A Unified Optimization Framework for Multiclass Classification with Structured Hyperplane Arrangements
This work addresses multiclass classification problems for machine learning practitioners, offering an incremental improvement by integrating existing methods into a more flexible and scalable framework.
The paper tackles multiclass classification by proposing a unified optimization framework based on hyperplane arrangements, which extends SVM principles to handle various geometric structures and scales efficiently with a dynamic clustering heuristic. It demonstrates competitive performance on synthetic and UCI datasets, with computational experiments showing efficiency gains.
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.