IEEE TRANSACTIONS ON NEURAL NETWORKS, VOL. 13, NO. 2, MARCH 2002415A Comparison of Methods for MulticlassSupport Vector MachinesChih-Wei Hsu and Chih-Jen LinAbstract— Support vector machines (SVMs) were originallydesigned for binary classification. How to effectively extend it formulticlass classification is still an ongoing research issue. Severalmethods have been proposed where typically we construct amulticlass classifier by combining several binary classifiers. Someauthors also proposed methods that consider all classes at once. Asit is computationally more expensive to solve multiclass problems,comparisons of these methods using large-scale problems havenot been seriously conducted. Especially for methods solvingmulticlass SVM in one step, a much larger optimization problemis required so up to now experiments are limited to small data sets.In this paper we give decomposition implementations for two such“all-together” methods. We then compare their performance withthree methods based on binary classifications: “one-against-all,”“one-against-one,” and directed acyclic graph SVM (DAGSVM).Our experiments indicate that the “one-against-one” and DAGmethodsare more suitable for practical use than the othermethods. Results also show that for large problems methods byconsidering all data at once in general need fewer support vectors.Index Terms— Decomposition methods, multiclass classification,support vector machines (SVMs).I. INTRODUCTIONSUPPORT vector machines (SVMs) [6] were originally de-signed for binary classification. How to effectively extendit for multiclass classification is still an ongoing research issue.Currently there are two types of approaches for multiclass SVM.One is by constructing and combining several binary classifie...
