Compressive Spectral Clustering

TL;DR

This paper introduces a fast approximation method for spectral clustering using graph signal processing techniques, significantly reducing computation time while maintaining accuracy.

Contribution

It presents a novel approach that speeds up spectral clustering steps through graph filtering and sampling, with theoretical error control.

Findings

Achieves several orders of magnitude faster computation.

Provides theoretical guarantees on approximation error.

Performs well on artificial and real-world data.

Abstract

Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features to separate objects into k classes. Each of these three steps becomes computationally intensive for large N and/or k. We propose to speed up the last two steps based on recent results in the emerging field of graph signal processing: graph filtering of random signals, and random sampling of bandlimited graph signals. We prove that our method, with a gain in computation time that can reach several orders of magnitude, is in fact an approximation of spectral clustering, for which we are able to control the error. We test the performance of our method on artificial and real-world network data.