Biarchetype analysis: simultaneous learning of observations and features based on extremes

A new exploratory technique called biarchetype analysis is defined. We extend archetype analysis to find the archetypes of both observations and features simultaneously. The idea of this new unsupervised machine learning tool is to represent observations and features by instances of pure types (biarchetypes) that can be easily interpreted as they are mixtures of observations and features. Furthermore, the observations and features are expressed as mixtures of the biarchetypes, which also helps understand the structure of the data. We propose an algorithm to solve biarchetype analysis. We show that biarchetype analysis offers advantages over biclustering, especially in terms of interpretability. This is because byarchetypes are extreme instances as opposed to the centroids returned by biclustering, which favors human understanding. Biarchetype analysis is applied to several machine learning problems to illustrate its usefulness.