A Non-Parametric Bootstrap for Spectral Clustering

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.