In recent years, Graph neural networks (GNNs) have emerged as a prominent tool for classification tasks in machine learning. However, their application in regression tasks remains underexplored. To tap the potential of GNNs in regression, this paper integrates GNNs with attention mechanism, a technique that revolutionized sequential learning tasks with its adaptability and robustness, to tackle a challenging nonlinear regression problem: network localization. We first introduce a novel network localization method based on graph convolutional network (GCN), which exhibits exceptional precision even under severe non-line-of-sight (NLOS) conditions, thereby diminishing the need for laborious offline calibration or NLOS identification. We further propose an attentional graph neural network (AGNN) model, aimed at improving the limited flexibility and mitigating the high sensitivity to the hyperparameter of the GCN-based method. The AGNN comprises two crucial modules, each designed with distinct attention architectures to address specific issues associated with the GCN-based method, rendering it more practical in real-world scenarios. Experimental results substantiate the efficacy of our proposed GCN-based method and AGNN model, as well as the enhancements of AGNN model. Additionally, we delve into the performance improvements of AGNN model by analyzing it from the perspectives of dynamic attention and computational complexity.

翻译：近年来，图神经网络（GNN）已成为机器学习分类任务中的重要工具。然而，其在回归任务中的应用仍待深入探索。为挖掘GNN在回归领域的潜力，本文结合GNN与注意力机制（一种凭借适应性和鲁棒性革新了序列学习任务的技术），以解决具有挑战性的非线性回归问题：网络定位。我们首先提出一种基于图卷积网络（GCN）的新型网络定位方法，该方法即使在严重非视距（NLOS）条件下仍展现出卓越精度，从而减少了对繁重离线校准或NLOS识别的需求。为进一步改善基于GCN方法中灵活性有限及对超参数高度敏感的问题，我们提出了注意力图神经网络（AGNN）模型。该AGNN包含两个关键模块，每个模块均采用不同的注意力架构设计，可解决基于GCN方法中的特定缺陷，使其在实际场景中更具实用性。实验结果验证了我们提出的基于GCN方法及AGNN模型的有效性，并证实了AGNN模型的性能提升。此外，我们从动态注意力与计算复杂度的角度对AGNN模型的性能改进进行了深入分析。