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Statistical analysis and inference on spike trains is one of the centraltopics in the neural coding. It is of great interest to understand theunderlying structure of given neural data. Based on the metric distancesbetween spike trains, recent investigations have introduced the notion of anaverage or prototype spike train to characterize the template pattern in theneural activity. However, as those metrics lack certain Euclidean properties,the defined averages are nonunique, and do not share the conventionalproperties of a mean. In this article, we propose a new framework to define themean spike train where we adopt a Euclidean-like metric from an $L^p$ family.We demonstrate that this new mean spike train properly represents the averagepattern in the conventional fashion, and can be effectively computed using atheoretically-proven convergent procedure. We compare this mean with otherspike train averages and demonstrate its superiority. Furthermore, we apply thenew framework in a recording from rodent geniculate ganglion, where backgroundfiring activity is a common issue for neural coding. We show that the proposedmean spike train can be utilized to remove the background noise and improvedecoding performance.

A new framework for Euclidean summary statistics in the neural spike train space