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Adaptive interpolation methods for spatiotemporal data
Interpolation methods are needed for spatiotemporal data sets to fill in missing data and predict the future. Spatiotemporal interpolation is more challenging than pure spatial or temporal interpolations, and currently there are only a few known spatiotemporal interpolation methods. We analyze spatiotemporal data sets by introducing spatial and temporal relationship strength measures for them. Based on the relative strengths of the spatial and the temporal relationships in the data sets, we classify them as being spatial-dominated or temporal-dominated. This analysis of spatiotemporal data sets allows us to introduce a class of adaptive spatiotemporal interpolation methods. An adaptive spatiotemporal interpolation method combines a spatial interpolation method with a temporal interpolation method in such a way that the degree of reliance on the two components is driven by the measured spatial and temporal relationship strengths. Hence a spatial-dominated spatiotemporal data set would be interpolated more like a spatial data set. Similarly, a temporal-dominated spatiotemporal data set would be interpolated more like a temporal data set. Adaptive spatiotemporal interpolation reduces in a flexible way the spatiotemporal interpolation problem to the problem of pure spatial and temporal interpolation. Adaptive reduction works in principle for both point-based and region-based spatiotemporal data sets. Although there are many point-based spatial interpolation methods, there is a lack of region-based spatial interpolation methods. As many spatiotemporal data sets are region-based, as a practical matter, we also propose two region-based variations on the well-known inverse distance weighting interpolation method. The first variation assigns uniform weights between neighbors and the second variation assigns weights proportional to the centroid distances. We also propose a new temporal interpolation method, called the exponential decay temporal interpolation method. Finally, we test the adaptive spatiotemporal interpolation methods on a spatial-dominated climate data set and on a temporal-dominated election data set.
Gao, Jun, "Adaptive interpolation methods for spatiotemporal data" (2006). ETD collection for University of Nebraska - Lincoln. AAI3237596.