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A method for decomposing multivariate time series into a causal hierarchy within specific frequency bands

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Abstract

We propose a method - Frequency extracted hierarchical decomposition (FEHD) - for studying multivariate time series that identifies linear combinations of its components that possess a causally hierarchical structure - the method orders the components so that those at the “top” of the hierarchy drive those below. The method shares many of the features of the “hierarchical decomposition” method of Repucci et al. (Annals of Biomedical Engineering, 29, 1135–1149, 2001) but makes a crucial advance - the proposed method is capable of determining this causal hierarchy over arbitrarily specified frequency bands. Additionally, a novel minimization strategy is used to generate the decomposition resulting in an increase in stability, reliability, and an improvement in the sensitivity to model parameters. We demonstrate the utility of the method by applying it to both artificial time series constructed to have specific causal graphs, and to the EEG of healthy volunteers and patient subjects who are recovering from a severe brain injury.

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Acknowledgments

We would like to acknowledge the NIH-NINDS RO1 HD91251, the James S. McDonnell Foundation and the Jerold B. Katz Foundation for their support. We would also like to thank Jonathan Victor for many helpful conversations and suggestions, and Esteban Fridman with assistance with displays of structural and metabolic brain imaging data. Finally, we would like to thank Mary Conte for reading the manuscript and offering an enormous amount of helpful feedback.

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  1. Weill Cornell Medical College, New York, NY, 10065, USA

    Jonathan D. Drover & Nicholas D. Schiff

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  1. Jonathan D. Drover
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  2. Nicholas D. Schiff
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Correspondence to Jonathan D. Drover.

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Action Editor: Abraham Zvi Snyder

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Drover, J.D., Schiff, N.D. A method for decomposing multivariate time series into a causal hierarchy within specific frequency bands. J Comput Neurosci 45, 59–82 (2018). https://doi.org/10.1007/s10827-018-0691-y

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  • DOI: https://doi.org/10.1007/s10827-018-0691-y

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