Prototype Construction for Clustering of Point Processes based on Imprecise Synchrony

We consider the task to cluster realizations of point processes, that is, lists of points in time. Our guiding principle is that two such lists are the more similar, the more (approximately) synchronous points they contain. This task occurs in the analysis of parallel spike trains in neurobiology, where it arises from the desire to detect assemblies of neurons, which are characterized by the synchronous spiking activity they exhibit. While earlier approaches along similar lines employed mainly hierarchical agglomerative clustering, based on distance measures for spike trains, we try to make prototype-based clustering approaches (like (fuzzy-)c-means clustering) applicable by proposing a method to construct cluster prototypes. For this we draw on an idea that is inspired by mountain clustering. In addition, we adapt a method that was originally developed for outlier detection in order to actually single out relevant groups of related realizations of point processes in front of a background of noise, and thus to identify neuron assemblies in parallel spike train data.