数学科学学院学术报告[2025]3号

(高水平大学建设系列报告1026号)

报告题目: Generalized Power Methods for Group Synchronization Problems

报告人：Man-Chung YUE

报告时间：2025年01月13日15:00-16:00

讲座地点：深圳大学粤海校区汇星楼金融科技学院1号教室

报告内容：Group synchronization problems (GSPs) aim at recovering a collection of group elements based on their noisy pairwise comparisons and find a wide range of applications in areas such as machine learning, molecular biology, robotics and computer vision. Existing approaches to GSPs are designed only for a specific subgroup, do not scale well and/or lack theoretical guarantees. In this talk, we present a unified approach to the important sub-class of GSPs associated with any closed subgroup of the orthogonal group, which consists of a suitable initialization and an iterative refinement step based on the generalized power method. Theoretically, we show that our approach enjoys a strong guarantee on the estimation error under certain conditions on the group, measurement graph, noise and initialization. We also show that the group condition is satisfied for the orthogonal group, the special orthogonal group, the permutation group and the cyclic group, which are all practically relevant subgroups of the orthogonal group. We then verify the conditions on the measurement graph and noise for standard random graph and random matrix models. Finally, based on the classical notion of metric entropy, we develop a novel spectral-type estimator for GSPs, which can be used as the initialization of our approach.

报告人简历：Dr. Man-Chung Yue is currently an Assistant Professor at the Musketeers Foundation Institute of Data Science and the Department of Data and Systems Engineering, The University of Hong Kong. He received his B.Sc. degree in Mathematics and Ph.D. degree in Systems Engineering and Engineering Management, both from The Chinese University of Hong Kong. Before joining The University of Hong Kong, he worked in The Hong Kong Polytechnic University as an Assistant Professor and Imperial College London as a Research Associate. His research focuses on continuous optimization and its interplay with decision-making under uncertainty, signal processing, machine learning and operations research.  

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邀请人：涂凯

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