Spatial Point Processes and Clustering Tendency in Exploratory Data Analysis

Abstract

Discriminating among random, clustered and regular arrangements of multidimensional patterns (data) is an important problem in exploratory data analysis, statistical pattern recognition and image processing. Clustering methods have been used extensively for this purpose. However, clustering algorithms will locate and specify clusters in data even non are present. It is therefore appropriate to measure the clustering tendency or randomness of a pattern set before subjecting it to a clustering algorithm. Spatial point process models are alternatives to structures obtained from cluster analysis and are a means for objectifying observed data. We survey the work that has been done in developing measures of clustering tendency, with special attention to distance-based methods. We review several models for spatial point processes with an eye towards identifying potential research problems in applying such models to clustering tendency. The successes and failures of these methods are discussed as well as suggestions and directions for future study.