用超平面排列统一建模多分类，效率更高且支持非线性边界。
A Unified Optimization Framework for Multiclass Classification with Structured Hyperplane Arrangements
- 基于超平面排列构建优化模型，保留SVM核心思想。
- 在UCI数据集上性能媲美scikit-learn最新方法，计算更快。
- 支持树结构、稀疏特征选择等复杂几何结构，适合大规模问题。
本文提出一种基于超平面排列的新型多分类优化模型。该方法在保持支持向量机（SVM）最大化类别分离与最小化误分类的核心理念基础上，计算效率优于先前的公式。我们还提出了基于核函数的扩展，可构造非线性决策边界。此外，框架能自然融合分类树、ℓ_p-SVM以及具有离散特征选择的模型等替代几何结构。为应对大规模实例，我们设计了一种利用所提MIP公式的动态聚类启发式算法。大量实验表明，该模型及启发式算法在合成数据集和来自UCI机器学习库的真实基准上均表现出高效性，分类性能与scikit-learn中的先进实现相当。
原文摘要 · Abstract (English)
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, $\ell_p$-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 scikit-learn.
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