Supplementary Material: Hierarchical Decomposition
supplementary material for

General Strategy for Hierarchical Decomposition of Multivariate Time Series: Implications for Temporal Lobe Seizures

Annals of Biomedical Engineering 29, 1135-1149 (2001)

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Authors

 Division of Systems Neurology and Neuroscience
Department of Neurology and Neuroscience
Weill Cornell Medical College

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Abstract

We describe a novel method for the analysis of multivariate time series that exploits the dynamic relationships among the multiple signals. The approach resolves the multivariate time series into hierarchically dependent underlying sources, each driven by noise input and influencing subordinate sources in the hierarchy. Implementation of this hierarchical decomposition (HD) combines principal components analysis (PCA), autoregressive modeling, and a novel search strategy among orthogonal rotations. For model systems conforming to this hierarchical structure, HD accurately extracts the underlying sources, whereas PCA or ICA (independent components analysis) does not. The interdependencies of cortical, subcortical, and brainstem networks suggest application of HD to multivariate measures of brain activity. We show first that HD indeed resolves temporal lobe ictal electrocorticographic data into nearly hierarchical form. A previous analysis of these data identified characteristic nonlinearities in the PCA-derived temporal components that resembled those seen in absence (petit mal) seizure electroencephalographic traces. However, the components containing these characteristic nonlinearities accounted for only a small fraction of the power. Analysis of these data with HD reveals furthermore that components containing characteristic nonlinearities, though small, can be at the origin of the hierarchy. This finding supports the link between temporal lobe and absence epilepsy.

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Related links

Schiff, N.D., Labar, D.R., and Victor, J.D. (1999) Common dynamics in temporal lobe seizures and absence seizures. Neuroscience 91, 417-428.
Abstract and key figure

Schiff, N.D., Victor, J.D., Canel, A., and Labar, D.R. (1995) Characteristic nonlinearities of the 3/second ictal EEG identified by nonlinear autoregressive analysis. Biological Cybernetics 72, 519-526.
Abstract and key figure

Schiff, N.D., Victor, J.D., and Canel, A. (1995) Nonlinear autoregressive analysis of the 3/second ictal EEG: implications for underlying dynamics. Biological Cybernetics 72, 527-532.
Abstract

Victor, J.D., and Canel, A. (1992) A relation between the Akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG. Annals of Biomedical Engineering 20, 167-180.
Abstract

Background on nonlinear autoregressive analysis

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