Accelerated Spectral Clustering Using Graph Filtering Of Random Signals

TL;DR

This paper introduces a faster spectral clustering method that estimates the clustering distance matrix through graph filtering of random signals, avoiding costly eigenvector computations and effectively handling large datasets.

Contribution

It proposes a novel graph filtering approach to estimate spectral clustering distances without eigenvector computation, also estimating the number of clusters from random signals.

Findings

Achieves at least twice the speed of classical spectral clustering on large datasets.

Maintains comparable clustering performance to traditional methods.

Effectively estimates the number of clusters using stochastic properties of random signals.

Abstract

We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first k eigenvectors of the similarity matrix' Laplacian, whose computation cost, even for sparse matrices, becomes prohibitive for large datasets. We show that we can estimate the spectral clustering distance matrix without computing these eigenvectors: by graph filtering random signals. Also, we take advantage of the stochasticity of these random vectors to estimate the number of clusters k. We compare our method to classical spectral clustering on synthetic data, and show that it reaches equal performance while being faster by a factor at least two for large datasets.