A Mathematical Optimization Approach to Multisphere Support Vector Data Description

• URL: http://arxiv.org/abs/2507.11106v1
• Date: Tue, 15 Jul 2025 08:57:27 GMT
• Title: A Mathematical Optimization Approach to Multisphere Support Vector Data Description
• Authors: Víctor Blanco, Inmaculada Espejo, Raúl Páez, Antonio M. Rodríguez-Chía,
• Abstract summary: We provide a primal formulation, in the shape of a Mixed Second Order Cone model, that constructs Euclidean hyperspheres to identify anomalous observations.<n>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.
• Score: 1.9499277906326784
• License: http://creativecommons.org/licenses/by/4.0/
• 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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