Compression-Based Graph Mining Exploiting Structure Primitives

How can we retrieve information from sparse graphs? Traditional graph mining approaches focus on discovering dense patterns inside complex networks, for example modularity-based or cut-based methods. However, most real world data sets are very sparse. Nevertheless, traditional approaches tend to omit interesting sparse patterns like stars. In this paper, we propose a novel graph mining technique modeling the transitivity and the hub ness of a graph using structure primitives. We exploit these structure primitives for effective graph compression using the Minimum Description Length Principle. The compression rate is an unbiased measure for the transitivity or hub ness and therefore provides interesting insights into the structure of even very sparse graphs. Since real graphs can be composed of sub graphs of different structures, we propose a novel algorithm CXprime (Compression-based exploiting Primitives) for clustering graphs using our coding scheme as an objective function. In contrast to traditional graph clustering methods, our algorithm automatically recognizes different types of sub graphs without requiring the user to specify input parameters. Additionally we propose a novel link prediction algorithm based on the detected substructures, which increases the quality of former methods. Extensive experiments evaluate our algorithms on synthetic and real data.