On Perfect Classification and Clustering for Gaussian Processes

Motivated by singularity of a certain class of Gaussian measures, we propose a data based transformation for infinite-dimensional data. For a classification problem, an appropriate joint transformation induces complete separation among the associated Gaussian processes. The misclassification probability of a simple classifier when applied on this transformed data asymptotically converges to zero. In a clustering problem, an appropriate modification of this transformation asymptotically leads to perfect separation of the populations. Theoretical properties are studied for the usual $k$-means clustering method when used on the transformed data. Good performance of the proposed methodology is demonstrated using simulated as well as benchmark data sets, when compared with some popular parametric and nonparametric classifiers for such functional data.