Graph neural networks (GNNs) are important tools for transductive learning tasks, such as node classification in graphs, due to their expressive power in capturing complex interdependency between nodes. To enable GNN learning, existing works typically assume that labeled nodes, from two or multiple classes, are provided, so that a discriminative classifier can be learned from the labeled data. In reality, this assumption might be too restrictive for applications, as users may only provide labels of interest in a single class for a small number of nodes. In addition, most GNN models only aggregate information from short distances ( e.g. , 1-hop neighbors) in each round, and fail to capture long-distance relationship in graphs. In this article, we propose a novel GNN framework, long-short distance aggregation networks, to overcome these limitations. By generating multiple graphs at different distance levels, based on the adjacency matrix, we develop a long-short distance attention model to model these graphs. The direct neighbors are captured via a short-distance attention mechanism, and neighbors with long distance are captured by a long-distance attention mechanism. Two novel risk estimators are further employed to aggregate long-short-distance networks, for PU learning and the loss is back-propagated for model learning. Experimental results on real-world datasets demonstrate the effectiveness of our algorithm.

中文翻译：

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学习具有正节点和未标记节点的图神经网络

图神经网络 (GNN) 是用于转换学习任务的重要工具，例如图中的节点分类，因为它们在捕获节点之间复杂的相互依赖关系方面具有表现力。为了启用 GNN 学习，现有工作通常假设提供了来自两个或多个类的标记节点，以便可以从标记数据中学习判别分类器。实际上，这种假设对于应用程序可能过于严格，因为用户可能只为少数节点提供单个类中感兴趣的标签。此外，大多数 GNN 模型仅聚合短距离的信息（例如, 1-hop 邻居）在每一轮中，并且未能捕获远距离谈恋爱在图表中。在本文中，我们提出了一种新颖的 GNN 框架，即长短距离聚合网络，以克服这些限制。通过在不同距离级别生成多个图，基于邻接矩阵，我们开发了一个长短距离注意力模型来对这些图进行建模。直接邻居通过短距离注意力机制捕获，远距离邻居通过长距离注意力机制捕获。两个新的风险估计器被进一步用于聚合长短距离网络，用于 PU 学习，损失反向传播用于模型学习。真实世界数据集的实验结果证明了我们算法的有效性。