Multicategory Support Vector Machines

Two-category support vector machines (SVM) have been very popular in the machine learning community for classification problems. Solving multicategory problems by a series of binary classifiers is quite common in the SVM paradigm; however, this approach may fail under various circumstances. We propose the multicategory support vector machine (MSVM), which extends the binary SVM to the multicategory case and has good theoretical properties. The proposed method provides a unifying framework when there are either equal or unequal misclassification costs. As a tuning criterion for the MSVM, an approximate leave-one-out cross-validation function, called Generalized Approximate Cross Validation, is derived, analogous to the binary case. The effectiveness of the MSVM is demonstrated through the applications to cancer classification using microarray data and cloud classification with satellite radiance profiles.