Abstract
Independent Component Analysis (ICA) is a recent and well known technique used to separate mixtures of signals. While in general the researchers put their attention on the type of signals and of mixing, we focus our attention on a quite general class of models which act as sources of the time series, the dynamical systems. In this paper we focus our attention on the general problem to understand the behaviour of ICA methods with respect to the time series deriving from a specific dynamical system, selecting large classes of them, and using ICA to make separation. This study gives some interesting results that are very useful both to highlight some properties related to dynamical systems and to clarify some general aspects of ICA, by using both synthetic and real data.
From one hand we study the features of the linear (simple and coupled) and non-linear (single and coupled) dynamical systems, stochastic resonances, chaotic and real dynamical systems. We have to stress that we obtain information about the separation of these systems and substantially how from the entropy of the complete system we can obtain the entropies of the single dynamical systems (so that we also could obtain a more realistic analogic circuit).
On the other hand these results show the high capability of the ICA method to recognize the dynamical systems independently from their complexity and in the case of stochastic series ICA perfectly recognizes the different dynamical systems also where the Fourier Transform is irresolute.
We also note that in the case of real dynamical systems we showed that ICA permits to recognize the information connected to the sources and to associate to it a phenomenological dynamical system that reproduce it (i.e. Organ Pipe, Stromboli Volcano, Aerosol Index).
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Ciaramella, A., Lauro, E., Martino, S. et al. ICA based identification of dynamical systems generating synthetic and real world time series. Soft Comput 10, 587–606 (2006). https://doi.org/10.1007/s00500-005-0515-7
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DOI: https://doi.org/10.1007/s00500-005-0515-7