Representational Similarity Learning with Application to Brain Networks

Abstract

Representational Similarity Learning (RSL) aims to discover features that are important in representing (human-judged) similarities among objects. RSL can be posed as a sparsity-regularized multi-task regression problem. Standard methods, like group lasso, may not select important features if they are strongly correlated with others. To address this shortcoming we present a new regularizer for multitask regression called Group Ordered Weighted \ell_1 (GrOWL). Another key contribution of our paper is a novel application to fMRI brain imaging. Representational Similarity Analysis (RSA) is a tool for testing whether localized brain regions encode perceptual similarities. Using GrOWL, we propose a new approach called Network RSA that can discover arbitrarily structured brain networks (possibly widely distributed and non-local) that encode similarity information. We show, in theory and fMRI experiments, how GrOWL deals with strongly correlated covariates.