提出新型哈尔回拉普拉斯矩阵，提升有向图的信号处理能力。
Haar-Laplacian for directed graphs
- 基于类哈尔变换构造满足谱图理论的埃尔米特矩阵
- 在有向图权重预测与去噪任务中性能优于现有方法
- 适合需要方向敏感性的图学习与信号处理场景
本文提出一种新型拉普拉斯矩阵，旨在构建谱卷积网络并拓展有向图的信号处理应用。该方法受类哈尔变换启发，生成一个与邻接矩阵一一对应、同时保留方向与权重信息的埃尔米特矩阵，具备缩放鲁棒性、灵敏度、连续性及方向性等优良特性。从理论角度支持其符合谱图理论，并应用于两个场景：图学习（引入基于该拉普拉斯矩阵的HaarNet谱图卷积网络）与图信号处理。实验表明，在有向图的权重预测与去噪任务中，本方法表现更优。
原文摘要 · Abstract (English)
This paper introduces a novel Laplacian matrix aiming to enable the construction of spectral convolutional networks and to extend the signal processing applications for directed graphs. Our proposal is inspired by a Haar-like transformation and produces a Hermitian matrix which is not only in one-to-one relation with the adjacency matrix, preserving both direction and weight information, but also enjoys desirable additional properties like scaling robustness, sensitivity, continuity, and directionality. We take a theoretical standpoint and support the conformity of our approach with the spectral graph theory. Then, we address two use-cases: graph learning (by introducing HaarNet, a spectral graph convolutional network built with our Haar-Laplacian) and graph signal processing. We show that our approach gives better results in applications like weight prediction and denoising on directed graphs.
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。