Special Seminar in Computing + Mathematical Sciences

In this talk, we will discuss a class of models and techniques that can effectively model and extract rich low-dimensional structures in high-dimensional data such as images and videos, despite nonlinear transformation, gross corruption, or severely compressed measurements. This work leverages recent advancements in convex optimization for recovering low-rank or sparse signals that provide both strong theoretical guarantees and efficient and scalable algorithms for solving such high-dimensional combinatorial problems. We illustrate how these new mathematical models and tools could bring disruptive changes to solutions to many challenging tasks in computer vision, image processing, and pattern recognition. We will also illustrate some emerging applications of these tools to other data types such as 3D range data, web documents, image tags, bioinformatics data, audio/music analysis, etc. In the end, we will discuss some extensions of such low-dimensional models, and their connections with other popular data-processing models such as deep neural networks.

This is joint work with John Wright of Columbia, Emmanuel Candes of Stanford, Zhouchen Lin of Peking University, Shenghua Gao of ShanghaiTech, and my former students Zhengdong Zhang, Xiao Liang of Tsinghua University, Arvind Ganesh, Zihan Zhou, Kerui Min of UIUC etc.