Archetypal Analysis for Nominal Observations

Archetypal analysis is a popular exploratory tool that explains a set of observations as compositions of few `pure' patterns. The standard formulation of archetypal analysis addresses this problem for real valued observations by finding the approximate convex hull. Recently, a probabilistic formulation has been suggested which extends this framework to other observation types such as binary and count. In this article we further extend this framework to address the general case of nominal observations which includes, for example, multiple-option questionnaires. We view archetypal analysis in a generative framework: this allows explicit control over choosing a suitable number of archetypes by assigning appropriate prior information, and finding efficient update rules using variational Bayes'. We demonstrate the efficacy of this approach extensively on simulated data, and three real world examples: Austrian guest survey dataset, German credit dataset, and SUN attribute image dataset.