Haar-Laplacian for directed graphs

• URL: http://arxiv.org/abs/2411.15527v2
• Date: Fri, 26 Sep 2025 18:55:58 GMT
• Title: Haar-Laplacian for directed graphs
• Authors: Theodor-Adrian Badea, Bogdan Dumitrescu,
• Abstract summary: This paper introduces a novel Laplacian matrix aiming to enable the construction of spectral convolutional networks.<n>We show that our approach gives better results in applications like weight prediction and denoising on directed graphs.
• Score: 0.9167082845109437
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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