On distances between point patterns and their applications

Various classes of distance metrics between two point process realizations observed on a common metric space are outlined. Examples include spike-time distance and its variants, proposed by Victor and Purpura (1997), and this list is extended to include cluster-based distances and distances based on classical statistical summaries of point patterns, such as the K-function or LISA functions. Applications to the summary and description of collections Jorge Mateu Department of Mathematics, University Jaume I, E-12071 Castellon, Spain E-mail: [email protected] Frederic P Schoenberg Department of Statistics, UCLA, 8125 Math-Sciences, Los Angeles, CA 90095, USA E-mail: [email protected] David Diez Department of Statistics, UCLA, 8125 Math-Sciences, Los Angeles, CA 90095, USA E-mail: [email protected] 2 Jorge Mateu et al. of independent point process realizations via prototypes or multidimensional scaling are explored.