Support Vector Machines for Unbalanced Multicategory Classification

Classification is a very important research topic and its applications are various, because data can be easily obtained in these days. Among many techniques of classification the support vector machine (SVM) is widely applied to bioinformatics or genetic analysis, because it gives sound theoretical background and its performance is superior to other methods. The SVM can be rewritten by a combination of the hinge loss function and the penalty function. The smoothly clipped absolute deviation penalty function satisfies desirably statistical properties. Since standard SVM techniques typically treat all classes equally, it is not well suited to unbalanced proportion data. We propose a robust method to treat unbalanced cases based on the weights of the class. Simulation and a numerical example show that the proposed method is effective to analyze unbalanced proportion data.