A hybrid recommendation technique optimized by dimension reduction

Ruan, Dongru; Meng, Tian-hong; Gao, Kai

doi:10.1109/icmic.2016.7804150

Cited by 2 publications

(1 citation statement)

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“…Estimation of correlation matrices is among the most fundamental statistical tasks, basic to standard methods and widely used in applications. Modern examples include viral sequence analysis and vaccine design in biology (Dahirel et al, 2011;Quadeer et al, 2014Quadeer et al, , 2018, large portfolio design in finance (Plerou et al, 2002), signal detection in radio astronomy (Leshem and van der Veen, 2001), and collaborative filtering (Liu et al, 2014;Ruan et al, 2016), among many others. In classical statistical settings, with a limited number of variables p and a large sample size n, the sample correlation matrix performs well.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics of eigenstructure of sample correlation matrices for high-dimensional spiked models

Morales-Jiménez¹,

Johnstone²,

McKay³

et al. 2021

STAT SINICA

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Sample correlation matrices are widely used, but surprisingly little is known about their asymptotic spectral properties for high-dimensional data beyond the case of "null models", for which the data is assumed to have independent coordinates. In the class of spiked models, we apply random matrix theory to derive asymptotic first-order and distributional results for both the leading eigenvalues and eigenvectors of sample correlation matrices, assuming a high dimensional regime in which the ratio p/n, of number of variables p to sample size n, converges to a positive constant. While the first order spectral properties of sample correlation matrices match those of sample covariance matrices, their asymptotic distributions can differ significantly. Indeed, the correlation-based fluctuations of both sample eigenvalues and eigenvectors are often remarkably smaller than those of their sample covariance counterparts.

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