## SAIMeR: Self-adapted method for the identification of metastable states in real-world time series

Please always quote using this URN: urn:nbn:de:0297-zib-50130
• In the framework of time series analysis with recurrence networks, we introduce SAIMeR, a heuristic self-adapted method that determines the elusive recurrence threshold and identifies metastable states in complex time series. To identify metastable states as well as the transitions between them, we use graph theory concepts and a fuzzy partitioning clustering algorithm. We illustrate SAIMeR by applying it to three real-world time series and show that it is able to identify metastable states in real-world data with noise and missing data points. Finally, we suggest a way to choose the embedding parameters used to construct the state space in which this method is performed, based on the analysis of how the values of these parameters affect two recurrence quantitative measurements: recurrence rate and entropy.

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Author: I. Vega, Christof Schütte, Tim Conrad ZIB-Report application in statistical physics; metastability; non-linear dynamics; recurrence quantification analysis; threshold; time series analysis 37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Mxx Approximation methods and numerical treatment of dynamical systems [See also 65Pxx] / 37M10 Time series analysis 46-XX FUNCTIONAL ANALYSIS (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx) / 46Nxx Miscellaneous applications of functional analysis [See also 47Nxx] / 46N55 Applications in statistical physics 62-XX STATISTICS / 62Hxx Multivariate analysis [See also 60Exx] / 62H30 Classification and discrimination; cluster analysis [See also 68T10] 2014/05/16 ZIB-Report (14-16) 1438-0064

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