Choquet Capacity networks for random point process classification

Mehran Mohammadi (1) , Santiago Velasco-Forero (2) , François Willot (3, 2, 1) , Mateus Sangalli (1) , Thomas Walter (1, 4) , Jesus Angulo (1)

1 CBIO - Centre de Bioinformatique
2 CMM - Centre de Morphologie Mathématique
3 CDM - Centre des Matériaux
4 Cancer et génome: Bioinformatique, biostatistiques et épidémiologie d'un système complexe

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.

Keywords: Choquet capacity; Max-Plus Algebra; Deep Learning

Domains: Computer Science [cs]

Mehran Mohammadi, Santiago Velasco-Forero, François Willot, Mateus Sangalli, Thomas Walter, et al.. Choquet Capacity networks for random point process classification. 2024. ⟨hal-04250560v2⟩