The Second International Workshop on Mining Ubiquitous and Social Environments

Despite the growing ubiquity of sensor deployments and the advances in sensor data analysis technology, relatively little attention has been paid to the spatial non-stationarity of sensed data which is an intrinsic property of the geographically distributed data. In this paper we deal with non-stationarity of geographically distributed data for the task of regression. At this purpose, we extend the Geographically Weighted Regression (GWR) method which permits the exploration of the geographical differences in the linear effect of one or more predictor variables upon a response variable. The parameters of this linear regression model are locally determined for every point of the space by processing a sample of weighted neighboring observations. Although the use of locally linear regression has proved appealing in the area of sensor data analysis, it also poses some problems. The parameters of the surface are locally estimated for every space point, but the form of the GWR regression surface is globally defined over the whole sample space. Moreover, the GWR estimation is founded on the assumption that all predictor variables are equally relevant in the regression surface, without dealing with spatially localized phenomena of collinearity. Our proposal overcomes these limitations with a novel tree-based approach which is adapted to the aim of recovering the functional form of a regression model only at the local level. A stepwise approach is then employed to determine the local form of each regression model by selecting only the most promising predictors and providing a mechanism to estimate parameters of these predictors at every point of the local area. Experiments with several geographically distributed datasets confirm that the tree based construction of GWR models improves both the local estimation of parameters of GWR and the global estimation of parameters performed by classical model trees.