Graph neural networks (GNNs) have gained significant popularity for classification tasks in machine learning, yet their applications to regression problems remain limited. Concurrently, attention mechanisms have emerged as powerful tools in sequential learning tasks. In this paper, we employ GNNs and attention mechanisms to address a classical but challenging nonlinear regression problem: network localization. We propose a novel GNN-based network localization method that achieves exceptional stability and accuracy in the presence of severe non-line-of-sight (NLOS) propagations, while eliminating the need for laborious offline calibration or NLOS identification. Extensive experimental results validate the effectiveness and high accuracy of our GNN-based localization model, particularly in challenging NLOS scenarios. However, the proposed GNN-based model exhibits limited flexibility, and its accuracy is highly sensitive to a specific hyperparameter that determines the graph structure. To address the limitations and extend the applicability of the GNN-based model to real scenarios, we introduce two attentional graph neural networks (AGNNs) that offer enhanced flexibility and the ability to automatically learn the optimal hyperparameter for each node. Experimental results confirm that the AGNN models are able to enhance localization accuracy, providing a promising solution for real-world applications. We also provide some analyses of the improved performance achieved by the AGNN models from the perspectives of dynamic attention and signal denoising characteristics.

翻译：图神经网络在机器学习分类任务中广受欢迎，但其在回归问题中的应用仍较有限。与此同时，注意力机制已成为序列学习任务中的强大工具。本文采用图神经网络与注意力机制解决经典且具挑战性的非线性回归问题——网络定位。我们提出一种新颖的基于图神经网络的网络定位方法，该方法在严重非视距传播环境下展现出卓越的稳定性和准确性，同时免除了繁琐的离线校准或非视距识别需求。大量实验结果验证了所提出的基于图神经网络的定位模型在具有挑战性的非视距场景中的有效性和高精度。然而，该模型灵活性有限，其精度对决定图结构的特定超参数高度敏感。为解决上述局限并扩展该模型在真实场景中的适用性，我们引入两种注意力图神经网络，它们具有更强的灵活性，能够为每个节点自动学习最优超参数。实验结果证实，注意力图神经网络模型可提升定位精度，为实际应用提供了有前景的解决方案。我们还从动态注意力与信号去噪特性的角度分析了注意力图神经网络模型性能提升的原因。