Parallel computing for Fast Spatiotemporal Weighted Regression

Abstract The Spatiotemporal Weighted Regression (STWR) model is an extension of the Geographically Weighted Regression (GWR) model for exploring the heterogeneity of spatiotemporal processes. A key feature of STWR is that it utilizes the data points observed at previous time stages to make better fit and prediction at the latest time stage. Because the temporal bandwidths and a few other parameters need to be optimized in STWR, the model calibration is computationally intensive. In particular, when the data amount is large, the calibration of STWR becomes heavily time-consuming. For example, with 10,000 points in 10 time stages, it takes about 2307 s for a single-core PC to process the calibration of STWR. Both the distance and the weighted matrix in STWR are memory intensive, which may easily cause memory insufficiency as data amount increases. To improve the efficiency of computing, we developed a parallel computing method for STWR by employing the Message Passing Interface (MPI). A cache in the MPI processing approach was proposed for the calibration routine. Also, a matrix splitting strategy was designed to address the problem of memory insufficiency. We named the overall design as Fast STWR (F-STWR). In the experiment, we tested F-STWR in a High-Performance Computing (HPC) environment with a total number of 204,611 observations in 19 years. The results show that F-STWR can significantly improve STWR's capability of processing large-scale spatiotemporal data.