Clustering based on the archetypal analysis

Abstract

Archetypal analysis is a dimensionality reduction technique, which is based on finding a small number of representative elements, called archetypes. The observations are then approximated by convex combinations of the archetypes. The coefficients of the convex combinations can be therefore interpreted as probabilities of discrete random variables. The values of the variables identify the classes, represented by the archetypes, to which the observation belongs. Based on this interpretation, we propose to use the Hellinger distance between probability distributions to measure the distance between the observations in the dataset and to use it as an input to clustering. We apply this procedure to monthly data of zero-coupon yield curves in 2003-2022. We identify the archetypal yield curves and cluster the observed curves into six clusters. Since the observations are measured in time, the resulting clustering also gives a segmentation of the time period under consideration.