Title: High Dimensional Sparse Canonical Correlation Analysis for Elliptical Symmetric Distributions
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: Canonical correlation analysis, Elliptical symmetric distributions, High dimensional data, Spatial-sign

Abstract: This paper proposes a robust high-dimensional sparse canonical correlation analysis (CCA) method for investigating linear relationships between two high-dimensional random vectors, focusing on elliptical symmetric distributions. Traditional CCA methods, based on sample covariance matrices, struggle in high-dimensional settings, particularly when data exhibit heavy-tailed distributions. To address this, we introduce the spatial-sign covariance matrix as a robust estimator, combined with a sparsity-inducing penalty to efficiently estimate canonical correlations. Theoretical analysis shows that our method is consistent and robust under mild conditions, converging at an optimal rate even in the presence of heavy tails. Simulation studies demonstrate that our approach outperforms existing sparse CCA methods, particularly under heavy-tailed distributions. A real-world application further confirms the method’s robustness and efficiency in practice. Our work provides a novel solution for high-dimensional CCA, offering significant advantages over traditional methods in terms of both stability and performance.

TL;DR: This paper proposes a robust high-dimensional sparse canonical correlation analysis (CCA) method for heavy-tailed data, focusing on elliptical symmetric distributions.