題  目：A Unified Framework for Non-Convex Low-Rank Matrix Recovery Problems

内容簡介：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.

報告人：蔡劍鋒

報告人簡介：香港科技大學數學系教授，主要研究興趣為信号，圖像和數據的理論和算法基礎。他在矩陣恢複，圖像重構和成像算法等領域，取得了一系列開創性的科研成果。其關于矩陣補全的SVT算法對學術研究和實際應用産生重要影響，該文章谷歌被引次數超6000次。蔡劍鋒教授關于圖像重構的工作發表于被譽為數學四大期刊之一的Journal of the AMS。蔡劍鋒教授在2017年和2018年被評為全球高被引學者，學術文章總被引超13000次。

時  間：2024年1月2日（周二）下午16：30 開始

地  點：南海樓124室

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