Fast and Simple Spectral Clustering in Theory and Practice

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: spectral clustering, power method, spectral graph theory, graph algorithms
TL;DR: We present and analyse a fast and simple spectral clustering algorithm based on an embedding of the graph vertices using O(log(k)) vectors.
Abstract: Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph Laplacian matrix. However, computing this embedding is computationally expensive and dominates the running time of the algorithm. In this paper, we present a simple spectral clustering algorithm based on a vertex embedding with $O(\log(k))$ vectors computed by the power method. The vertex embedding is computed in nearly-linear time with respect to the size of the graph, and the algorithm provably recovers the ground truth clusters under natural assumptions on the input graph. We evaluate the new algorithm on several synthetic and real-world datasets, finding that it is significantly faster than alternative clustering algorithms, while producing results with approximately the same clustering accuracy.
Supplementary Material: zip
Submission Number: 14251