用分数阶热核提升小样本图学习的标签传播效果
Fractional Heat Kernel for Semi-Supervised Graph Learning with Small Training Sample Size
- 引入带源项的分数阶热核动态进行标签传播与自训练
- 在仅有少量标注样本时，标签扩散更全局、更稳定
- 适用于小样本场景的图神经网络，尤其适合标签稀疏任务
本文提出基于分数阶热核动态的标签传播与自训练新算法。通过信息论与抛物型演化方程的物理对应关系，将分数阶拉普拉斯算子引入图神经网络（如图卷积网络、图注意力网络），实现自适应的多跳扩散，增强模型表达能力。利用切比雪夫多项式近似，使大规模图计算可行。变分推导表明，扩展经典扩散模型至拉普拉斯算子的分数阶幂，可捕获非局部交互，实现更全局的标签扩散。在仅含少量标注样本的场景下，该方法在已知标签监督与图内扩散间取得良好平衡，显著提升性能。实验验证了其在标准数据集上的有效性。
原文摘要 · Abstract (English)
In this work, we introduce novel algorithms for label propagation and self-training using fractional heat kernel dynamics with a source term. We motivate the methodology through the classical correspondence of information theory with the physics of parabolic evolution equations. We integrate the fractional heat kernel into Graph Neural Network architectures such as Graph Convolutional Networks and Graph Attention, enhancing their expressiveness through adaptive, multi-hop diffusion. By applying Chebyshev polynomial approximations, large graphs become computationally feasible. Motivating variational formulations demonstrate that by extending the classical diffusion model to fractional powers of the Laplacian, nonlocal interactions deliver more globally diffusing labels. The particular balance between supervision of known labels and diffusion across the graph is particularly advantageous in the case where only a small number of labeled training examples are present. We demonstrate the effectiveness of this approach on standard datasets.
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