Margin Optimal Classification Trees

New optimization models for optimal classification trees

“…The aim is to build a robust tree classier, where the splitting rules are based on the possibility of relabeling some samples as described in [Blanco et al, 2022a]. Finally, in [D'Onofrio et al, 2022] a novel mixed-integer quadratic formulation to train multivariate optimal classication trees which employ maximum margin hyperplanes by following the soft SVM paradigm is introduced. In our case, we are only interested to focus on the post-processing phase for our formulations, in contrast to the approaches mentioned above that include the full process of computing an OCT.…”

Mixed-integer programming techniques for the minimum sum-of-squares clustering problem

“…Verwer and Zhang (2019) propose a binary linear formulation in which the problem size is largely independent of the size of the training data. MIP approaches that consider support vector machines (Cortes and Vapnik 1995) to split the tree also have been explored, as can be seen in Blanco et al (2022a), Blanco et al (2022b), andD'Onofrio et al (2023).…”