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The Merriam-Webster Online Dictionary defines an archetype as the original pattern or model of which all things of the same type are representations or copies. Then, the aim of the archetypal analysis is to find the "pure types", the archetypes, within a set defined in a specific context. The concept of archetypes is used in many different areas, the set can be defined in terms of literature, philosophy, psychology and also statistics. Here, the concrete problem is to find a few, not necessaily observed, points (archetypes) in a set of multivariate observations such that all the data can be well represented as convex mixtures of the archetypes.

Probabilistic formulation

Archetypal analysis for nominal observations
Sohan Seth and Manuel J. A. Eugster. IEEE Transactions on Pattern Analysis and Machine Intelligence, to appear.
[ URL | Code ]

Probabilistic archetypal analysis
Sohan Seth and Manuel J. A. Eugster. Machine Learning, to appear.
[ URL | Preprint | Code ]

Original algorithm and extensions

Weighted and robust archetypal analysis
Manuel J. A. Eugster and Friedrich Leisch. Computational Statistics and Data Analysis, 55(3):1215-1225, 2011.
[ PDF | Preprint | R package ]

From Spider-man to Hero -- Archetypal analysis in R
Manuel J. A. Eugster and Friedrich Leisch. Journal of Statistical Software, 30(8):1-23, 2009.
[ PDF | R package ]