A “spike train distance” (or, equivalently, a “spike metric”) is a means for comparing two samples of stereotyped event sequences. While spike train distances can be applied to any kind of stereotyped event sequence, we focus here on their application to neuroscience, in which the event sequences represent the sequence of action potentials emitted by a neuron, or a set of neurons.
Spike train distances are “metrics”, namely, rules for assigning a notion of distance, or dis‐similarity, to elements in a topological space. Two considerations give this general framework a special flavor when applied to neural data. The first consideration is mathematical: the topology of event sequences combines a discrete component with a continuous component. The discrete component is that the number of events in a spike train must be an integer; the continuous component is that each of these events can occur across a continuum of times. The second consideration is biological: much is known about the physiology of neurons and neural circuits, and spike train distances are typically designed with the goal of capturing the biologically‐significant aspects of neuronal activity.
As detailed in this entry, two contrasting ideas concerning the biological meaning of a spike train serve as anchor points: (a), the firing events in a spike train might serve primarily as a means to represent an underlying firing rate, vs. (b) the times of these firing events might have individual significance, enabling neural computations to be based on coincident firing events across neurons and other aspects of fine temporal structure.