Haar-Laplacian for directed graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914068700332032 |
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| author | Badea, Theodor-Adrian Dumitrescu, Bogdan |
| author_facet | Badea, Theodor-Adrian Dumitrescu, Bogdan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15527 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Haar-Laplacian for directed graphs Badea, Theodor-Adrian Dumitrescu, Bogdan Machine Learning Social and Information Networks 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. |
| title | Haar-Laplacian for directed graphs |
| topic | Machine Learning Social and Information Networks |
| url | https://arxiv.org/abs/2411.15527 |