On clustering on graphs with multiple edge types

Abstract

We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured by many different metrics. For instance, similarity between two papers can be based on common authors, where they were published, keyword similarity, citations, etc. As such, graphs with multiple edges give a more accurate model to describe similarities between objects than models using single-edge graphs. Each edge/metric provides only partial information about the data; recovering full information requires aggregation of all the similarity metrics. Clustering becomes much more challenging in this context, since in addition to the difficulties of the traditional clustering problem, we have to deal with a space of clusterings. Reducing the multidimensional space into a single dimension poses significant challenges. At the same time, the multidimensional space can contain latent structures, and searching this multidimensional space can reveal important information about the graph. We generalize the concept of clustering in single-edge graphs to multiedged graphs and investigate problems such as the following: Can we find a clustering that remains good, even if we change the relative weights of metrics? How can we describe the space of clusterings efficiently? Can we find unexpected clusterings (a good clustering that is distant from all given clusterings)? If we are given the ground-truth clustering, can we recover how the weights for edge types were aggregated?.