Physics – Data Analysis – Statistics and Probability
Scientific paper
2007-07-17
Physical Review E 76, 066207, 2007
Physics
Data Analysis, Statistics and Probability
Follow-up to arXiv:0706.3375. Journal submission 9 Jul 2007. Published 19 Dec 2007
Scientific paper
10.1103/PhysRevE.76.066207
Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors of R for cluster identification, analogous to several recent attempts at group identification using eigenvectors of the correlation matrix. All of these approaches assumed a one-to-one correspondence of dominant eigenvectors and clusters, which has however been shown to be wrong in important cases. We clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes, and derive an enhanced clustering method harnessing recent insights from the coarse-graining of finite-state Markov processes. We illustrate the operation of our method using a simulated system of coupled Lorenz oscillators, and we demonstrate its superior performance over the previous approach. Finally we investigate the question of robustness of the algorithm against small sample size, which is important with regard to field applications.
Allefeld Carsten
Bialonski Stephan
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