In this paper, we introduce a new setting for graph embedding, which considers embedding communities instead of individual nodes. We find that community embedding is not only useful for community-level applications such as graph visualization but also provide an exciting opportunity to improve community detection and node classification. Specifically, we consider the interaction between community embedding and detection as a closed loop, through node embedding. On the one hand, node embedding can improve community detection since the detected communities are used to fit a community embedding. On the other hand, community embedding can be used to optimize node embedding by introducing a community-aware high-order proximity. However, in practice, the number of communities can be unknown beforehand; thus we extend our previous Community Embedding (ComE) model. We propose ComE+, a new model which handles both: the unknown truth community assignments and the unknown number of communities present in the dataset. We further develop an efficient inference algorithm for ComE+ for keeping complexity low. Our extensive evaluation shows that ComE+ improves the state-of-the-art baselines in various application tasks, e.g., community detection and node classification.

中文翻译：

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在图上嵌入有限和无限社区 [应用说明]

在本文中，我们为图嵌入引入了一种新设置，它考虑嵌入社区而不是单个节点。我们发现社区嵌入不仅对图可视化等社区级应用有用，而且为改进社区检测和节点分类提供了一个令人兴奋的机会。具体来说，我们通过节点嵌入将社区嵌入和检测之间的交互视为一个闭环。一方面，节点嵌入可以改进社区检测，因为检测到的社区用于拟合社区嵌入。另一方面，社区嵌入可用于通过引入社区感知的高阶邻近度来优化节点嵌入。然而，在实践中，社区的数量可能是事先未知的；因此，我们扩展了我们之前的社区嵌入 (ComE) 模型。我们提出了 ComE+，这是一种新模型，它可以处理：未知真相社区分配和数据集中存在的未知社区数量。我们进一步为 ComE+ 开发了一种有效的推理算法，以保持低复杂度。我们的广泛评估表明，ComE+ 改进了各种应用任务（例如社区检测和节点分类）中最先进的基线。