On Perfect Clustering for Gaussian Processes

Abstract

In this paper, we propose a data based transformation for infinite-dimensional Gaussian processes and derive its limit theorem. For a clustering problem using mixture models, an appropriate modification of this transformation asymptotically leads to perfect separation of the populations under rather general conditions, except the scenario in which differences between clusters depend only on the locations; in which case our procedure is useless. Theoretical properties related to label consistency are studied for the k-means clustering algorithm when used on this transformed data. Good empirical performance of the proposed methodology is demonstrated using simulated as well as benchmark data sets, when compared with some popular parametric and nonparametric methods for such functional data.