Data Clustering and Graph Partitioning via Simulated Mixing

TL;DR

This paper introduces a novel spectral clustering algorithm that avoids eigenvector computation by using a mixing process on graphs, leading to improved accuracy and scalability for large datasets.

Contribution

The proposed method replaces eigenvector computation with a mixing process, enabling faster and more accurate clustering without eigen-decomposition.

Findings

Achieves better clustering accuracy than standard spectral methods.

Easily implementable in distributed environments.

Effective on large-scale real datasets.

Abstract

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue decompositions. Several algorithms have been proposed in the recent past to accelerate spectral clustering, however they compromise on the accuracy of the spectral clustering to achieve faster speed. In this paper, we propose a novel spectral clustering algorithm based on a mixing process on a graph. Unlike the existing spectral clustering algorithms, our algorithm does not require computing eigenvectors. Specifically, it finds the equivalent of a linear combination of eigenvectors of the normalized similarity matrix weighted with corresponding eigenvalues. This linear combination is then used to partition the dataset into meaningful clusters. Simulations on real datasets show that partitioning datasets based on such linear combinations of eigenvectors achieves better accuracy than standard spectral clustering methods as the number of clusters increase. Our algorithm can easily be implemented in a distributed setting.