Archetypal analysis of spatio-temporal dynamics. (English) Zbl 0900.76189

Summary: A comparison is made between the principal component or Karhunen-Loève decomposition (KL) of two sets of spatio-temporal data (one numerical, the other experimental) and a new procedure called archetypal analysis. Archetypes characterize the convex hull of the data set and the data set can be reconstructed in terms of these values. Archetypes may be more appropriate than KL when the data do not have elliptical distributions, and 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. Other advantages and disadvantages of each method are discussed.


76F99 Turbulence
37N99 Applications of dynamical systems


Full Text: DOI


[1] Aubry, N.; Holmes, P.; Lumley, J.L.; Stone, E., The dynamics of coherent structures in the wall region of a turbulent boundary layer, J. fluid mech., 192, 115, (1988) · Zbl 0643.76066
[2] Kirby, M.; Armbruster, D., Reconstructing phase-space from PDE simulations, Zamp, 43, 999, (1992) · Zbl 0764.35008
[3] Cutler, A.; Breiman, L., Archetypal analysis, Technometrics, 36, 338, (1994) · Zbl 0804.62002
[4] Berkooz, G.; Holmes, P.; Lumley, J.L., The proper orthogonal decomposition in the analysis of turbulent flow, Ann. rev. fluid mech., 25, 115, (1993)
[5] Sirovich, L., Turbulence and the dynamics of coherent structures, parts I-III, Quart. appl. math., Vol. XLV, 3, 561, (1987) · Zbl 0676.76047
[6] Lumley, J.L., The structure of inhomogeneous turbulent flows, (), 166
[7] Armbruster, D.; Heiland, R.; Kostelich, E., KLTOOL: a tool to analyze spatio-temporal complexity, Chaos, 4, 2, 421, (1994)
[8] Kirby, M.; Sirovich, L., Application of the Karhunen-Loève procedure for the characterization of human faces, IEEE trans. PAMI, 12, 103, (1990)
[9] Gorman, M.; el-Hamdi, M.; Robbins, K.A., Spatio-temporal chaotic dynamics of pre-mixed flames, (), 403
[10] M. el-Hamdi, M. Gorman and K.A. Robbins, Deterministic Chaos in Laminar premixed flames: experimental classification of chaotic dynamics, Combust. Sci. Technol., to appear.
[11] Sivashinsky, G.I., Nonlinear analysis of hydrodynamic stability of laminar flames — derivation of basic equations, Acta astr., 4, 1177, (1977) · Zbl 0427.76047
[12] Kevrikidis, I.G.; Nicolaenko, B.; Scovel, C., Back in the saddle again: a computer assisted study of the Kuramoto-Sivashinsky equation, SIAM J. appl. math., 50, 760, (1990) · Zbl 0722.35011
[13] Hyman, J.M.; Nicolaenko, B.; Zaleski, S., Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces, Physica D, 23, 265, (1986) · Zbl 0621.76065
[14] Watanabe, S., The Karhunen Loève expansion and factor analysis, theoretical remarks and applications, ()
[15] Armbruster, D.; Guckenheimer, J.; Holmes, P., Kuramoto-Sivashinsky dynamics on the center-unstable manifold, SIAM J. appl. math., 49, 676, (1989) · Zbl 0687.34036
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