Inverse Distance Weighted Random Forests: Modeling Unevenly Distributed Non-Stationary Geographic Data

Recent years saw explosive growth of Human Geography Data, in which spatial non-stationarity is often observed, i.e., relationships between features depend on the location. For these datasets, a single global model cannot accurately describe the relationships among features that vary across space. To address this problem, a viable solution- that has been adopted by many studies-is to create multiple local models instead of a global one, with each local model representing a subregion of the space. However, the challenge with this approach is that the local models are only fitted to nearby observations. For sparsely sampled regions, the data could be too few to generate any high-quality model. This is especially true for Human Geography datasets, as human activities tend to cluster at a few locations. In this paper, we present a modeling method that addresses this problem by letting local models operate within relatively large subregions, where overlapping is allowed. Results from all local models are then fused using an inverse distance weighted approach, to minimize the impact brought by overlapping. Experiments showed that this method handles non-stationary geographic data very Well, even When they are unevenly distributed.