Identifying Graph Clusters using Variational Inference and links to Covariance Parameterisation
Royal Society Philosophical Transactions A
including 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.