A framework for interpretation and testing of sparse canonical correlations

TL;DR

This paper introduces a new sparse CCA method using soft-thresholding that enhances interpretability and reduces computational complexity, validated through simulations and real cancer genomics data analysis.

Contribution

A novel sparse CCA approach based on soft-thresholding that avoids penalty tuning and improves interpretability over existing methods.

Findings

Improved interpretability of canonical components.

Comparable or better signal discovery performance.

Less dependence on initialisation compared to alternatives.

Abstract

In clinical and biomedical research, multiple high-dimensional datasets are nowadays routinely collected from omics and imaging devices. Multivariate methods, such as Canonical Correlation Analysis (CCA), integrate two (or more) datasets to discover and understand underlying biological mechanisms. For an explorative method like CCA, interpretation is key. We present a sparse CCA method based on soft-thresholding that produces near-orthogonal components, allows for browsing over various sparsity levels, and permutation-based hypothesis testing. Our soft-thresholding approach avoids tuning of a penalty parameter. Such tuning is computationally burdensome and may render unintelligible results. In addition, unlike alternative approaches, our method is less dependent on the initialisation. We examined the performance of our approach with simulations and illustrated its use on real cancer genomics data from drug sensitivity screens. Moreover, we compared its performance to Penalised Matrix Analysis (PMA), which is a popular alternative of sparse CCA with a focus on yielding interpretable results. Compared to PMA, our method offers improved interpretability of the results, while not compromising, or even improving, signal discovery. he software and simulation framework are available at https://github.com/nuria-sv/toscca.