On the Computation and Application of Prototype Point Patterns

This work addresses computational problems related to the implementation of Victor and Purpura's spike-time distance metric for temporal point process data. Three computational algorithms are presented that facilitate the calculation of spike-time distance. In addition, recommendations for penalty parameters are provided, and several properties and extensions of the spike-time metric, and of point pattern distance metrics more generally, are discussed. Applications include the formation of prototype point patterns that can be used for describing a typical point pattern in a collection of point patterns, and various clustering algorithms that can be modified for application to point process data through the use of spike-time distance and prototype patterns. Extensions of these techniques to multidimensional point patterns are also addressed.