Choquet Capacity networks for random point process classification

Mehran Mohammadi (1) , Santiago Velasco-Forero (1) , François Willot (2, 1) , Mateus Sangalli (1) , Jesus Angulo (1)

1 CMM - Centre de Morphologie Mathématique
2 CDM - Centre des Matériaux

In this study, we revisit the Choquet capacity in the framework of convolutional neural networks, in (max, +)-algebra. By incorporating a discrete and learnable Choquet capacity model, we enhance the ability to represent the spatial arrangement and density variations in random point processes of convolutional neural networks. To validate the effectiveness of our approach, numerical experiments are conducted on synthetic datasets simulating diverse spatial point patterns of the Neyman-Scott process. When compared to classical convolutional neural networks, the proposed approach exhibits comparable or improved performances in terms of classification. Superior results are also observed in regression problems involving the Neyman-Scott parameter that monitors the point patterns spatial dispersion.

Mots clés: Choquet capacity; Max-Plus Algebra; Deep Learning

Domaines: Informatique [cs]

Mehran Mohammadi, Santiago Velasco-Forero, François Willot, Mateus Sangalli, Jesus Angulo. Choquet Capacity networks for random point process classification. Proceedings of the 14th International Symposium on Continuum Models and Discrete Systems, Jun 2023, Paris, France. ⟨hal-04250560v1⟩