提出可处理高阶与方向关系的超图信号处理框架
A Framework for Directed Hypergraph Signal Processing via tensor t-SVD
- 用张量t-SVD构建有向超图邻接张量
- 实现无损的有向超图傅里叶变换
- 在交通网络去噪中优于传统图和超图方法
我们提出有向超图信号处理（DHGSP），一种统一框架，同时支持高阶（多元）关系和非对称（方向性）关系。通过在t-积代数中使用张量奇异值分解（t-SVD），我们定义了新的有向超图邻接张量、拓扑忠实的移位算子，以及无损的有向超图傅里叶变换（t-DHGFT）。在真实交通网络上的实验表明，DHGSP在去噪任务中优于基于矩阵的（图与有向图）和无向张量基（超图）基线方法。
原文摘要 · Abstract (English)
We introduce Directed Hypergraph Signal Processing (DHGSP), a unified framework that extends graph signal processing to accommodate both higher-order (polyadic) and asymmetric (directional) relationships simultaneously. Using the tensor singular value decomposition (t-SVD) within the t-product algebra, we define a novel adjacency tensor for directed hypergraphs, a topologically faithful shift operator, and a lossless Directed Hypergraph Fourier Transform (t-DHGFT). Experiments on real traffic networks demonstrate that DHGSP outperforms matrix-based (graph and digraph) and undirected tensor-based (hypergraph) baselines in denoising tasks.
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