Affiliation:
1. Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
2. Department of Mathematics and Statistics, University of Victoria, British Columbia, Canada
Abstract
Motivated by the general matrix deviation inequality for i.i.d. ensemble Gaussian matrix [R. Vershynin, High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, 2018), doi:10.1017/9781108231596 of Theorem 11.1.5], we show that this property holds for the [Formula: see text]-norm with [Formula: see text] and i.i.d. ensemble sub-Gaussian matrices, i.e. random matrices with i.i.d. mean-zero, unit variance, sub-Gaussian entries. As a consequence of our result, we establish the Johnson–Lindenstrauss lemma from [Formula: see text]-space to [Formula: see text]-space for all i.i.d. ensemble sub-Gaussian matrices.
Funder
National Science and Technology Council
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory