TY - JOUR

T1 - Matrix deviation inequality for p-norm

AU - Sheu, Yuan Chung

AU - Wang, Te Chun

N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.

PY - 2023

Y1 - 2023

N2 - 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 p-norm with 1 ≤ p < ∞ 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 2n-space to pm-space for all i.i.d. ensemble sub-Gaussian matrices.

AB - 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 p-norm with 1 ≤ p < ∞ 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 2n-space to pm-space for all i.i.d. ensemble sub-Gaussian matrices.

KW - concentration inequality

KW - Johnson-Lindenstrauss lemma

KW - Matrix deviation inequality

KW - sub-Gaussian matrix

UR - http://www.scopus.com/inward/record.url?scp=85162808369&partnerID=8YFLogxK

U2 - 10.1142/S2010326323500077

DO - 10.1142/S2010326323500077

M3 - Article

AN - SCOPUS:85162808369

SN - 2010-3263

JO - Random Matrices: Theory and Application

JF - Random Matrices: Theory and Application

M1 - 2350007

ER -