Clustering and Community Detection with Imbalanced Clusters

TL;DR

This paper introduces a novel graph partitioning method that effectively handles imbalanced clusters by adaptively modulating node degrees and optimizing over a family of cuts, improving clustering and community detection results.

Contribution

It proposes a new approach for clustering with imbalanced clusters by parameterizing graph cuts with adaptive node degrees and optimizing over these parameters.

Findings

Outperforms traditional spectral clustering on imbalanced data

Provides rigorous theoretical analysis of limit cuts

Demonstrates effectiveness on synthetic and real datasets

Abstract

Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced cluster sizes since they tend to emphasize cut sizes over cut values. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on partitions to deal with imbalanced cluster sizes. Our approach parameterizes a family of graphs by adaptively modulating node degrees on a fixed node set, yielding a set of parameter dependent cuts reflecting varying levels of imbalance. The solution to our problem is then obtained by optimizing over these parameters. We present rigorous limit cut analysis results to justify our approach and demonstrate the superiority of our method through experiments on synthetic and real datasets for data clustering, semi-supervised learning and community detection.