Probabilistic Archetypal Analysis

Archetypal analysis (AA) represents observations as composition of pure patterns, i.e., archetypes, or equivalently convex combinations of extreme values (Cutler and Breiman, 1994). Although AA bears resemblance with many well established prototypical analysis tools, such as principal component analysis (PCA, Mohamed et al, 2009), nonnegative matrix factorization (NMF, F evotte and Idier, 2011), probabilistic latent semantic analysis (Hofmann, 2013), andk -means (Steinley, 2006); AA is arguably unique, both conceptually and computationally . Conceptually, AA imitates the human tendency of representing a group of objects by its extreme elements (Davis and Love, 2010): this makes AA an interesting exploratory tool for applied scientists (e.g., Eugster, 2012; Seiler and Wohlrabe, 2013). Computationally, AA is data-driven, and requires the factors to be probability vectors: these make AA a computationally demanding tool, yet brings better interpretability . The concept of AA was originally formulated by Cutler and Breiman (1994).