Neural Networks for Spatial Models

Cécile Hardouin (1) , Jean-Charles Lamirel (2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 SYNALP - Natural Language Processing : representations, inference and semantics

The aim of spatial econometrics is to analyze and/or predict the relationship between one dependent variable Y with other variables, building a model that takes into account the spatial dependence. Usual spatial econometric models are based on a neighbourhood matrix whose elements are linked to geographical distances. We propose to use distances between prototypes resulting from a neural classification instead. The results are at least as well as the ones obtained from the geographical distances based design. In some cases, we need two neighbourhood matrices and the difficulty rising then is to find a second matrix; then this issue is simply solved by using one matrix based on geographical distances and the other based on neural distances. Finally, the use of neural distances opens the door to use spatial econometrics methods for the analysis and the modelling of any data sets, non necessary geographically referenced. We illustrate our approach with two studies of real datasets.

Mots clés: SOM; Spatial statistics; Clustering; Growing Neural Networks

Domaines: Statistiques [math.ST]

Cécile Hardouin, Jean-Charles Lamirel. Neural Networks for Spatial Models. Advances in Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization, 533, Springer International Publishing, pp.21-30, 2022, Lecture Notes in Networks and Systems, 978-3-031-15443-0. ⟨10.1007/978-3-031-15444-7_3⟩. ⟨hal-03857345⟩