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

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 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.

Utility of Independent Component Analysis for Interpretation of Intracranial EEG

“…Different FIRDA trains appearing on different combinations of channels through the course of the 20-min recording will necessarily be accounted for by more than one ICA component signal. Else, the source generators of FIRDA may have been hierarchical rather than independent, as is suggested by a novel analysis of ictal epilepsy data (Repucci et al, 2001). Alternatively, the FIRDA signal could be a traveling wave that extends beyond the cm 2 scale over which ICA spatial stationarity is assumed with this methodology.…”

Hemodynamics in Prefrontal and Temporal Cortex during Attentional Control Task

“…This study used the hierarchical decomposition analysis, HDA [8], which consists of the principal components analysis, PCA, and multivariable autoregressive (MAR) modelling technique. HDA reconstructs the estimated parameters into a hierarchical structure or an upper triangular form.…”

Change of Hemodynamics in Prefrontal Cortex Caused by Repeating the Attentional Control Task

“…The method applied in this paper is hierarchical components analysis, HDA [7], which consists of the principal components analysis and multivariable autoregressive modeling technique. If the data is processed appropriately by HDA, the estimated parameters are reconstructed into hierarchical structure, which means upper triangular from.…”