BSmCCA: A block sparse multiple-set canonical correlation analysis algorithm for multi-subject fMRI data sets

Abstract

Multiple-set canonical correlation analysis (mCCA) is a generalization of canonical correlation analysis (CCA) to three or more sets of variables. It aims to study the relationships between several sets of variables and it subsumes a number of interesting multivariate data analysis techniques as special cases. The quality and interpretability of the mCCA components are likely to be affected by the usefulness and relevance of each set of variables. Therefore, it is an important issue to identify each set of significant variables that are active in the relationships between sets. In this paper mCCA is extended to address the issue of variable set selection. Specifically a block sparse multiple set canonical correlation analysis (BSmCCA) algorithm is proposed to combine mCCA with ℓ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -norm type penalty in a unified framework. Within this framework sets of variables that are not necessarily relevant are removed. This makes BSmCCA a flexible method for analyzing for Multi-Subject functional magnetic resonance imaging (fMRI) data sets. The performances of the proposed BSmCCA algorithm are illustrated through on block design paradigm finger taping fMRI datasets.