范大学）
Online Parallel Multi-Task Relationship Learning via Alternating Direction Method of Multipliers
School of Computer Science and Technology, Xidian University（西安电子科技大学计算机科学与技术学院）；Tencent AI Lab, Tencent Inc（腾讯公司腾讯AI实验室）；MBZUAI（穆罕默德·本·扎耶德人工智能大学）；School of Intelligent Engineering, Henan Institute of Technology（河南工程学院智能工程学院）
Spectrally Grouped Total Variation Reconstruction for Scatter Imaging Using ADMM
Department of Electrical and Computer Engineering, Duke University（电子与计算机工程系，达特茅斯大学）；Mallinckrodt Institute of Radiology, Washington University in Saint Louis（圣路易斯华盛顿大学放射医学研究所）；Department of Electrical and Systems Engineering, Washington University in Saint Louis（电子与系统工程系，圣路易斯华盛顿大学）
