Spectral Clustering using Eigenspectrum Shape Based Nystrom Sampling

TL;DR

This paper introduces a scalable spectral clustering method that uses a novel eigen-spectrum shape-based Nystrom sampling technique, improving efficiency while maintaining accuracy for large datasets.

Contribution

It proposes a new sampling procedure, CMS3, based on eigen-spectrum shape, and a heuristic for its application, enhancing Nystrom-based clustering scalability.

Findings

CMS3 yields competitive low-rank approximations.

The heuristic effectively determines when to use CMS3.

The method improves scalability without sacrificing accuracy.

Abstract

Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating algorithms are proposed, including the Nystrom method - an approach with proven approximate error bounds. There are several algorithms that provide recipes to construct Nystrom approximations with variable accuracies and computing times. This paper proposes a scalable Nystrom-based clustering algorithm with a new sampling procedure, Centroid Minimum Sum of Squared Similarities (CMS3), and a heuristic on when to use it. Our heuristic depends on the eigen spectrum shape of the dataset, and yields competitive low-rank approximations in test datasets compared to the other state-of-the-art methods