A unified optimization framework for multiclass classification with structured hyperplane arrangements
提出一个基于超平面排列的多类分类优化模型，保留SVM最大化类间间隔的核心，计算效率更高，并支持核扩展、分类树等结构，通过动态聚类启发式算法处理大规模问题。
Abstract In this paper, we propose a new mathematical optimization model for multiclass classification based on arrangements of hyperplanes. Our approach preserves the core support vector machine (SVM) paradigm of maximizing class separation while minimizing misclassification errors, and it is computationally more efficient than a previous formulation. We present a kernel-based extension that allows it to construct nonlinear decision boundaries. Furthermore, we show how the framework can naturally incorporate alternative geometric structures, including classification trees, $$\ell _p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:math> -SVMs, and models with discrete feature selection. To address large-scale instances, we develop a dynamic clustering matheuristic that leverages the proposed MIP formulation. Extensive computational experiments demonstrate the efficiency of the proposed model and dynamic clustering heuristic, and we report competitive classification performance on both synthetic datasets and real-world benchmarks from the UCI machine learning repository, comparing our method with state-of-the-art implementations available in .