Robust spectral clustering using LASSO regularization

TL;DR

This paper introduces a robust spectral clustering method using LASSO regularization, which promotes sparsity in the eigenbasis to better recover graph partitions, especially under noise.

Contribution

It proposes a novel 1-spectral clustering approach with theoretical guarantees on partition recovery under a new random model related to stochastic block models.

Findings

Effective in recovering graph partitions

Robust to small noise perturbations

Validated on simulated and real data

Abstract

Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is currently one of the most widely used due to its speed and simplicity. Yet, there are few theoretical guarantee to recover the underlying partitions of the graph for general models. This paper therefore presents a variant of spectral clustering, called 1-spectral clustering, performed on a new random model closely related to stochastic block model. Its goal is to promote a sparse eigenbasis solution of a 1 minimization problem revealing the natural structure of the graph. The effectiveness and the robustness to small noise perturbations of our technique is confirmed through a collection of simulated and real data examples.