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arXiv · 2507.11106

A Mathematical Optimization Approach to Multisphere Support Vector Data Description

Víctor Blanco·Inmaculada Espejo·Raúl Páez·Antonio M. Rodríguez-Chía
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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.

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Víctor Blanco, Inmaculada Espejo, Raúl Páez, Antonio M. Rodríguez-Chía. 2025-07-15. A Mathematical Optimization Approach to Multisphere Support Vector Data Description. https://arxiv.org/abs/2507.11106

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