# Multiclass Optimal Classification Trees with SVM-splits

arXiv: https://arxiv.org/abs/2111.08674 · HTML: https://mlsanity.com/paper/2111.08674/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 66 references that are in the map.
- First posted on arXiv 16 Nov 2021.

## Builds on (most cited first, 12 of 12)

- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model](https://mlsanity.com/paper/1511.01644/) (2015)
- [Optimal Sparse Decision Trees](https://mlsanity.com/paper/1904.12847/) (2019)
- [Generalized and Scalable Optimal Sparse Decision Trees](https://mlsanity.com/paper/2006.08690/) (2020)
- [MurTree: Optimal Classification Trees via Dynamic Programming and Search](https://mlsanity.com/paper/2007.12652/) (2020)
- [Computing Optimal Decision Sets with SAT](https://mlsanity.com/paper/2007.15140/) (2020)
- [Optimal randomized classification trees](https://mlsanity.com/paper/2110.11952/) (2021)
- [Optimal Decision Trees for Nonlinear Metrics](https://mlsanity.com/paper/2009.06921/) (2020)
- [A novel embedded min-max approach for feature selection in nonlinear support vector machine classification](https://mlsanity.com/paper/2004.09863/) (2020)
- [Robust Optimal Classification Trees under Noisy Labels](https://mlsanity.com/paper/2012.08560/) (2020)
- [A Mathematical Programming approach to Binary Supervised Classification with Label Noise](https://mlsanity.com/paper/2004.10170/) (2020)
- [A Branch-and-Price approach for the Continuous Multifacility Monotone Ordered Median Problem](https://mlsanity.com/paper/2108.00407/) (2021)

## Built on by (most cited first, 6 of 6)

- [Margin Optimal Classification Trees](https://mlsanity.com/paper/2210.10567/) (2022)
- [An improved column-generation-based matheuristic for learning classification trees](https://mlsanity.com/paper/2308.11477/) (2023)
- [A Mathematical Programming Approach to Optimal Classification Forests](https://mlsanity.com/paper/2211.10502/) (2022)
- [ODTE -- An ensemble of multi-class SVM-based oblique decision trees](https://mlsanity.com/paper/2411.13376/) (2024)
- [Local Duality for Sparse Support Vector Machines](https://mlsanity.com/paper/2601.20170/) (2026)
- [Hierarchical Support Vector State Partitioning for Distilling Black Box Reinforcement Learning Policies](https://mlsanity.com/paper/2605.04254/) (2026)

## Abstract (arXiv)

In this paper we present a novel mathematical optimization-based methodology to construct tree-shaped classification rules for multiclass instances. Our approach consists of building Classification Trees in which, except for the leaf nodes, the labels are temporarily left out and grouped into two classes by means of a SVM separating hyperplane. We provide a Mixed Integer Non Linear Programming formulation for the problem and report the results of an extended battery of computational experiments to assess the performance of our proposal with respect to other benchmarking classification methods.