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Title: Using neural clustering in spatial and non spatial models Authors:  Cecile Hardouin - University Paris Nanterre (France)
Jean-Charles Lamirel - LORIA (France) [presenting]
Abstract: The aim of spatial econometrics is to analyze and/or predict the relationship between one dependent variable Y with other variables, taking into account spatial dependence. In the framework of Spatial Autoregressive Models (SAR), $Y$ is linked to covariates and to the values of its own adjacent values via a neighbourhood matrix $W=(w_{ij})$. Weights $w_{ij}$ are usually linked to the geographical distances between the locations where the data were collected from. Considering that similar values of the dependent variable can result from geographical proximity, but also from the similarity of the variables, we propose weights based on neural clustering. Kohonen SOM or Growing Neural Gas algorithms provide distances between nodes that we use directly to define weights $w_{ij}$. In the general spatial model setting, we need two neighbourhood matrices and the difficulty rising then is to find a second matrix; this issue is simply solved by using neural distances. The results we obtained are at least as well as the ones obtained from the geographical distances-based design. This approach can be generalized to non-geographical data; SAR models with neural distances design can be used to model any data set, non necessarily geographically referenced. We illustrate our approach with the study of real data sets.