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We address the issue of classification problems in the following situation: test data include data belonging to unlearned classes. To address this issue, most previous works have taken two-stage strategies where unclear data are detected using an anomaly detection algorithm in the first stage while the rest of data are classified into learned classes using a classification algorithm in the second stage. In this study, we propose anomaly detection support vector machine (ADSVM) which unifies classification and anomaly detection. ADSVM is unique in comparison with the previous work in that it addresses the two problems simultaneously. We also propose a multiclass extension of ADSVM that uses a pairwise voting strategy. We empirically present that ADSVM outperforms two-stage algorithms in application to an real automobile fault dataset, as well as to UCI benchmark datasets.