Extensions of Distance and Prototype Methods for Point Patterns

David Diez
Ph.D., 2010
Advisor: Rick Paik Schoenberg
Many applications involve datasets that may be considered repeated observations of a point process over identical (or similar) spaces. In this work, distance measure techniques and their application to point pattern prototypes were expanded and developed for realizations of collections of point processes. These new methods readily extend to multiple dimensions. A combination of distance and prototype approaches were used to analyze neuronal spike data of cats in different behavioral states and across animals, and results are compared to previous time series analyses that used averaged frequency histograms. An R package has also been constructed to make these developments more widely available to researchers and practitioners, and this package is described in detail.