Integrated subset selection and bandwidth estimation algorithm for geographically weighted regression

IF 7.5 1区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Hyunwoo Lee , Young Woong Park
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引用次数: 0

Abstract

This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and regression coefficients to vary across study areas. Unlike standard approaches in the literature, in which bandwidth and regression parameters are estimated separately for each focal point on the basis of different criteria, our model uses a single objective function for the integrated estimation of regression and bandwidth parameters across all focal points, based on the regression likelihood function and variance modeling. The proposed model further integrates a procedure to select a single subset of independent variables for all focal points, whereas existing approaches may return heterogeneous subsets across focal points. We then propose an alternative direction method to solve the nonconvex mathematical model and show that it converges to a partial minimum. The computational experiment indicates that the proposed algorithm provides competitive explanatory power with stable spatially varying patterns, with the ability to select the best subset and account for additional constraints.
地理加权回归的综合子集选择和带宽估计算法
本研究提出了一种基于数学规划的算法,用于地理加权回归中变量子集的综合选择和带宽估计,这是一种允许核带宽和回归系数在研究区域之间变化的局部回归方法。与文献中的标准方法不同,标准方法根据不同的标准分别估计每个焦点的带宽和回归参数,我们的模型使用单一目标函数,基于回归似然函数和方差建模,对所有焦点的回归和带宽参数进行综合估计。提出的模型进一步集成了一个过程,为所有焦点选择独立变量的单个子集,而现有的方法可能会返回跨焦点的异构子集。然后,我们提出了一种替代方向法来求解非凸数学模型,并证明了它收敛于部分极小值。计算实验表明,该算法具有稳定的空间变化模式,具有竞争性的解释力,能够选择最佳子集并考虑附加约束。
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来源期刊
Pattern Recognition
Pattern Recognition 工程技术-工程:电子与电气
CiteScore
14.40
自引率
16.20%
发文量
683
审稿时长
5.6 months
期刊介绍: The field of Pattern Recognition is both mature and rapidly evolving, playing a crucial role in various related fields such as computer vision, image processing, text analysis, and neural networks. It closely intersects with machine learning and is being applied in emerging areas like biometrics, bioinformatics, multimedia data analysis, and data science. The journal Pattern Recognition, established half a century ago during the early days of computer science, has since grown significantly in scope and influence.
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