Point Process Prototypes, and Other Applications of Point Pattern Distance Metrics

Katherine Eleanor Tranbarger
Ph.D., 2005
Advisor: Frederic Paik Schoenberg
This work discusses a series of non-parametric alternatives for analyzing point pattern data. A recent paper by Victor and Purpura proposed three distance metrics for use in neuron spike-train analysis. Here, computational problems related to implementation of Victor and Purpura spike time distance metric for point processes are discussed and three algorithms for calculation are examined. Introduced in this work is the construct of a prototype pattern, useful for describing what a typical pattern is for a given dataset. Application extensions presented include clustering applications, identification problems, and model evaluation. Further, ways in which spike-time distance can be applied to points in more than one dimension are discussed. As an example of how these methods can be used, earthquake aftershock behavior is investigated to determine what a typical sequence of aftershocks is for a 7.5-8.0 mainshock quake. An additional example explores ways computer users can be identified based on their user activity.