General strategy for hierarchical decomposition of multivariate time series: implications for temporal lobe seizures.

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 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.