Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909652524990464 |
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| author | Anh, Le Vu Dik, Mehmet Anh, Nguyen Viet |
| author_facet | Anh, Le Vu Dik, Mehmet Anh, Nguyen Viet |
| contents | Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters. We introduce a boundary-weighted operator that rescales each edge according to how far its endpoints drift toward the graph's Gromov boundary. Using Busemann functions on delta-hyperbolic networks, we prove a closed-form upper bound on the operator's spectral norm: every signal loses a curvature-controlled fraction of its energy at each pass. The result delivers a parameter-free, lightweight filter whose stability follows directly from geometric first principles, offering a new analytic tool for graph signal processing on data with dense or hidden hierarchical structure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_15464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs Anh, Le Vu Dik, Mehmet Anh, Nguyen Viet Metric Geometry Information Theory Machine Learning Social and Information Networks Hierarchical graphs often exhibit tree-like branching patterns, a structural property that challenges the design of traditional graph filters. We introduce a boundary-weighted operator that rescales each edge according to how far its endpoints drift toward the graph's Gromov boundary. Using Busemann functions on delta-hyperbolic networks, we prove a closed-form upper bound on the operator's spectral norm: every signal loses a curvature-controlled fraction of its energy at each pass. The result delivers a parameter-free, lightweight filter whose stability follows directly from geometric first principles, offering a new analytic tool for graph signal processing on data with dense or hidden hierarchical structure. |
| title | Spectral Contraction of Boundary-Weighted Filters on delta-Hyperbolic Graphs |
| topic | Metric Geometry Information Theory Machine Learning Social and Information Networks |
| url | https://arxiv.org/abs/2506.15464 |