Self-Adaptive Skeleton Approaches to Detect Self-Organized Coalitions From Brain Functional Networks Through Probabilistic Mixture Models

Detecting self-organized coalitions from functional networks is one of the most important ways to uncover functional mechanisms in the brain. Determining these raises well-known technical challenges in terms of scale imbalance, outliers and hard-examples. In this article, we propose a novel self-adaptive skeleton approach to detect coalitions through an approximation method based on probabilistic mixture models. The nodes in the networks are characterized in terms of robust k-order complete subgraphs (k-clique) as essential substructures. The k-clique enumeration algorithm quickly enumerates all k-cliques in a parallel manner for a given network. Then, the cliques, from max-clique down to min-clique, of each order k, are hierarchically embedded into a probabilistic mixture model. They are self-adapted to the corresponding structure density of coalitions in the brain functional networks through different order k. All the cliques are merged and evolved into robust skeletons to sustain each unbalanced coalition by eliminating outliers and separating overlaps. We call this the k-CLIque Merging Evolution (CLIME) algorithm. The experimental results illustrate that the proposed approaches are robust to density variation and coalition mixture and can enable the effective detection of coalitions from real brain functional networks. There exist potential cognitive functional relations between the regions of interest in the coalitions revealed by our methods, which suggests the approach can be usefully applied in neuroscientific studies.