A Tutorial on Spectral Clustering

TL;DR

This tutorial explains spectral clustering, a popular and efficient clustering method, providing intuition, mathematical foundations, algorithm derivations, and discussing their advantages and disadvantages.

Contribution

It offers a comprehensive, accessible overview of spectral clustering, including derivations and comparisons of different algorithms, which was lacking in prior literature.

Findings

Spectral clustering often outperforms traditional methods like k-means.

Different graph Laplacians have distinct properties affecting clustering results.

The tutorial clarifies the mathematical foundations and practical considerations of spectral clustering.

Abstract

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.