A Spike Train Distance Robust to Firing Rate Changes Based on the Earth Mover's Distance

Neural spike train analysis methods are mainly used for understanding the temporal aspects of neural information processing. One approach is to measure the dissimilarity between the spike trains of a pair of neurons, often referred to as the spike train distance. The spike train distance has been often used to classify neuronal units with similar temporal patterns. Several methods to compute spike train distance have been developed so far. Intuitively, a desirable distance should be the shortest length between two objects. The Earth Mover's Distance (EMD) can compute spike train distance by measuring the shortest length between two spike trains via shifting a fraction of spikes from one spike train to another. The EMD could accurately measure spike timing differences, temporal similarity, and spikes time synchrony. It is also robust to firing rate changes. Victor and Purpura (1996) distance measures the minimum cost between two spike trains. Although it also measures the shortest path between spike trains, its output can vary with the time-scale parameter. In contrast, the EMD measures distance in a unique way by calculating the genuine shortest length between spike trains. The EMD also outperforms other existing spike train distance methods in measuring various aspects of the temporal characteristics of spike trains and in robustness to firing rate changes. The EMD can effectively measure the shortest length between spike trains without being considerably affected by the overall firing rate difference between them. Hence, it is suitable for pure temporal coding exclusively, which is a predominant premise underlying the present study.