Spectral Clustering with Unbalanced Data

TL;DR

This paper introduces a novel graph partitioning framework that adaptively adjusts node degrees in k-NN graphs, improving spectral clustering performance on unbalanced data and small cluster detection.

Contribution

The paper proposes a new graph construction and model selection scheme tailored for unbalanced data, enhancing spectral clustering and semi-supervised learning.

Findings

Outperforms traditional methods on synthetic and real datasets.

Effectively detects small and unbalanced clusters.

Theoretically justified through limit cut analysis.

Abstract

Spectral clustering (SC) and graph-based semi-supervised learning (SSL) algorithms are sensitive to how graphs are constructed from data. In particular if the data has proximal and unbalanced clusters these algorithms can lead to poor performance on well-known graphs such as $k$-NN, full-RBF, $\epsilon$-graphs. This is because the objectives such as Ratio-Cut (RCut) or normalized cut (NCut) attempt to tradeoff cut values with cluster sizes, which are not tailored to unbalanced data. We propose a novel graph partitioning framework, which parameterizes a family of graphs by adaptively modulating node degrees in a $k$-NN graph. We then propose a model selection scheme to choose sizable clusters which are separated by smallest cut values. Our framework is able to adapt to varying levels of unbalancedness of data and can be naturally used for small cluster detection. We theoretically justify our ideas through limit cut analysis. Unsupervised and semi-supervised experiments on synthetic and real data sets demonstrate the superiority of our method.