Minimizing the error of linear separators on linearly inseparable data

Boris Aronov, Delia Garijo, Yurai Núñez-Rodríguez, David Rappaport, Carlos Seara, Jorge Urrutia
2012 Discrete Applied Mathematics  
Given linearly inseparable sets R of red points and B of blue points, we consider several measures of how far they are from being separable. Intuitively, given a potential separator ("classifier"), we measure its quality ("error") according to how much work it would take to move the misclassified points across the classifier to yield separated sets. We consider several measures of work and provide algorithms to find linear classifiers that minimize the error under these different measures.
doi:10.1016/j.dam.2012.03.009 fatcat:2bl4zouehvdufbwunw6xqvztu4