VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915795298156544 |
|---|---|
| author | Johnson, David R. Sietsema, Alexander Anand, Rishabh Needell, Deanna Krishnaswamy, Smita Perlmutter, Michael |
| author_facet | Johnson, David R. Sietsema, Alexander Anand, Rishabh Needell, Deanna Krishnaswamy, Smita Perlmutter, Michael |
| contents | We introduce vector diffusion wavelets (VDWs), a novel family of wavelets inspired by the vector diffusion maps algorithm that was introduced to analyze data lying in the tangent bundle of a Riemannian manifold. We show that these wavelets may be effectively incorporated into a family of geometric graph neural networks, which we refer to as VDW-GNNs. We demonstrate that such networks are effective on synthetic point cloud data, as well as on real-world data derived from wind-field measurements and neural activity data. Theoretically, we prove that these new wavelets have desirable frame theoretic properties, similar to traditional diffusion wavelets. Additionally, we prove that these wavelets have desirable symmetries with respect to rotations and translations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01022 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks Johnson, David R. Sietsema, Alexander Anand, Rishabh Needell, Deanna Krishnaswamy, Smita Perlmutter, Michael Machine Learning Signal Processing 68T07 I.5.1; I.2.6 We introduce vector diffusion wavelets (VDWs), a novel family of wavelets inspired by the vector diffusion maps algorithm that was introduced to analyze data lying in the tangent bundle of a Riemannian manifold. We show that these wavelets may be effectively incorporated into a family of geometric graph neural networks, which we refer to as VDW-GNNs. We demonstrate that such networks are effective on synthetic point cloud data, as well as on real-world data derived from wind-field measurements and neural activity data. Theoretically, we prove that these new wavelets have desirable frame theoretic properties, similar to traditional diffusion wavelets. Additionally, we prove that these wavelets have desirable symmetries with respect to rotations and translations. |
| title | VDW-GNNs: Vector diffusion wavelets for geometric graph neural networks |
| topic | Machine Learning Signal Processing 68T07 I.5.1; I.2.6 |
| url | https://arxiv.org/abs/2510.01022 |