A Mathematical Optimization Approach to Multisphere Support Vector Data Description
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915390739709952 |
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| author | Blanco, Víctor Espejo, Inmaculada Páez, Raúl Rodríguez-Chía, Antonio M. |
| author_facet | Blanco, Víctor Espejo, Inmaculada Páez, Raúl Rodríguez-Chía, Antonio M. |
| contents | We present a novel mathematical optimization framework for outlier detection in multimodal datasets, extending Support Vector Data Description approaches. We provide a primal formulation, in the shape of a Mixed Integer Second Order Cone model, that constructs Euclidean hyperspheres to identify anomalous observations. Building on this, we develop a dual model that enables the application of the kernel trick, thus allowing for the detection of outliers within complex, non-linear data structures. An extensive computational study demonstrates the effectiveness of our exact method, showing clear advantages over existing heuristic techniques in terms of accuracy and robustness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11106 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Mathematical Optimization Approach to Multisphere Support Vector Data Description Blanco, Víctor Espejo, Inmaculada Páez, Raúl Rodríguez-Chía, Antonio M. Optimization and Control Machine Learning We present a novel mathematical optimization framework for outlier detection in multimodal datasets, extending Support Vector Data Description approaches. We provide a primal formulation, in the shape of a Mixed Integer Second Order Cone model, that constructs Euclidean hyperspheres to identify anomalous observations. Building on this, we develop a dual model that enables the application of the kernel trick, thus allowing for the detection of outliers within complex, non-linear data structures. An extensive computational study demonstrates the effectiveness of our exact method, showing clear advantages over existing heuristic techniques in terms of accuracy and robustness. |
| title | A Mathematical Optimization Approach to Multisphere Support Vector Data Description |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2507.11106 |