Joint Simplicial Complex Learning via Binary Linear Programming
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912888238637056 |
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| author | Sarathchandran, Varun Leus, Geert |
| author_facet | Sarathchandran, Varun Leus, Geert |
| contents | Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet learning their structure is challenging due to the strong coupling across different simplicial levels imposed by the inclusion property. In this work, we propose a joint framework for simplicial complex learning that enforces the inclusion property through a linear constraint, enabling the formulation of the problem as a binary linear program. The objective function consists of a combination of smoothness measures across all considered simplicial levels, allowing for the incorporation of arbitrary smoothness criteria. This formulation enables the simultaneous estimation of edges and higher-order simplices within a single optimization problem. Experiments on simulated and real-world data demonstrate that the proposed joint approach outperforms hierarchical and greedy baselines, while more faithfully enforcing higher-order structural priors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07896 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Joint Simplicial Complex Learning via Binary Linear Programming Sarathchandran, Varun Leus, Geert Signal Processing Learning the topology of higher-order networks from data is a fundamental challenge in many signal processing and machine learning applications. Simplicial complexes provide a principled framework for modeling multi-way interactions, yet learning their structure is challenging due to the strong coupling across different simplicial levels imposed by the inclusion property. In this work, we propose a joint framework for simplicial complex learning that enforces the inclusion property through a linear constraint, enabling the formulation of the problem as a binary linear program. The objective function consists of a combination of smoothness measures across all considered simplicial levels, allowing for the incorporation of arbitrary smoothness criteria. This formulation enables the simultaneous estimation of edges and higher-order simplices within a single optimization problem. Experiments on simulated and real-world data demonstrate that the proposed joint approach outperforms hierarchical and greedy baselines, while more faithfully enforcing higher-order structural priors. |
| title | Joint Simplicial Complex Learning via Binary Linear Programming |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2602.07896 |