Miklós Kurucz

Spectral clustering in telephone call graphs

We evaluate various heuristics for hierarchical spectral clustering in large telephone call graphs. Spectral clustering without additional heuristics often produces very uneven cluster sizes or low quality clusters that may consist of several disconnected components, a fact that appears to be common for several data sources but, to our knowledge, not described in the literature. Divide-and-Merge, a recently described postfiltering procedure may be used to eliminate bad quality branches in a binary tree hierarchy. We propose an alternate solution that enables k-way cuts in each step by immediately filtering unbalanced or low quality clusters before splitting them further. Our experiments are performed on graphs with various weight and normalization built based on call detail records. We investigate a period of eight months of more than two millions of Hungarian landline telephone users. We measure clustering quality both by cluster ratio as well as by the geographic homogeneity of the clusters obtained from telephone location data. Although divide-and-merge optimizes its clusters for cluster ratio, our method produces clusters of similar ratio much faster, furthermore we give geographically much more homogeneous clusters with the size distribution of our clusters resembling to that of the settlement structure.

Spectral Clustering in Social Networks

We evaluate various heuristics for hierarchical spectral clustering in large telephone call and Web graphs. Spectral clustering without additional heuristics often produces very uneven cluster sizes or low quality clusters that may consist of several disconnected components, a fact that appears to be common for several data sources but, to our knowledge, no general solution provided so far. Divide-and-Merge, a recently described postfiltering procedure may be used to eliminate bad quality branches in a binary tree hierarchy. We propose an alternate solution that enables k -way cuts in each step by immediately filtering unbalanced or low quality clusters before splitting them further. Our experiments are performed on graphs with various weight and normalization built based on call detail records and Web crawls. We measure clustering quality both by modularity as well as by the geographic and topical homogeneity of the clusters. Compared to divide-and-merge, we give more homogeneous clusters with a more desirable distribution of the cluster sizes.

Telephone Call Network Data Mining: A Survey with Experiments

We survey some results of social network modeling and analysis relevant for telephone call networks and illustrate these results over the call logs of major Hungarian telephone companies. Our unique data sets include millions of users, long time range, and sufficiently strong sociodemographic information on the users. We explore properties that give stronger intuition on how contacts within real social networks arise, and suggest properties unexplained by current network evolution models.

Geographically Organized Small Communities and the Hardness of Clustering Social Networks

Spectral clustering, while perhaps the most efficient heuristics for graph partitioning, has recently gathered bad reputation for failure over large-scale power law graphs. In this chapter we identify the abundance of small-size communities connected by long tentacles as the major obstacle for spectral clustering. These subgraphs hide the higher level structure and result in a highly degenerate adjacency matrix with several hundreds of eigenvalues very close to 1. Our results on clustering social networks, telephone call graphs, and Web graphs are twofold. (1) We show that graphs generated by existing social network models are not as difficult to cluster as they are in the real world. For this end we give a new combined model that yields degenerate adjacency matrices and hard-to-partition graphs. (2) We give heuristics for spectral clustering for large-scale real-world social networks that handle tentacles and small dense communities. Our algorithm outperforms all previous methods for power law graph partitioning both in speed and in cluster quality. In a combination of heuristics for the contraction of tentacles as well as the removal of community cores that involve the recent SCAN (Structural Clustering Algorithm for Networks) algorithm, we are able to efficiently find balanced partitioning of over 10 million edge power law graphs. In particular, our heuristics promise similar or better performance than semidefinite relaxation with orders of magnitude lower running time.