Large Scale Spectral Clustering Using Approximate Commute Time Embedding

TL;DR

This paper introduces a fast, accurate spectral clustering method that uses approximate commute time embedding with random projection and linear solvers, avoiding eigen decomposition and sampling, suitable for large datasets.

Contribution

It presents a novel spectral clustering approach that bypasses eigen decomposition and sampling, improving speed and accuracy for large-scale data.

Findings

Outperforms existing approximate methods in clustering quality

Faster computation on synthetic and real datasets

Does not require eigenvector calculation or sampling

Abstract

Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for large scale systems. Recently, many methods have been proposed to accelerate the computational time of spectral clustering. These approximate methods usually involve sampling techniques by which a lot information of the original data may be lost. In this work, we propose a fast and accurate spectral clustering approach using an approximate commute time embedding, which is similar to the spectral embedding. The method does not require using any sampling technique and computing any eigenvector at all. Instead it uses random projection and a linear time solver to find the approximate embedding. The experiments in several synthetic and real datasets show that the proposed approach has better clustering quality and is faster than the state-of-the-art approximate spectral clustering methods.