Archetypal analysis for machine learning and data mining 
Morten Mørup, Lars K. Hansen

Abstract  Archetypal analysis AA) proposed by Cutler and Breiman (1994) estimates the principal convex hull PCH) of a data set. As such AA favors features that constitute representative corners of the data, i.e. distinct aspects or archetypes. We currently show that AA enjoys the interpretability of clustering  without being limited to hard assignment and the uniqueness of SVD  without being limited to orthogonal representations. In order to do large scale AA, we derive an efficient algorithm based on projected gradient as well as an initialization procedure we denote FURTHESTSUM that is inspired by the FURTHESTFIRST approach widely used for Kmeans (Hochbaum and Shmoys, 1985). We generalize the AA procedure to KERNELAA in order to extract the principal convex hull in potential infinite Hilbert spaces and derive a relaxation of AA when the archetypes cannot be represented as convex combinations of the observed data. We further demonstrate that the AA model is relevant for feature extraction and dimensionality reduction for a large variety of machine learning problems taken from computer vision, neuroimaging, chemistry, text mining and collaborative filtering leading to highly interpretable representations of the dynamics in the data. Matlab code for the derived algorithms is available for download from www.mortenmorup.dk. 
Keywords  Archetypal Analysis 
Type  Journal paper [With referee] 
Journal  Neurocomputing 
Year  2012 pp. 5463 
ISBN / ISSN  09252312 
Publication link  http://www.sciencedirect.com/science/article/pii/S0925231211006060 
BibTeX data  [bibtex] 
IMM Group(s)  Intelligent Signal Processing 