Data Driven Constraints for the SVM

Abstract

We propose a generalized data driven constraint for support vector machines exemplified by classification of paired observations in general and specifically on the human ear canal. This is particularly interesting in dynamic cases such as tissue movement or pathologies developing over time. Assuming that two observations of the same subject in different states span a vector, we hypothesise that such structure of the data contains implicit information which can aid the classification, thus the name data driven constraints. We derive a constraint based on the data which allow for the use of the ℓ₁-norm on the constraint while still allowing for the application of kernels. We specialize the proposed constraint to orthogonality of the vectors between paired observations and the estimated hyperplane. We show that imposing the constraint of orthogonality on the paired data yields a more robust classifier solution, compared to the SVM i.e. reduces variance and improves classification rates. We present a quantitative measure of the information level contained in the pairing and test the method on simulated as well as a high-dimensional paired data set of ear-canal surfaces.