报告题目：Preconditioned Riemannian Gradient Descent for Low-Rank Matrix Recovery Problems

报告人：蔡剑锋教授 香港科技大学

报告时间：2024年4月1日（星期一），上午9:00-10:00

报告地点：兴庆校区数学楼2-1会议室

报告摘要：The challenge of recovering low-rank matrices from linear samples is a common issue in various fields, including machine learning, imaging, signal processing, and computer vision. Non-convex algorithms have proven to be highly effective and efficient for low-rank matrix recovery, providing theoretical guarantees despite the potential for local minima. This talk presents a unifying framework for non-convex low-rank matrix recovery algorithms using Riemannian gradient descent. We demonstrate that numerous well-known non-convex low-rank matrix recovery algorithms can be considered special instances of Riemannian gradient descent, employing distinct Riemannian metrics and retraction operators. Consequently, we can pinpoint the optimal metrics and develop the most efficient non-convex algorithms. To illustrate this, we introduce a new preconditioned Riemannian gradient descent algorithm, which accelerates matrix completion tasks by more than ten times compared to traditional methods.

个人简介：蔡剑锋现任香港科技大学数学系教授。主要研究兴趣为信号，图像和数据的理论和算法基础。他在矩阵恢复，图像重构和成像算法等领域，取得了一系列开创性的科研成果。他关于矩阵补全的SVT算法对学术研究和实际应用产生重要影响，被广泛引用。他在2017年和2018年被评为全球高被引学者，学术文章总被引超13000次。