Low rank and sparsity constrained method for identifying overlapping functional brain networks.

Analysis of functional magnetic resonance imaging (fMRI) data has revealed that brain regions can be grouped into functional brain networks (fBNs) or communities. A community in fMRI analysis signifies a group of brain regions coupled functionally with one another. In neuroimaging, functional connectivity (FC) measure can be utilized to quantify such functionally connected regions for disease diagnosis and hence, signifies the need of devising novel FC estimation methods. In this paper, we propose a novel method of learning FC by constraining its rank and the sum of non-zero coefficients. The underlying idea is that fBNs are sparse and can be embedded in a relatively lower dimension space. In addition, we propose to extract overlapping networks. In many instances, communities are characterized as combinations of disjoint brain regions, although recent studies indicate that brain regions may participate in more than one community. In this paper, large-scale overlapping fBNs are identified on resting state fMRI data by employing non-negative matrix factorization. Our findings support the existence of overlapping brain networks.