Archetypal analysis. (English) Zbl 0804.62002

Cutler, Adele; Breiman, Leo

Technometrics 36, No. 4, 338-347 (1994).

Summary: Archetypal analysis represents each individual in a data set as a mixture of individuals of pure type or archetypes. The archetypes themselves are restricted to being mixtures of the individuals in the data set. Archetypes are selected by minimizing the squared error in representing each individual as a mixture of archetypes. The usefulness of archetypal analysis is illustrated on several data sets. Computing the archetypes is a nonlinear least squares problem, which is solved using an alternating minimizing algorithm.

MSC:

62-07	Data analysis (statistics) (MSC2010)
62H25	Factor analysis and principal components; correspondence analysis
62A09	Graphical methods in statistics
90C25	Convex programming

Keywords:

convex hull; nonlinear optimization; principal components; archetypes; squared error; mixture of archetypes; nonlinear least squares