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

内容簡介：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.

報告人：蔡劍鋒

報告人簡介：香港科技大學數學系教授。2000年獲複旦大學學士學位，2007年獲香港中文大學博士學位。曾先後在新加坡國立大學，美國洛杉矶加州大學，和美國愛荷華大學工作。2015年加入香港科技大學數學系。研究興趣是數據科學和成像技術中的算法設計和分析。在2017年和2018年被評選為全球高被引學者。

時  間：2022年5月12日(周四)  下午14：00—16：00

地  點：騰訊在線會議ID：651-789-825

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