题  目：Unifying Non-Convex Low-Rank Matrix Recovery Algorithms by Riemannian Gradient Descent

内容简介：The problem of low-rank matrix recovery from linear samples arises from numerous practical applications in machine learning, imaging, signal processing, computer vision, etc. Non-convex algorithms are usually very efficient and effective for low-rank matrix recovery with a theoretical guarantee, despite of possible local minima. In this talk, non-convex low-rank matrix recovery algorithms are unified under the framework of Riemannian gradient descent. We show that many popular non-convex low-rank matrix recovery algorithms are special cases of Riemannian gradient descent with different Riemannian metrics and retraction operators. Moreover, we identify the best choice of metrics and construct the most efficient non-convex algorithms for low-rank matrix recovery, by considering properties of sampling operators for different tasks such as matrix completion and phase retrieval.

报告人：蔡剑锋

报告人简介：香港科技大学数学系教授。2000年获复旦大学学士学位，2007年获香港中文大学博士学位。曾先后在新加坡国立大学，美国洛杉矶加州大学，和美国爱荷华大学工作。2015年加入香港科技大学数学系。研究兴趣是数据科学和成像技术中的算法设计和分析。在2017年和2018年被评选为全球高被引学者。

时  间：2022年5月12日(周四)  下午14：00—16：00

地  点：腾讯在线会议ID：651-789-825

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2022年4月29日