A Non-Parametric Bootstrap for Spectral Clustering

TL;DR

This paper introduces two novel algorithms that enhance spectral clustering by integrating spectral decomposition with a non-parametric bootstrap, improving convergence and avoiding sub-optimal solutions in finite mixture modeling.

Contribution

The paper proposes new algorithms combining spectral decomposition and bootstrap sampling to improve finite mixture model clustering, addressing EM algorithm limitations.

Findings

Algorithms are validated through simulations.

Methods demonstrate flexibility and computational efficiency.

Techniques show better convergence consistency than existing methods.

Abstract

Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. A common method for fitting finite mixture models is to employ spectral clustering, which can utilize the expectation-maximization (EM) algorithm. However, the EM algorithm falls victim to a number of issues, including convergence to sub-optimal solutions. We address this issue by developing two novel algorithms that incorporate the spectral decomposition of the data matrix and a non-parametric bootstrap sampling scheme. Simulations display the validity of our algorithms and demonstrate not only their flexibility, but also their computational efficiency and ability to avoid poor solutions when compared to other clustering algorithms for estimating finite mixture models. Our techniques are more consistent in their convergence when compared to other bootstrapped algorithms that fit finite mixture models.