METRIC-SPACE ANALYSIS OF SPIKE TRAINS - THEORY, ALGORITHMS AND APPLICATION

We present the mathematical basis of a new approach to the analysis of temporal coding. The foundation of the approach is the construction o f several families of novel distances (metrics) between neuronal impul se trains. In contrast to most previous approaches to the analysis of temporal coding, the present approach does not attempt to embed impuls e trains in st vector space, and does not assume a Euclidean notion of distance. Rather, the proposed metrics formalize physiologically base d hypotheses for those aspects of the firing pattern that might be sti mulus dependent, and make essential use of the point-process nature of neural discharges. We show that these families of metrics endow the s pace of impulse trains with related but inequivalent topological struc tures. We demonstrate how these metrics can be used to determine wheth er a set of observed responses has a stimulus-dependent temporal struc ture without a vector-space embedding. We show how multidimensional sc aling can be used to assess the similarity of these metrics to Euclide an distances. For two of these families of metrics (one based on spike times and one based on spike intervals), we present highly efficient computational algorithms for calculating the distances. We illustrate these ideas by application to artificial data sets and to recordings f rom auditory and visual cortex.