High-Dimension, Low Sample Size Asymptotics of Canonical Correlation Analysis

TL;DR

This paper investigates the asymptotic behavior of canonical correlation analysis in high-dimensional, low sample size settings, identifying conditions for its success or failure.

Contribution

It provides theoretical conditions and extensive simulations for when CCA works or fails in HDLSS scenarios with a simplified model.

Findings

Identifies conditions for CCA success in HDLSS settings.

Shows when CCA fails due to high dimensionality.

Supports findings with proofs and simulations.

Abstract

An asymptotic behavior of canonical correlation analysis is studied when dimension d grows and the sample size n is fxed. In particular, we are interested in the conditions for which CCA works or fails in the HDLSS situation. This technical report investigates those conditions in a rather simplified setting where there exists one pair of directions in two sets of random variables with non-zero correlation between two sets of scores on them. Proofs and an extensive simulation study supports the findings.