l₀-Norm Variable Adaptive Selection for Geographically Weighted Regression Model

A geographically weighted regression (GWR) model with fewer explanatory variables and higher prediction accuracy is required in spatial analysis and other practical applications. This article proposes an (Formula presented.) -norm variable adaptive selection method to enhance performances of a GWR by simultaneously performing model selection and coefficient optimization. Specifically, we formulate a regularized GWR model with an additional (Formula presented.) -norm constraint to shrink those unimportant regression coefficients toward zero and propose an adaptive variable selection algorithm by iteratively distinguishing the important variables from the variable set. At each location, the best variable subset and optimizing coefficient estimations are simultaneously achieved under the (Formula presented.) -GWR framework. Moreover, two novel criteria, the modified Bayesian information criterion and the interpretability of coefficient symbol, which specify the variable selection and model interpretation, respectively, are also introduced to improve the performance of the (Formula presented.) -GWR. Experiments on both simulated and actual data sets demonstrate that the proposed algorithm can significantly improve the estimation accuracy of coefficients and can also enhance the interpretative ability of the established model.