Chapter 8: Measuring Representational Distances: The Spike-Train Metrics Approach

Conor Houghton and Jonathan D. Victor
Department of Neurology and Neuroscience, Cornell University

Since 1926 when Adrian and Zotterman reported evidence that the firing rates of somatosensory receptor cells depend on stimulus strength, it has become apparent that a significant amount of the information propagating through the sensory pathways is encoded in neuronal firing rates. However, while it is easy to define the average firing rate for a cell over the lengthy presentation of a time-invariant stimulus, it is more difficult to quantify how temporal features of spike trains relate to the stimulus. With a real, experimental, data set, for example, extracting a time-dependent rate function is model dependent since calculating it requires a choice of a binning or smoothing procedure.

The spike train metric approach is a framework that distills and addresses these problems. One family of metrics are "edit distances" that quantify the changes required to match one spike train to another; another family of metrics first maps spike trains into vector spaces of functions. Both these metrics appear successful in that the distances calculated between spike trains seems to reflect the differences in the information the spike trains contain. Studying the properties of these metrics illuminates the temporal coding properties of spike trains. The approach can be extended to multi-neuronal activity patterns, with the anticipation that it will prove similarly useful in understanding aspects of population coding.

Key words: Spike trains, metrics, neural coding, sensory pathway.