Graph representation learning has achieved a remarkable success in many graph-based applications, such as node classification, link prediction, and community detection. These models are usually designed to preserve the vertex information at different granularity and reduce the problems in discrete space to some machine learning tasks in continuous space. However, regardless of the fruitful progress, for some kind of graph applications, such as graph compression and edge partition, it is very hard to reduce them to some graph representation learning tasks. Moreover, these problems are closely related to reformulating a global layout for a specific graph, which is an important NP-hard combinatorial optimization problem: graph ordering. In this paper, we propose to attack the graph ordering problem behind such applications by a novel learning approach. Distinguished from greedy algorithms based on predefined heuristics, we propose a neural network model: Deep Order Network (DON) to capture the hidden locality structure from partial vertex order sets. Supervised by sampled partial order, DON has the ability to infer unseen combinations. Furthermore, to alleviate the combinatorial explosion in the training space of DON and make the efficient partial vertex order sampling , we employ a reinforcement learning model: the Policy Network, to adjust the partial order sampling probabilities during the training phase of DON automatically. To this end, the Policy Network can improve the training efficiency and guide DON to evolve towards a more effective model automatically. Comprehensive experiments on both synthetic and real data validate that DON-RL outperforms the current state-of-the-art heuristic algorithm consistently. Two case studies on graph compression and edge partitioning demonstrate the potential power of DON-RL in real applications.

中文翻译：

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图排序：通过学习走向最优

图表示学习在许多基于图的应用中取得了显着的成功，例如节点分类、链接预测和社区检测。这些模型通常旨在保留不同粒度的顶点信息，并将离散空间中的问题减少到连续空间中的一些机器学习任务中。然而，尽管取得了丰硕的进展，但对于某些图应用，例如图压缩和边缘分割，很难将它们简化为一些图表示学习任务。此外，这些问题与为特定图重新制定全局布局密切相关，这是一个重要的 NP-hard 组合优化问题：图排序。在本文中，我们建议通过一种新颖的学习方法来解决此类应用程序背后的图排序问题。与基于预定义启发式的贪婪算法不同，我们提出了一种神经网络模型：深度顺序网络（DON），用于从部分顶点顺序集中捕获隐藏的局部结构。在采样偏序的监督下，DON 能够推断出看不见的组合。此外，为了减轻 DON 训练空间中的组合爆炸并进行有效的偏顶点阶采样，我们采用强化学习模型：策略网络，在 DON 的训练阶段自动调整偏阶采样概率。为此，Policy Network 可以提高训练效率，引导 DON 自动向更有效的模型演进。对合成数据和真实数据的综合实验证实，DON-RL 始终优于当前最先进的启发式算法。图压缩和边分区的两个案例研究证明了 DON-RL 在实际应用中的潜在能力。