Archetypal Distribution

Abstract

Archetypal analysis is an unsupervised learning tool commonly used in exploratory data analysis dimensionality reduction interpretation and visualization. We extend this idea to find archetypal distributions given a set of probability distributions. This is useful for example when we report the uncertainty in a measurement alongside the measured value. We propose a principled approach to tackle this situation using partial membership model. We discuss the connection between the proposed approach and existing extensions of archetypal analysis namely probabilistic archetypal analysis kernel archetypal analysis interval archetypal analysis and statistical archetypal analysis and apply this approach to both synthetic and real data to investigate its properties and effectiveness.