A Restarted Large-Scale Spectral Clustering with Self-Guiding and Block Diagonal Representation

TL;DR

This paper introduces a novel restarted spectral clustering framework with self-guiding and block diagonal representation, improving large-scale clustering efficiency and accuracy by reclassifying samples iteratively and utilizing Nyström approximation.

Contribution

It is the first to apply a restarting strategy to spectral clustering, reclassifying samples in each cycle and using Nyström approximation for efficient similarity matrix construction.

Findings

Outperforms state-of-the-art algorithms on benchmark datasets

Effective for large-scale clustering problems

Works well even with random initial guesses

Abstract

Spectral clustering is one of the most popular unsupervised machine learning methods. Constructing similarity matrix is crucial to this type of method. In most existing works, the similarity matrix is computed once for all or is updated alternatively. However, the former is difficult to reflect comprehensive relationships among data points, and the latter is time-consuming and is even infeasible for large-scale problems. In this work, we propose a restarted clustering framework with self-guiding and block diagonal representation. An advantage of the strategy is that some useful clustering information obtained from previous cycles could be preserved as much as possible. To the best of our knowledge, this is the first work that applies restarting strategy to spectral clustering. The key difference is that we reclassify the samples in each cycle of our method, while they are classified only once in existing methods. To further release the overhead, we introduce a block diagonal representation with Nystr\"{o}m approximation for constructing the similarity matrix. Theoretical results are established to show the rationality of inexact computations in spectral clustering. Comprehensive experiments are performed on some benchmark databases, which show the superiority of our proposed algorithms over many state-of-the-art algorithms for large-scale problems. Specifically, our framework has a potential boost for clustering algorithms and works well even using an initial guess chosen randomly.