A general multiblock method for structured variable selection
This work addresses variable selection in multiblock data analysis for fields like bioinformatics, but it is incremental as it builds directly on existing SGCCA and RGCCA methods.
The authors tackled the limitation of Sparse GCCA (SGCCA) by extending it to the full RGCCA model, enabling variable selection beyond the covariance link, and incorporated structured penalties to exploit within-block variable relationships. They demonstrated the method on a glioma dataset for tumor location prediction and on simulated data for weight vector reconstruction.
Regularised canonical correlation analysis was recently extended to more than two sets of variables by the multiblock method Regularised generalised canonical correlation analysis (RGCCA). Further, Sparse GCCA (SGCCA) was proposed to address the issue of variable selection. However, for technical reasons, the variable selection offered by SGCCA was restricted to a covariance link between the blocks (i.e., with $τ=1$). One of the main contributions of this paper is to go beyond the covariance link and to propose an extension of SGCCA for the full RGCCA model (i.e., with $τ\in[0, 1]$). In addition, we propose an extension of SGCCA that exploits structural relationships between variables within blocks. Specifically, we propose an algorithm that allows structured and sparsity-inducing penalties to be included in the RGCCA optimisation problem. The proposed multiblock method is illustrated on a real three-block high-grade glioma data set, where the aim is to predict the location of the brain tumours, and on a simulated data set, where the aim is to illustrate the method's ability to reconstruct the true underlying weight vectors.