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Seminar abstract

High-Dimensional Robust PCA

Huan Xu
the Department of Electrical and Computer Engineering
The University of Texas at Austin

Abstract :

The analysis of very high dimensional data has drawn increasing attention due to a broad array of applications. This exciting new regime poses severe challenges and many of our tried-and-true statistical techniques fail in this regime. In this talk we revisit one of the perhaps most widely used statistical techniques for dimensionality reduction: Principal Component Analysis (PCA). PCA is well-known to be exceptionally brittle -- even a single corrupted point can lead to arbitrarily bad PCA output. We consider PCA in the high-dimensional regime, where a constant fraction of the observations in the data set are arbitrarily corrupted. We show that many existing techniques for controlling the effect of outliers fail in this setting, and discuss some of the unique challenges (and also opportunities) that the high-dimensional regime poses. Then, we propose a High-dimensional Robust Principal Component Analysis (HR-PCA) algorithm that is computationally tractable, provably robust to contaminated points, and easily kernelizable. The resulting subspace has a bounded deviation from the desired one, achieves maximal robustness, and unlike ordinary PCA algorithms, achieves optimality (i.e., exact recovery) in the limiting case where the proportion of corrupted points goes to zero. To the best of our knowledge, this is the very first robust PCA algorithm that works in the high-dimensional regime.


Huan Xu is a postdoctoral associate in the Department of Electrical and Computer Engineering at The University of Texas at Austin. He received the B.Eng. degree in automation from Shanghai Jiaotong University, Shanghai, China in 1997, the M.Eng. degree in electrical engineering from the National University of Singapore in 2003, and the Ph.D. degree in electrical engineering from McGill University, Canada in 2009. His research interests include high-dimensional data analysis, machine learning, robust optimization, and decision making and control under uncertainty. Starting from Jan. 2011, he will join the Department of Mechanical Engineering of the National University of Singapore as an Assistant Professor.

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