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 ψ-loss and propose an efficient algorithm for computation. Besides commonly used L2 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. [ABSTRACT FROM AUTHOR]