Multicategory large margin classification with unequal costs

In this paper, we propose a multicategory large margin classification with unequal costs. In addition to extending the standard multicategory SVM to the case of unequal costs, we also develop an unequal costs classification for psi-loss and propose an efficient algorithm for computation. Besides commonly used L-2 penalty, the adaptive LASSO is also examined to remove irrelevant variables. Theoretically, we derive the Bayes rules under the generalized cost and reduce the infinite sum-to-zero constraint to a finite constraint. Numerically, we demonstrate the good performance of our methodology on two simulated examples and one real-life dataset.