Discovering latent blockmodels in sparse and noisy graphs using non-negative matrix factorisation

Blockmodelling is an important technique in social network analysis for discovering the latent structure in graphs. A blockmodel partitions the set of vertices in a graph into groups, where there are either many edges or few edges be- tween any two groups. For example, in the reply graph of a question and answer forum, blockmodelling can identify the group of experts by their many replies to questioners, and the group of questioners by their lack of replies among themselves but many replies from experts. Non-negative matrix factorisation has been successfully applied to many problems, including blockmodelling. How- ever, these existing approaches can fail to discover the true latent structure when the graphs have strong background noise or are sparse, which is typical of most real graphs. In this paper, we propose a new non-negative matrix factorisation approach that can discover blockmodels in sparse and noisy graphs. We use synthetic and real datasets to show that our approaches have much higher accuracy and comparable running times.