提出高效求解超图p-拉普拉斯方程的新方法，提升数据插值与半监督学习性能。
Hypergraph $p$-Laplacian equations for data interpolation and semi-supervised learning
- 从p-拉普拉斯正则化导出超图方程，解决非可微与解不唯一难题。
- 简化方程有效抑制插值中的尖峰现象，半监督分类准确率显著提升。
- 计算成本极低，适合大规模数据应用，适合做图像/图学习研究者参考。
超图学习结合p-拉普拉斯正则化因能灵活建模数据中的高阶关系而受到广泛关注。本文聚焦其快速数值实现，挑战在于目标函数不可微及最小化解不唯一。我们从p-拉普拉斯正则化的次微分推导出超图p-拉普拉斯方程，并提出一个数学适定且计算高效的简化版本。数值实验表明，该简化方程能有效抑制数据插值中的尖峰解，提升半监督学习的分类准确率。其显著降低的计算开销为更多实际应用提供了可能。
原文摘要 · Abstract (English)
Hypergraph learning with $p$-Laplacian regularization has attracted a lot of attention due to its flexibility in modeling higher-order relationships in data. This paper focuses on its fast numerical implementation, which is challenging due to the non-differentiability of the objective function and the non-uniqueness of the minimizer. We derive a hypergraph $p$-Laplacian equation from the subdifferential of the $p$-Laplacian regularization. A simplified equation that is mathematically well-posed and computationally efficient is proposed as an alternative. Numerical experiments verify that the simplified $p$-Laplacian equation suppresses spiky solutions in data interpolation and improves classification accuracy in semi-supervised learning. The remarkably low computational cost enables further applications.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。