The adaptive block sparse PCA and its application to multi-subject FMRI data analysis using sparse mCCA

Motivated by the problem of multi-subject functional magnetic resonance imaging (fMRI) data sets analysis using multiple-set canonical correlation analysis (mCCA), in this paper we propose a new variant of the principal component analysis (PCA) method, namely the adaptive block sparse PCA. It has the advantage to produce modified principal components with block sparse loadings. It is derived using penalized rank one matrix approximation where the penalty is introduced in the minimization problem to promote block sparsity of the loading vectors. An efficient algorithm is proposed for its computation. The effectiveness of the proposed method is illustrated on the problem of multi-subject fMRI data sets analysis using mCCA which is a generalization of canonical correlation analysis (CCA) to three or more sets of variables. This application is obtained by deriving the connection between mCCA and the singular value decomposition (SVD).