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arXiv 2109.13441cs.LGcs.AI
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DynG2G:一种有效的时间图随机图嵌入方法

DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs

Brown University(布朗大学);McGovern Institute for Brain Research, Massachusetts Institute of Technology(麻省理工学院麦戈文脑科学研究所);National Institute of Technology, Silchar(锡尔查尔国家理工学院)

Mengjia Xu, Apoorva Vikram Singh, George Em Karniadakis

摘要:

动态图嵌入由于能够学习复杂时序图的低维图表示并具有较高的精度而受到广泛关注。然而,最近的进展主要集中在学习节点嵌入作为静态图的确定性“向量”,而忽略了关键图的时间动态和与潜在空间中的节点嵌入相关的不断变化的不确定性。在这项工作中,我们提出了一种有效的随机动态图嵌入方法(DynG2G),该方法应用了一种使用基于节点三元组的对比损失训练的感应前馈编码器。每个时间戳的每个节点被编码为潜在空间中的时间相关概率多元高斯分布,因此我们可以实时量化节点嵌入的不确定性。我们采用了八种不同的基准,代表了大小的多样性(从96个节点到87,626个节点,从13,398条边到4,870,863条边)和动态的多样性。我们通过对这八个动态图基准测试的广泛实验证明,DynG2G在捕获底层时间节点嵌入方面实现了新的最先进的性能。我们还证明了DynG2G可以预测不断变化的节点嵌入不确定性,这在量化动态系统随时间的内在维数方面起着至关重要的作用。我们得到的最佳嵌入维数,$L_o$,与有效维数的不确定性,$D_u$的普遍关系,我们推断,$L_o=D_u$的所有情况下。这意味着我们在DynG2G中采用的不确定性量化方法正确地捕获了这种不断发展的图形的动态的内在维度,尽管每个时间戳的图形具有不同的性质和组成。此外,该$L_0 - D_u$相关性提供了清晰的路径,以通过设置$L \ge D_u$来自适应地选择每个时间戳处的最佳嵌入大小。

英文摘要:

Dynamic graph embedding has gained great attention recently due to its capability of learning low dimensional graph representations for complex temporal graphs with high accuracy. However, recent advances mostly focus on learning node embeddings as deterministic "vectors" for static graphs yet disregarding the key graph temporal dynamics and the evolving uncertainties associated with node embedding in the latent space. In this work, we propose an efficient stochastic dynamic graph embedding method (DynG2G) that applies an inductive feed-forward encoder trained with node triplet-based contrastive loss. Every node per timestamp is encoded as a time-dependent probabilistic multivariate Gaussian distribution in the latent space, hence we can quantify the node embedding uncertainty on-the-fly. We adopted eight different benchmarks that represent diversity in size (from 96 nodes to 87,626 and from 13,398 edges to 4,870,863) and diversity in dynamics. We demonstrate via extensive experiments on these eight dynamic graph benchmarks that DynG2G achieves new state-of-the-art performance in capturing the underlying temporal node embeddings. We also demonstrate that DynG2G can predict the evolving node embedding uncertainty, which plays a crucial role in quantifying the intrinsic dimensionality of the dynamical system over time. We obtain a universal relation of the optimal embedding dimension, $L_o$, versus the effective dimensionality of uncertainty, $D_u$, and we infer that $L_o=D_u$ for all cases. This implies that the uncertainty quantification approach we employ in the DynG2G correctly captures the intrinsic dimensionality of the dynamics of such evolving graphs despite the diverse nature and composition of the graphs at each timestamp. Moreover, this $L_0 - D_u$ correlation provides a clear path to select adaptively the optimum embedding size at each timestamp by setting $L \ge D_u$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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