  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, and
compare them with existing metrics. Some of our new metrics (the modulus-metric
and the max-metric) have characteristics that are qualitatively different than
those of classical metrics like the van Rossum distance or the Victor & Purpura
distance. The modulus-metric and the max-metric are particularly suitable for
measuring distances between spike trains where information is encoded in
bursts, but the number and the timing of spikes inside a burst does not carry
information. 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.
