arXiv:2410.16593eess.SPcs.AI2024-10被引 1

用节点特征设计采样策略,让GNN在小图上训练后能更好迁移到大图。

Sampling Transferable Graph Neural Networks with Limited Graph Information

  • 基于特征与图谱结构的对齐关系,设计无需完整图结构的采样方法
  • 最大化拉普拉斯矩阵迹的采样规则显著提升模型迁移能力
  • 适合缺乏完整图结构信息时的高效GNN训练,尤其适用于真实数据

图神经网络(GNN)在图学习任务中表现优异,但在大规模网络上训练仍计算成本高。已有研究表明,固定权重的GNN可从较小图泛化到同家族的大图,这促使利用采样子图提升训练效率。然而多数现有采样策略依赖精确的图结构信息,而实际中该信息可能噪声大、不完整或不可用。为此,本文研究基于特征的子图采样以实现可迁移的GNN,目标是保留控制GNN表达能力的图算子谱特性。我们从特征统计与图谱结构的对齐视角出发,提出两种互补的特征-图对齐概念:粗粒度对齐通过拉普拉斯基底度量特征主成分与图特征向量的对齐程度,并建立拉普拉斯迹的下界;细粒度对齐假设特征协方差与拉普拉斯共享特征基,证明对单调滤波器而言协方差对角元反映节点度序。实验证明滤波器单调性决定特征方差与谱能量的关系。在真实数据集上,选择最大化拉普拉斯迹的保留规则始终带来更强的迁移性能和更小的泛化差距。

原文摘要 · Abstract (English)

Graph neural networks (GNNs) achieve strong performance on graph learning tasks, but training on large-scale networks remains computationally challenging. Transferability results show that GNNs with fixed weights can generalize from smaller graphs to larger ones drawn from the same family, motivating the use of sampled subgraphs to boost training efficiency. Yet most existing sampling strategies rely on reliable access to the target graph structure, which in practice may be noisy, incomplete, or unavailable prior to training. In lieu of precise connectivity information, we study feature-driven subgraph sampling for transferable GNNs, with the goal of preserving spectral properties of graph operators that control GNN expressivity. We adopt an alignment-based perspective linking node feature statistics to graph spectral structure and develop two complementary notions of feature-graph alignment. For coarse alignment, we formalize feature homophily through a Laplacian-based measure quantifying the alignment of feature principal components with graph eigenvectors, and establish a lower bound on the Laplacian trace in terms of feature statistics. This motivates a simple, non-sequential sampling algorithm that operates on the feature matrix and preserves a trace-based proxy for operator rank. For fine alignment, we assume a stationary model where the feature covariance and Laplacian share an eigenbasis, and establish that diagonal covariance entries reflect node-degree ordering under monotone filters. We empirically validate that filter monotonicity dictates the relationship between feature variance and spectral energy. On real-world benchmarks, selecting the retention rule that maximizes the Laplacian trace consistently yields GNNs with superior transferability and reduced generalization gaps.

图神经网络特征采样迁移学习谱分析

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