Supervised Classification via Neural Networks for Replicated Point Patterns

Abstract

AbstractA spatial point pattern is a collection of points observed in a bounded region of $${\bf{\mathbb{R}}}^d$$, $$d \ge 2$$. Individual points represent, e.g., observed locations of cell nuclei in a tissue (d = 2) or centers of undesirable air bubbles in industrial materials (d = 3). The main goal of this paper is to show the possibility of solving the supervised classification task for point patterns via neural networks with general input space. To predict the class membership for a newly observed pattern, we compute an empirical estimate of a selected functional characteristic (e.g., the pair correlation function). Then, we consider this estimated function to be a functional variable that enters the input layer of the network. A short simulation example illustrates the performance of the proposed classifier in the situation where the observed patterns are generated from two models with different spatial interactions. In addition, the proposed classifier is compared with convolutional neural networks (with point patterns represented by binary images) and kernel regression. Kernel regression classifiers for point patterns have been studied in our previous work, and we consider them a benchmark in this setting.