A Framework of Non-Convex Methods for Low-Rank Matrix Reconstruction: Algorithms and Theory


Jianfeng Cai, The Hong Kong University of Science and Technology


2018.12.11 14:00-15:00


601 Pao Yue-Kong Library


Low-rank matrix is a versatile model that describes the structure of many datasets of practical interests arising from machine learning, bioinformatics, computer vision etc. Under this model, it is a fundamental problem how to recover a low-rank matrix from small amount linear samples. We present a framework of non-convex methods for low-rank matrix recovery. Our methods will be applied to several concrete example problems such as matrix completion, phase retrieval, and robust principle component analysis. We will also provide theoretical guarantee of our methods for the convergence to the correct low-rank matrix.

Short Bio

Jian-Feng Cai is an associate professor from Department of Mathematics, Hong Kong University of Science and Technology (HKUST). He obtained his Bachelor degree in Computational Mathematics from Fudan University, and PhD degree in Mathematics from Chinese University of Hong Kong. Before joining HKUST in 2015, he has been worked at National University of Singapore, UCLA, and University of Iowa. His research focuses on the design and analysis of algorithms for problems in imaging and data sciences, using tools from computational harmonic analysis, numerical linear algebra, optimization, and high-dimensional probability.