Clustering and Classification through Normalizing Flows in Feature Space

J. P. Agnelli, M. Cadeiras, Esteban G. Tabak, Cristina Vilma Turner, Eric Vanden-Eijnden

Abstract: A unified variational methodology is developed for classification and clustering problems and is tested in the classification of tumors from gene expression data. It is based on fluid-like flows in feature space that cluster a set of observations by transforming them into likely samples from p isotropic Gaussians, where p is the number of classes sought. The methodology blurs the distinction between training and testing populations through the soft assignment of both to classes. The observations act as Lagrangian markers for the flows, comparatively active or passive depending on the current strength of the assignment to the corresponding class.