Friday, 11:00 - 11:25 h, Room: H 2013


James Brooks
Counting misclassifications: Robust support vector machines via integer programming


The support vector machine (SVM) for classification is a method for generating rules for assigning data points to categories. The traditional formulation is commonly expressed as a convex quadratic program where the error for an observation is based on its distance to the separating boundary in the feature space. In the interest of enhancing the robustness to outlier observations, we present two formulations that reflect the notion that errors should be counted.
Convex quadratic integer programming formulations are presented for the ramp loss and hard margin loss SVM. We show that the formulations accommodate the kernel trick for SVM while preserving the original geometric interpretation. Solution methods are presented for the formulations, including facets for the convex hull of integer feasible solutions. The consistency of SVM with the alternative loss functions is established. Computational tests indicate that the proposed formulations produce better classification rules on datasets containing unbalanced outliers.


Talk 2 of the invited session Fri.1.H 2013
"Integer programming in data mining" [...]
Cluster 11
"Integer & mixed-integer programming" [...]


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