Given a node-attributed graph, how can we efficiently represent it with few numerical features that expressively reflect its topology and attribute information? We propose A-DOGE, for Attributed DOS-based Graph Embedding, based on density of states (DOS, a.k.a. spectral density) to tackle this problem. A-DOGE is designed to fulfill a long desiderata of desirable characteristics. Most notably, it capitalizes on efficient approximation algorithms for DOS, that we extend to blend in node labels and attributes for the first time, making it fast and scalable for large attributed graphs and graph databases. Being based on the entire eigenspectrum of a graph, A-DOGE can capture structural and attribute properties at multiple ("glocal") scales. Moreover, it is unsupervised (i.e. agnostic to any specific objective) and lends itself to various interpretations, which makes it is suitable for exploratory graph mining tasks. Finally, it processes each graph independent of others, making it amenable for streaming settings as well as parallelization. Through extensive experiments, we show the efficacy and efficiency of A-DOGE on exploratory graph analysis and graph classification tasks, where it significantly outperforms unsupervised baselines and achieves competitive performance with modern supervised GNNs, while achieving the best trade-off between accuracy and runtime.
翻译:根据一个互不关联的图表,我们如何能以少量数字特征有效地代表它,表达其地形和属性信息?我们建议A-DOGE,用于基于国家密度(DOS, a.k.a.光谱密度)的基于 DOS 的成像嵌入,以解决这一问题。A-DOGE旨在完成长期的可取特性的脱线。最值得注意的是,它利用了DOS的高效近似算法,我们首次将之推广到节点标签和属性的混合,使它能够快速和可缩放用于大型可分数图表和图表数据库。A-DOGE可以基于一个图表的整个eigenspecrectrm,在多个(“glocal”)尺度上捕捉到结构和属性属性。此外,A-DG可以不受监督地(即对任何特定目标的认知性能)和特性进行长期的剥离。它本身的诠释,因此它适合探索性图表采矿任务。最后,它处理每张图,使它适合流环境,作为平行的平行和平行的。通过广泛的实验,我们通过一个图表,通过一个图表,在运行的图表中分析,我们展示性图表中能和测试性地分析,我们能够实现A-DODODODO的运行的精确的模型的模型,然后实现最佳的测试,从而实现最佳的测试,然后实现S-DO-DA-CA-CA-A-CA-CA-A-A-cal的运行的精确的精确性平压式分析。