提出高阶超图正则化新方法，提升模型泛化能力。
Higher-Order Regularization Learning on Hypergraphs
- 用多尺度拉普拉斯幂构建高阶平滑正则项
- 证明截断版本一致收敛，给出明确收敛速率
- 在主动学习与非几何数据上表现优异
高阶超图学习（HOHL）是一种新兴的超图正则化方法，通过超图结构诱导的多尺度拉普拉斯算子的幂次来强制高阶平滑性。已有研究在几何设定下通过渐近一致性分析建立了其适定性与不适定性。本文进一步扩展该理论基础，证明了截断版HOHL的一致性，并推导出在全监督学习中作为正则项使用时的显式收敛速率。实验表明，该方法在主动学习及缺乏底层几何结构的数据集上均表现出强大性能，凸显其在多样学习场景中的通用性与鲁棒性。
原文摘要 · Abstract (English)
Higher-Order Hypergraph Learning (HOHL) was recently introduced as a principled alternative to classical hypergraph regularization, enforcing higher-order smoothness via powers of multiscale Laplacians induced by the hypergraph structure. Prior work established the well- and ill-posedness of HOHL through an asymptotic consistency analysis in geometric settings. We extend this theoretical foundation by proving the consistency of a truncated version of HOHL and deriving explicit convergence rates when HOHL is used as a regularizer in fully supervised learning. We further demonstrate its strong empirical performance in active learning and in datasets lacking an underlying geometric structure, highlighting HOHL's versatility and robustness across diverse learning settings.
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