A new and fast GTWR approach, FastGTWR, was proposed. The performance of the proposed FastGTWR approach was compared with that of the classical GWR and GTWR approaches. Experimental evaluations conducted on real and synthetic datasets showed that FastGTWR approach outperformed other approaches.Geographically Weighted Regression (GWR) method, which is one of the widely used spatial analysis methods, is the local spatial regression technique used to model the changing relationships on geography.Geographically and Temporal Weighted Regression (GTWR) is an approach developed by including temporal relations into the GWR approach. Although the GTWR approach produces much better models than the GWR approach in the dataset containing spatial-temporal heterogeneity, there are still challenges given the complexity of spatial-temporal approaches. Because of this reason, in the literature GTWR models can able to handle limited number of data. In this study, we propose the FastGTWR approach to reduce the algorithmic complexity of GTWR approach and to overcome data size restriction. The proposed FastGTWR approach was run on real data set. The performance of the proposed FastGTWR approach was compared with the performances of the classical GWR and GTWR approaches. Experimental results showed that the proposed FastGTWR approach works faster than the GWR and GTWR approaches.
Figure A. Comparisons of GWR approachesPurpose: The purpose of this study is to develop a fast GTWR approach of FastGTWR to reduce the algorithmic complexity of GTWR approach and to overcome data size restriction
Theory and Methods:In this study, the FastGTWR algorithm is proposed to increase the speed of the GTWR algorithm and so to overcome data size restriction. It is observed that that the calculation and storage cost of GTWR approach is due to , , matrix multiplication and calculation of inverse of this matrix. The size of neighborhood matrix , , is ( is the number of regression points). In the proposed FastGTWR approach, the W matrix was reorganized and converted into a vector format and dot matrix multiplication was used to reduce the complexity of the matrix operations. In addition, considering the fact that , , matrix is a symmetrical matrix, only the values at the top or bottom of the diagonal of the matrix were calculated. Thus, the calculation and storage complexity of the GTWR approach was reduced.
Results:The performance of the proposed FastGTWR algorithm was compared with that of the GWR and GTWR approaches using synthetic and real meteorological data of Turkey. Experimental evaluations showed that on a standard computer, proposed FastGTWR algorithm can handle 1,000,000 observation points, while the GWR and GTWR algorithms can process a maximum of 40,000 observation points.
Conclusion:Experimental evaluations show that the proposed FastGTWR approach is computationally efficient than the GWR and GTWR approaches and can be handle large scale datasets .
