Clustering with Simultaneous Local and Global View of Data: A message passing based approach

A good clustering algorithm should not only be able to discover clusters of arbitrary shapes (global view) but also provide additional information, which can be used to gain more meaningful insights into the internal structure of the clusters (local view). In this work we use the mathematical framework of factor graphs and message passing algorithms to optimize a pairwise similarity based cost function, in the same spirit as was done in Affinity Propagation. Using this framework we develop two variants of a new clustering algorithm, EAP and SHAPE. EAP/SHAPE can not only discover clusters of arbitrary shapes but also provide a rich local view in the form of meaningful local representatives (exemplars) and connections between these local exemplars. We discuss how this local information can be used to gain various insights about the clusters including varying relative cluster densities and indication of local strength in different regions of a cluster . We also discuss how this can help an analyst in discovering and resolving potential inconsistencies in the results. The efficacy of EAP/SHAPE is shown by applying it to various synthetic and real world benchmark datasets.