Spectral clustering with imbalanced data

Spectral clustering is sensitive to how graphs are constructed from data. In particular, if the data has proximal and imbalanced clusters, spectral clustering can lead to poor performance on well-known graphs such as k-NN, ϵ-neighborhood and full-RBF graphs. We propose a graph partitioning problem that seeks minimum cut partitions under minimum size constraints on clusters to deal with imbalanced data. Our approach parameterizes a family of graphs by adaptively modulating node degrees on a fixed node set, to yield 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 asymptotic limit cut analysis to justify our approach. Experiments on synthetic and real data sets demonstrate the superiority of our method.