Graph learning, such as node classification, is typically carried out in a closed-world setting. A number of nodes are labeled, and the learning goal is to correctly classify remaining (unlabeled) nodes into classes, represented by the labeled nodes. In reality, due to limited labeling capability or dynamic evolving nature of networks, some nodes in the networks may not belong to any existing/seen classes and therefore cannot be correctly classified by closed-world learning algorithms. In this paper, we propose a new open-world graph learning paradigm, where the learning goal is to correctly classify nodes belonging to labeled classes into correct categories and also classify nodes not belonging to labeled classes to an unseen class. Open-world graph learning has three major challenges: (1) Graphs do not have features to represent nodes for learning; (2) unseen class nodes do not have labels and may exist in an arbitrary form different from labeled classes; and (3) graph learning should differentiate whether a node belongs to an existing/seen class or an unseen class. To tackle the challenges, we propose an uncertain node representation learning principle to use multiple versions of node feature representation to test a classifier’s response on a node, through which we can differentiate whether a node belongs to the unseen class. Technical wise, we propose constrained variational graph autoencoder, using label loss and class uncertainty loss constraints, to ensure that node representation learning is sensitive to the unseen class. As a result, node embedding features are denoted by distributions, instead of deterministic feature vectors. In order to test the certainty of a node belonging to seen classes, a sampling process is proposed to generate multiple versions of feature vectors to represent each node, using automatic thresholding to reject nodes not belonging to seen classes as unseen class nodes. Experiments, using graph convolutional networks and graph attention networks on four real-world networks, demonstrate the algorithm performance. Case studies and ablation analysis also show the advantage of the uncertain representation learning and automatic threshold selection for open-world graph learning.

图学习，例如节点分类，通常在封闭世界环境中进行。许多节点被标记，学习目标是将剩余（未标记）节点正确分类为由标记节点表示的类。实际上，由于网络的标记能力或动态演化特性有限，网络中的某些节点可能不属于任何现有/可见的类，因此无法通过封闭世界学习算法进行正确分类。在本文中，我们提出了一个新的开放世界图学习范式，其中学习目标是将属于标记类的节点正确分类为正确的类别，并将不属于标记类的节点分类为不可见的类。开放世界图学习面临三大挑战：（1）图不具备表示学习节点的特征；(2) 看不见的类节点没有标签，可能以不同于标签类的任意形式存在；(3) 图学习应该区分一个节点是属于现有/可见类还是不可见类。为了应对挑战，我们提出了一种不确定节点表示学习原理，使用多个版本的节点特征表示来测试分类器对节点的响应，通过它我们可以区分节点是否属于看不见的类。技术方面，我们提出了约束变分图自动编码器，使用标签损失和类不确定性损失约束，以确保节点表示学习对看不见的类敏感。因此，节点嵌入特征由分布表示，而不是确定性特征向量。为了测试属于已见类的节点的确定性，提出了一个采样过程来生成多个版本的特征向量来表示每个节点，使用自动阈值法将不属于已见类的节点拒绝为未见类节点。在四个真实世界网络上使用图卷积网络和图注意力网络的实验证明了算法性能。