Eigenspectrum Shape Based Nyström Sampling

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 Nyström method - an approach with proven approximate error bounds. There are several algorithms that provide recipes to construct Nyström approximations with variable accuracies and computing times. This paper proposes a scalable Nyström-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 eigenspectrum shape of the dataset, and yields competitive low-rank approximations in test datasets compared to the other state-of-the-art methods.