A new class of metrics for spike trains

The distance between a pair of spike trains, quantifying the differences between them, can be measured using various metrics. Here we introduce a new class of spike train metrics, inspired by the Pompeiu-Hausdorff distance. Some of our new metrics (the max-metric and the modulus-metric) are sensitive to differences in the precise timings of spikes in the considered spike trains that cannot be discriminated by existing metrics like the van Rossum distance or the Victor & Purpura distance. The modulus-metric does not depend on any parameters and can be computed using a fast algorithm, in a time that depends linearly on the number of spikes in the two spike trains. We also introduce localized versions of the new metrics, which could have the biologically-relevant interpretation of measuring the differences between spike trains as they are perceived at a particular moment in time by a neuron receiving these spike trains.