# A Framework for Directed Hypergraph Signal Processing via tensor t-SVD

arXiv: https://arxiv.org/abs/2606.25112 · HTML: https://mlsanity.com/paper/2606.25112/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 23 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Signal Processing on Directed Graphs](https://mlsanity.com/paper/2008.00586/) (2020)
- [Introducing Hypergraph Signal Processing: Theoretical Foundation and Practical Applications](https://mlsanity.com/paper/1907.09203/) (2019)
- [Graph Fourier transform based on singular value decomposition of directed Laplacian](https://mlsanity.com/paper/2205.06242/) (2022)

## Abstract (arXiv)

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.