arXiv：cs.LG· Farid Bozorgnia, Vyacheslav Kungurtsev, Shirali Kadyrov, Mohsen Yousefnezhad·· 3 小时前
小训练样本下半监督图学习的分数阶热核方法
Fractional Heat Kernel for Semi-Supervised Graph Learning with Small Training Sample Size
AI 导读
研究者提出一种源驱动的分数阶热核框架用于半监督图学习，通过固定非零标签源防止长扩散时间下坍缩到拉普拉斯零空间，从而缓解过平滑。在 Two-Moon 数据集上，每类仅用 1 个训练标签、分数阶为 0.8 和 1 时，兼容源驱动扩散的平均准确率超过 96%；在 Cora 和 CiteSeer 上，每类 1 个标签时该流程比 GAT 平均准确率分别提升 9.2 和 8.0 个百分点。
正文
Abstract:We develop a source-driven fractional heat-kernel framework for semi-super\-vised graph learning that combines nonlocal propagation with sustained label information. A fixed nonzero label source compatible with the Laplacian null space prevents asymptotic collapse into that space, providing a mechanism for mitigating oversmoothing at long diffusion times. The fractional order controls the relative modal attenuation and the spectral weighting of the sustained response, while the diffusion time sets the propagation horizon. We characterize conservation laws and equilibria on normalized and disconnected graphs, develop a null-space deflation, and analyze the approximation of the propagators. On Two-Moon, fractional orders improve source-free propagation, while compatible source-driven diffusion exceeds $96\%$ mean accuracy with one training label per class at orders $0.8$ and $1$. On Cora and CiteSeer, the source-driven pipeline improves mean accuracy over GAT by $9.2$ and $8.0$ percentage points at one training label per class, with model selection on $500$ labeled validation nodes and closely comparable classical and fractional pipeline configurations; it matches GAT on PubMed and trails it at ten and twenty labels per class on Cora. Within GraphHeat, validation-based exponent selection at a common diffusion time yields a paired gain of $1.45$ percentage points at one label per class.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2510.04440 [cs.LG] |
| (or arXiv:2510.04440v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2510.04440 arXiv-issued DOI via DataCite |
Submission history
From: Farid Bozorgnia [view email]
[v1]
Mon, 6 Oct 2025 02:15:46 UTC (215 KB)
[v2]
Thu, 8 Oct 2026 12:32:57 UTC (551 KB)
来源：arXiv：cs.LG · arxiv.org