Clustering and Community Detection with Imbalanced Clusters
This addresses clustering and community detection issues in applications with imbalanced data, but it is incremental as it builds on existing graph partitioning methods.
The paper tackles the problem of spectral clustering being sensitive to imbalanced cluster sizes by proposing a graph partitioning method with minimum size constraints, showing superior performance in experiments on synthetic and real datasets.
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.