Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to model complex patterns is essentially constrained by its polynomially growing capacity. Recently, hyperbolic spaces have emerged as a promising alternative for processing graph data with tree-like structure or power-law distribution, owing to the exponential growth property. Different from Euclidean space, which expands polynomially, the hyperbolic space grows exponentially which makes it gains natural advantages in abstracting tree-like or scale-free graphs with hierarchical organizations. In this tutorial, we aim to give an introduction to this emerging field of graph representation learning with the express purpose of being accessible to all audiences. We first give a brief introduction to graph representation learning as well as some preliminary Riemannian and hyperbolic geometry. We then comprehensively revisit the hyperbolic embedding techniques, including hyperbolic shallow models and hyperbolic neural networks. In addition, we introduce the technical details of the current hyperbolic graph neural networks by unifying them into a general framework and summarizing the variants of each component. Moreover, we further introduce a series of related applications in a variety of fields. In the last part, we discuss several advanced topics about hyperbolic geometry for graph representation learning, which potentially serve as guidelines for further flourishing the non-Euclidean graph learning community.
翻译:图表结构数据在现实世界的应用中非常普遍,例如社交网络、推荐系统、知识图、化学分子等。尽管欧clidean空间在与图形有关的学习任务中取得了成功,但其建模复杂模式的能力基本上受到其多元性增长能力的制约。最近,由于指数增长特性,超双曲线空间已成为处理图形数据的有希望的替代方法,如树形结构或电法分布。与欧clidean空间不同,它扩展了多元性,超双曲线空间成倍增长,使其在与等级组织抽取类似树形的或无比例的图表方面获得了自然优势。在此教义中,我们力求介绍这个新兴的图形代表学习领域,其明确的目的是让所有受众都能使用。我们首先简要介绍图形代表学习以及一些初步的里曼式和超偏斜式的地形测量特性。我们随后全面重新审视超曲线嵌入技术,包括超曲线浅浅色浅质模型和超曲线神经网络。此外,我们还介绍了当前超曲线型图表型图绘制图的技术性细节技术细节,作为我们深层次图中的一系列变异性模型的一部分,用于我们再将一系列的深度的数学结构的学习。