Neural networks with functional inputs for multi-class supervised classification of replicated point patterns

A spatial point pattern is a collection of points observed in a bounded region of the Euclidean plane or space. With the dynamic development of modern imaging methods, large datasets of point patterns are available representing for example sub-cellular location patterns for human proteins or large forest populations. The main goal of this paper is to show the possibility of solving the supervised multi-class classification task for this particular type of complex data via functional neural networks. To predict the class membership for a newly observed point pattern, we compute an empirical estimate of a selected functional characteristic. Then, we consider such estimated function to be a functional variable entering the network. In a simulation study, we show that the neural network approach outperforms the kernel regression classifier that we consider a benchmark method in the point pattern setting. We also analyse a real dataset of point patterns of intramembranous particles and illustrate the practical applicability of the proposed method.