{"ID":2894313,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.11106","arxiv_id":"2507.11106","title":"A Mathematical Optimization Approach to Multisphere Support Vector Data Description","abstract":"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.","short_abstract":"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....","url_abs":"https://arxiv.org/abs/2507.11106","url_pdf":"https://arxiv.org/pdf/2507.11106v1","authors":"[\"Víctor Blanco\",\"Inmaculada Espejo\",\"Raúl Páez\",\"Antonio M. Rodríguez-Chía\"]","published":"2025-07-15T08:57:27Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\"]","methods":"[]","has_code":false}