地理加权回归分析是空间统计学领域中探索空间数据关系异质性的重要技术手段之一，已被广泛应用于多个学科领域。空间距离度量是这项技术的基础元素之一。在传统应用中，空间距离的量算一般被默认为欧式距离，即直线距离，忽略了在复杂的地理空间中对距离度量多样性的要求，大大限制了模型解算的精度和准度。针对存在的这些问题，本课题拟拓展非欧式空间距离度量在地理加权回归分析技术中的应用。研究内容包括：1）基于非欧式空间距离度量的地理加权回归分析模型基础理论和算法；2) 针对地理加权回归分析模型的距离度量优选方法，利用闵可夫斯基距离函数实现对“最优”距离度量的最大逼近；3)模型变量-空间距离度量对应的地理加权回归分析模型解算方法。根据本课题所研究的理论与算法，将研发地理加权回归分析开源软件工具包，提供便捷实用的新型应用工具。本项目将推动地理空间中距离度量的研究，对地理加权回归分析技术的发展具有重要的理论和实践意义。

Geographically weighted regression (GWR) is an important local technique for exploring spatial heterogeneity in data relationships. It has been broadly applied in various disciplines since its emergence. Distance metric plays a fundamental role in calibrating a GWR model, and the Euclidean distance (i.e. straight line distance) is traditionally employed as default. However, the complexity of our real world ensures that the scope of possible distance metrics is far larger than the traditional Euclidean choice, which has greatly restricted the accuracy in GWR model calibration. Accordingly, this project intends to incorporate a range of different non-Euclidean distance metrics in GWR. The contents of this project include: 1) the methodology and relative algorithms will be developed for basic GWR using non-Euclidean distance metrics; 2) the Minkowski distance function will be used to approach an optimum distance metric so as to select a proper distance metric for a given GWR model; 3) GWR with non-Euclidean distance metrics can also be extended into a new approach on calibrating GWR with parameter-specific distance metrics. With all the methods and algorithms proposed, open-source package and toolkit for GWR will be developed, specifically for applications with various choices of distance metric. This project contributes in studies on distance metrics within the real geographical space, and has great theoretical and practical significance for developing the GWR technique.