Graph-based Learning with Unbalanced Clusters

TL;DR

This paper introduces a new graph construction method for spectral clustering and SSL that effectively handles unbalanced and proximal data by adaptively modulating neighborhood degrees, improving clustering performance.

Contribution

A novel adaptive graph construction technique based on modulating neighborhood degrees in k-NN graphs, enhancing spectral methods for unbalanced data.

Findings

Outperforms standard graphs in unbalanced data scenarios

Effectively detects small clusters in various datasets

Theoretically justified through limit cut analysis

Abstract

Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, $\epsilon$-graphs and $k$-NN graphs can lead to poor performance in the presence of proximal and unbalanced data. This is because spectral methods based on minimizing RatioCut or normalized cut on these graphs tend to put more importance on balancing cluster sizes over reducing cut values. We propose a novel graph construction technique and show that the RatioCut solution on this new graph is able to handle proximal and unbalanced data. Our method is based on adaptively modulating the neighborhood degrees in a $k$-NN graph, which tends to sparsify neighborhoods in low density regions. Our method adapts to data with varying levels of unbalancedness and can be naturally used for small cluster detection. We justify our ideas through limit cut analysis. Unsupervised and semi-supervised experiments on synthetic and real data sets demonstrate the superiority of our method.