Exploring archetypal dynamics of pattern formation in cellular flames

The application of archetypal analysis to high-dimensional data arising from video-taped images is presented. Included in the analysis are intermittent regimes which have not been analyzed previously by other statistical methods such as principal component analysis (PCA). A hybrid PCA/archetypes technique has been developed to overcome the difficulties of applying archetypes to data sets with points living in a space of dimension higher than about 500. The advantages of the method lie in the creation of patterns typical of the set as a whole, and an expression of the dynamics in terms of these patterns. Archetypes are particularly useful in identifying intermittent regimes, where low energy events that might be missed by a severe principal component truncation are none-the-less crucial to understanding the dynamics. They are part of a suite of data analysis techniques that can be used on dynamic data sets (such as FFT, PCA and other spectral decompositions). This hybrid method extends the application of archetypes to spatio-temporal dynamics in two-dimensional patterns.