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Analysis of spectral clustering algorithms for linear and nonlinear time series

In this work a modified spectral clustering algorithm for time-series data is introduced. The presented modification is to replace the distance measure for static data with an appropriate one for time series. The performed analysis considers several distance measures for time series, and it includes the use of different similarity graphs and graph Laplacians. We consider the discrimination of time-series generated using different linear ARMA models, and we also investigated the clustering of nonlinear time series generated using autoregressive conditional heteroskedasticity (ARCH) models. The Hubert-Arabie adjusted Rand's index is used as an external criterion for evaluating the partitions obtained with modified spectral clustering and various linkage algorithms. Guidelines are discussed, in particular the use of cepstral coefficients proves to be efficient both for linear and nonlinear data.