Inspired by the success of Geographically Weighted Regression and its accounting for spatial variations, we propose GeogGNN -- A graph neural network model that accounts for geographical latitude and longitudinal points. Using a synthetically generated dataset, we apply the algorithm for a 4-class classification problem in cybersecurity with seemingly realistic geographic coordinates centered in the Gulf Cooperation Council region. We demonstrate that it has higher accuracy than standard neural networks and convolutional neural networks that treat the coordinates as features. Encouraged by the speed-up in model accuracy by the GeogGNN model, we provide a general mathematical result that demonstrates that a geometrically weighted neural network will, in principle, always display higher accuracy in the classification of spatially dependent data by making use of spatial continuity and local averaging features.

翻译：受地理加权回归及其对空间变异性的成功考虑所启发，我们提出了GeogGNN——一种考虑地理经纬度坐标的图神经网络模型。通过使用合成生成的数据集，我们将该算法应用于网络安全领域的四分类问题，数据集中包含以海湾合作委员会区域为中心、看似真实的地理坐标。我们证明，该模型比将坐标作为特征处理的标准神经网络和卷积神经网络具有更高的准确率。受GeogGNN模型在准确率上加速提升的鼓舞，我们提供了一个通用的数学结果，证明通过利用空间连续性和局部平均特性，几何加权神经网络在原则上始终能在空间依赖性数据的分类中表现出更高的准确率。