A fundamental problem in studying population codes is how to compare population activity patterns. Population activity patterns are not just spatial, but spatiotemporal. Thus, a principled approach to the problem of the comparison of population activity patterns begins with the comparison of the temporal activity patterns of a single neuron, and then, to the extension of the scope of this comparison to populations spread across space.
Since 1926 when Adrian and Zotterman reported 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 the temporal features of spike trains. With an experimental data set 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 capture the differences between the stimuli that elicit them. Studying the properties of these metrics illuminates the temporal coding properties of spike trains.
The approach can be extended to multineuronal activity patterns, with the anticipation that it will prove similarly useful in understanding aspects of population coding. The multineuronal metric approach forms a conceptual bridge between metrics applicable to time series and metrics applicable to spatial activity patterns.
Finally, since the metrics presented here are unlikely to exhaust the possible ways to usefully quantify distances between spike trains, the chapter concludes with some comments on how the properties of neuronal computation could be used to derive other spike train metrics.