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

Speaker:
Yuantao Gu, Tsinghau University, Beijing
Prof. Yuxin Chen
Location:
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 $1 - {\rm e}^{-\mathcal{O}(n)}$.