Princeton University

School of Engineering & Applied Science

Restricted Isometry Property of Gaussian Random Matrix for Low-Dimensional Subspaces

Yuantao Gu, Tsinghau University, Beijing
Prof. Yuxin Chen
Engineering Quadrangle B205
Monday, February 12, 2018 - 12:30pm

Abstract: Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this talk I will introduce the Restricted Isometry Property (RIP) of Gaussian random projections for low-dimensional subspaces in $\mathbb{R}^N$, and rigorously prove that the projection Frobenius norm distance between any two subspaces spanned by the projected data in $\mathbb{R}^n$ ($n<N$) remain almost the same as the distance between the original subspaces with probability no less than $1 - {\rm e}^{-\mathcal{O}(n)}$.

Previously the well-known Johnson-Lindenstrauss (JL) Lemma and RIP for sparse vectors have been the foundation of sparse signal processing including Compressed Sensing. As an analogy to JL Lemma and RIP for sparse vectors, this work allows the use of random projections to reduce the ambient dimension with the theoretical guarantee that the distance between subspaces after compression is well preserved.

Bio: Yuantao Gu received the B.E. degree from Xi'an Jiaotong University in 1998, and the Ph.D. degree with honor from Tsinghua University in 2003, both in Electronic Engineering. He joined the faculty of Tsinghua University in 2003 and is now a Tenured Associate Professor with Department of Electronic Engineering. He was a visiting scientist at Microsoft Research Asia during 2005 to 2006, Research Laboratory of Electronics at Massachusetts Institute of Technology during 2012 to 2013, and Department of Electrical Engineering and Computer Science at the University of Michigan in Ann Arbor during 2015. His research interests include high-dimensional statistics, sparse signal recovery, temporal-space and graph signal processing, related topics in wireless communications and information networks.

He has been an Associate Editor of the IEEE Transactions on Signal Processing since 2015, a Handling Editor for EURASIP Digital Signal Processing since February 2015, and an Elected Member of the IEEE Signal Processing Theory and Methods (SPTM) Technical Committee since 2017. He is a senior member of IEEE.
He received the Best Paper Award of IEEE Global Conference on Signal and Information Processing (GlobalSIP) in 2015, the Award for Best Presentation of Journal Paper of IEEE International Conference on Signal and Information Processing (ChinaSIP) in 2015, and Zhang Si-Ying (CCDC) Outstanding Youth Paper Award (with his student) in 2017.