Alternative Blockmodelling

Abstract: Many approaches have been proposed to discover clusters within networks. Community finding field encompasses approaches which try to discover clusters where nodes are tightly related within them but loosely related with nodes of other clusters. However, a community network configuration is not the only possible latent structure in a graph. Core-periphery and hierarchical network configurations are valid structures to discover in a relational dataset. On the other hand, a network is not completely explained by only knowing the membership of each node. A high level view of the inter-cluster relationships is needed. Blockmodelling techniques deal with these two issues. Firstly, blockmodelling allows finding any network configuration besides to the well-known community structure. Secondly, blockmodelling is a summary representation of a network which regards not only membership of nodes but also relations between clusters. Finally, a unique summary representation of a network is unlikely. Networks might hide more than one blockmodel. Therefore, our proposed problem aims to discover a secondary blockmodel representation of a network that is of good quality and dissimilar with respect to a given blockmodel. Our methodology is presented through two approaches, (a) inclusion of cannot-link constraints and (b) dissimilarity between image matrices. Both approaches are based on non-negative matrix factorisation NMF which fits the blockmodelling representation. The evaluation of these two approaches regards quality and dissimilarity of the discovered alternative blockmodel as these are the requirements of the problem.