Rough set based 1-v-1 and 1-v-r approaches to support vector machine multi-classification

Support vector machines (SVMs) are essentially binary classifiers. To improve their applicability, several methods have been suggested for extending SVMs for multi-classification, including one-versus-one (1-v-1), one-versus-rest (1-v-r) and DAGSVM. In this paper, we first describe how binary classification with SVMs can be interpreted using rough sets. A rough set approach to SVNI classification removes the necessity of exact classification and is especially useful when dealing with noisy data. Next, by utilizing the boundary region in rough sets, we suggest two new approaches, extensions of 1-v-r and 1-v-1, to SVM multi-classification that allow for an error rate. We explicitly demonstrate how our extended 1-v-r may shorten the training time of the conventional 1-v-r approach. In addition, we show that our 1-v-1 approach may have reduced storage requirements compared to the conventional 1-v-1 and DAGSVM techniques. Our techniques also provide better semantic interpretations of the classification process. The theoretical conclusions are supported by experimental findings involving a synthetic dataset. (C) 2007 Elsevier Inc. All rights reserved.