Copula Archetypal Analysis

We present an extension of classical archetypal analysis (AA). It is motivated by the observation that classical AA is not invariant against strictly monotone increasing transformations. Establishing such an invariance is desirable since it makes AA independent of the chosen measure: representing a data set in meters or log(meters) should lead to approximately the same archetypes. The desired invariance is achieved by introducing a semi-parametric Gaussian copula. This ensures the desired invariance and makes AA more robust against outliers and missing values. Furthermore, our framework can deal with mixed discrete/continuous data, which certainly is the most widely encountered type of data in real world applications. Since the proposed extension is presented in form of a preprocessing step, updating existing classical AA models is especially effortless.