A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering

TL;DR

This paper introduces a PAC-Bayesian framework for graph clustering, providing theoretical guarantees and an algorithm that balances data fit with information preservation, validated by real-world experiments.

Contribution

It adapts PAC-Bayesian analysis to graph clustering, offering a new theoretical bound and an effective minimization algorithm for practical applications.

Findings

The PAC-Bayesian bound is reasonably tight.

The algorithm performs well on real-life problems.

The approach balances empirical fit with mutual information.

Abstract

We formulate weighted graph clustering as a prediction problem: given a subset of edge weights we analyze the ability of graph clustering to predict the remaining edge weights. This formulation enables practical and theoretical comparison of different approaches to graph clustering as well as comparison of graph clustering with other possible ways to model the graph. We adapt the PAC-Bayesian analysis of co-clustering (Seldin and Tishby, 2008; Seldin, 2009) to derive a PAC-Bayesian generalization bound for graph clustering. The bound shows that graph clustering should optimize a trade-off between empirical data fit and the mutual information that clusters preserve on the graph nodes. A similar trade-off derived from information-theoretic considerations was already shown to produce state-of-the-art results in practice (Slonim et al., 2005; Yom-Tov and Slonim, 2009). This paper supports the empirical evidence by providing a better theoretical foundation, suggesting formal generalization guarantees, and offering a more accurate way to deal with finite sample issues. We derive a bound minimization algorithm and show that it provides good results in real-life problems and that the derived PAC-Bayesian bound is reasonably tight.