Minimizing the error of linear separators on linearly inseparable data |
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| Authors: | Boris Aronov Delia Garijo Yurai Núñez-Rodríguez David Rappaport Carlos Seara Jorge Urrutia |
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| Affiliation: | 1. Department of Computer Science and Engineering, Polytechnic Institute of NYU, USA;2. Dept. de Matemática Aplicada I, Universidad de Sevilla, Spain;3. Lakes Environmental Software, 60 Bathurst Dr. Unit 6, Waterloo, ON, N2V2A9, Canada;4. School of Computing, Queen’s University, Kingston, Canada;5. Dept. de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Spain;6. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico |
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| Abstract: | Given linearly inseparable sets of red points and 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. |
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