Identifying Graph Clusters using Variational Inference and links to Covariance Parameterisation ## Abstractincluding Social Network, Web and molecular interaction analyses. From a computational viewpoint, nding these clusters or graph communities is a dicult problem. We consider the framework of Clique Matrices to decompose a graph into a set of possibly overlapping clusters, dened as well-connected subsets of vertices. The decomposition is based on a statistical description which encourages clusters to be well connected and few in number. The formal intractability of inferring the clusters is addressed using a variational approximation which has links to mean- eld theories in statistical mechanics. Clique matrices also play a natural role in parameterising positive denite matrices under zero constraints on elements of the matrix. We show that clique matrices can parameterise all positive denite matrices restricted according to a decomposable graph and form a structured Factor Analysis approximation in the non-decomposable case.
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