A dendrogram approach to the structure of spike trains
© Houghton; licensee BioMed Central Ltd. 2011
Published: 18 July 2011
A novel mathematical description for the temporal structure of spike trains is presented. This works by mapping the spike train to a dendrogram produced by hierarchical clustering. The branch-length structure of the dendrogram is equivalent to the distribution of inter-spike intervals, but morphological descriptions of the dendrogram can be used to quantify other aspects of the temporal structure of spike trains. In this way, it is shown that example sets of spike trains have more structure than is accounted for by the distribution of inter-spike intervals. The goal is to segregate the loose notion of “sparseness” into two different aspects of temporal structure, the distribution of inter-spike intervals and the morphology of the dendrogram constructed during clustering and to provide a tool for analyzing and comparing spike train properties.
This quantification is applied to an example spike-train data set described in  and made available on http://neurodatabase.org. The data consist of single cell recordings from the nucleus of the solitary tract in rat during presentation of taste stimuli. With a clear separation between the stimulus timescale and the temporal scale of spiking, these data are chosen to present a kind of worst-case scenario for the proposal. Nonetheless, when the real data is compared to artificial data produced by shuffling the inter-spike intervals, the Mann–Whitney U test shows that real data has a significantly higher value of the morphological parameter introduced here.
Thanks to Patricia Di Lorenzo , Jonathan Victor and http://neurodatabase.org for making the data analyzed here available; Science Foundation Ireland for grant 08/RFP/MTH1280 and the James S McDonnell Foundation for an Understanding Human Cognition Scholar award.
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