Rigorous Restricted Isometry Property of Low-Dimensional Subspaces
Gen Li, Qinghua Liu, Yuantao Gu · arXiv (Cornell University) · 2018
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 work we study 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