INTRODUCTION TO ARCHETYPAL ANALYSIS OF SPATIOTEMPORAL DYNAMICS

A comparison is made between the principal component or Karhunen-Loeve (KL) decomposition of spatio-temporal data and a new procedure called archetypal analysis (Cutler and Breiman, 1994). Archetypes characteri ze the convex hull of the data set and the data set can be reconstruct ed in terms of these values. We show that archetypes may be more appro priate than KL when the data do not have elliptical distributions, and they are often well-suited to studying regimes in which the system sp ends a long time near a ''steady'' state, punctuated with quick excurs ions to outliers in the data set, which may represent intermittency. W e also introduce a variation of archetypal analysis that is designed t o track moving structures, such as traveling waves or solitons. By usi ng 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.