Spatial point processes are useful mathematical models describing the arrangement of objects randomly placed in space. Such models are of particular interest in many scientific disciplines, including biology, ecology or material science. In practical applications, we observe a random number of points on some bounded region in a plane or space, and we call these points a point pattern.
Classification task, one of the fundamental problems in machine learning and also in statistics, aims to classify a new observation to one of the k possible classes. In the point pattern setting, its purpose is to label the incoming observed pattern with one of the k possible labels.
While analyzing point patterns, various summary characteristics such as pair correlation function or L-function are employed. They contain valuable information about the hidden structure of the investigated pattern. A dissimilarity measure, quantifying how similar or better dissimilar two point patterns are, can thus be built, using these functional characteristics. Once we have a dissimilarity measure, we can solve the classification task using, for example, the kernel regression method.
In other words, we propose to work with random functions computed over the point pattern data, rather than using point patterns themselves. Instead of classifying point patterns, the same task could be solved for functional data, using well-known methods from functional data analysis.