Power Spectrum Signatures of Graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866915198570332160 |
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| author | Djima, Karamatou Yacoubou Yim, Ka Man |
| author_facet | Djima, Karamatou Yacoubou Yim, Ka Man |
| contents | Point signatures based on the Laplacian operators on graphs, point clouds, and manifolds have become popular tools in machine learning for graphs, clustering, and shape analysis. In this work, we propose a novel point signature, the power spectrum signature, a measure on $\mathbb{R}$ defined as the squared graph Fourier transform of a graph signal. Unlike eigenvectors of the Laplacian from which it is derived, the power spectrum signature is invariant under graph automorphisms. We show that the power spectrum signature is stable under perturbations of the input graph with respect to the Wasserstein metric. We focus on the signature applied to classes of indicator functions, and its applications to generating descriptive features for vertices of graphs. To demonstrate the practical value of our signature, we showcase several applications in characterizing geometry and symmetries in point cloud data, and graph regression problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power Spectrum Signatures of Graphs Djima, Karamatou Yacoubou Yim, Ka Man Machine Learning Social and Information Networks Point signatures based on the Laplacian operators on graphs, point clouds, and manifolds have become popular tools in machine learning for graphs, clustering, and shape analysis. In this work, we propose a novel point signature, the power spectrum signature, a measure on $\mathbb{R}$ defined as the squared graph Fourier transform of a graph signal. Unlike eigenvectors of the Laplacian from which it is derived, the power spectrum signature is invariant under graph automorphisms. We show that the power spectrum signature is stable under perturbations of the input graph with respect to the Wasserstein metric. We focus on the signature applied to classes of indicator functions, and its applications to generating descriptive features for vertices of graphs. To demonstrate the practical value of our signature, we showcase several applications in characterizing geometry and symmetries in point cloud data, and graph regression problems. |
| title | Power Spectrum Signatures of Graphs |
| topic | Machine Learning Social and Information Networks |
| url | https://arxiv.org/abs/2503.09660 |