BLOCCS: Block Sparse Canonical Correlation Analysis With Application To Interpretable Omics Integration

TL;DR

BLOCCS introduces a block sparse canonical correlation analysis method that improves interpretability and stability in multi-omic data integration by estimating multiple orthogonal canonical directions simultaneously.

Contribution

It extends sparse CCA by estimating multiple canonical pairs at once, enhancing interpretability and computational efficiency, with a gradient descent optimization on the Stiefel manifold.

Findings

Outperforms existing sCCA methods in computational cost and stability

Produces more interpretable solutions with orthogonal canonical directions

Effectively captures meaningful biological associations in cancer data

Abstract

We introduce Block Sparse Canonical Correlation Analysis which estimates multiple pairs of canonical directions (together a "block") at once, resulting in significantly improved orthogonality of the sparse directions which, we demonstrate, translates to more interpretable solutions. Our approach builds on the sparse CCA method of (Solari, Brown, and Bickel 2019) in that we also express the bi-convex objective of our block formulation as a concave minimization problem over an orthogonal k-frame in a unit Euclidean ball, which in turn, due to concavity of the objective, is shrunk to a Stiefel manifold, which is optimized via gradient descent algorithm. Our simulations show that our method outperforms existing sCCA algorithms and implementations in terms of computational cost and stability, mainly due to the drastic shrinkage of our search space, and the correlation within and orthogonality between pairs of estimated canonical covariates. Finally, we apply our method, available as an R-package called BLOCCS, to multi-omic data on Lung Squamous Cell Carcinoma(LUSC) obtained via The Cancer Genome Atlas, and demonstrate its capability in capturing meaningful biological associations relevant to the hypothesis under study rather than spurious dominant variations.