Robust Sparse Canonical Correlation Analysis

TL;DR

This paper introduces a robust sparse canonical correlation analysis method that enhances interpretability and outlier resistance by combining sparse estimation with robust regression techniques, demonstrated through simulations and real data.

Contribution

It proposes a novel Robust Sparse CCA approach that integrates sparse Least Trimmed Squares estimation within an alternating regression framework for improved robustness and interpretability.

Findings

Effective outlier handling demonstrated in simulations

Improved interpretability of canonical vectors

Strong performance in real data applications

Abstract

Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal correlation. This paper discusses a method for Robust Sparse CCA. Sparse estimation produces canonical vectors with some of their elements estimated as exactly zero. As such, their interpretability is improved. We also robustify the method such that it can cope with outliers in the data. To estimate the canonical vectors, we convert the CCA problem into an alternating regression framework, and use the sparse Least Trimmed Squares estimator. We illustrate the good performance of the Robust Sparse CCA method in several simulation studies and two real data examples.