Introduction to archetypal analysis of spatio-temporal dynamics

A comparison is made between the principal component or Karhunen-Loève (KL) decomposition of spatio-temporal data and a new procedure called archetypal analysis (Cutler and Breiman, 1994). Archetypes characterize the convex hull of the data set and the data set can be reconstructed in terms of these values. We show that archetypes may be more appropriate than KL when the data do not have elliptical distributions, and they are often well-suited to studying regimes in which the system spends a long time near a "steady" state, punctuated with quick excursions to outliers in the data set, which may represent intermittency. We also introduce a variation of archetypal analysis that is designed to track moving structures, such as traveling waves or solitons. By using this method the traveling part of the motion is separated from the stationary (or semi-stationary) pattern. Advantages and disadvantages of each method are discussed.