Abstract
Classification with reject option allows classifiers to abstain from the classification of unclear cases. While it has been shown that global reject options are optimal for probabilistic classifiers, local reject schemes can enhance the performance of deterministic classifiers which do not provide faithful probability estimates [6, 10]. A first efficient scheme how to optimise local threshold parameters has recently been introduced [8]. In this contribution, we improve and simplify this scheme by restricting to a fewer number of possible candidates, and we demonstrate its performance for a one-versus-rest SVM classifier. Further, we have a glimpse at accompanying generalisation bounds.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bartlett, P.L., Mendelson, S.: Rademacher and gaussian complexities: risk bounds and structural results. J. Mach. Learn. Res. 3, 463–482 (2002)
Bartlett, P.L., Wegkamp, M.H.: Classification with a reject option using a hinge loss. J. Mach. Learn. Res. 9, 1823–1840 (2008)
Chang, C.-C., Lin, C.-J.: Libsvm: a library for support vector machines. ACM Trans. Intell. Syst. Technol. 2(3), 27:1–27:27 (2011)
Chow, C.: On optimum recognition error and reject tradeoff. IEEE Trans. Inf. Theor. 16(1), 41–46 (2006)
Dudzinski, K., Walukiewicz, S.: Exact methods for the knapsack problem and its generalizations. Eur. J. Oper. Res. 28(1), 3–21 (1987)
Fischer, L., Hammer, B., Wersing, H.: Local rejection strategies for learning vector quantization. In: Wermter, S., Weber, C., Duch, W., Honkela, T., Koprinkova-Hristova, P., Magg, S., Palm, G., Villa, A.E.P. (eds.) ICANN 2014. LNCS, vol. 8681, pp. 563–570. Springer, Heidelberg (2014)
Fischer, L., Hammer, B., Wersing, H.: Combining offline and online classifiers for life-long learning. In: IJCNN (2015)
Fischer, L., Hammer, B., Wersing, H.: Optimum local rejection for classifiers. Neurocomputing (accepted 2016)
Fischer, L., Nebel, D., Villmann, T., Hammer, B., Wersing, H.: Rejection strategies for learning vector quantization – a comparison of probabilistic and deterministic approaches. In: Villmann, T., Schleif, F.-M., Kaden, M., Lange, M. (eds.) Advances in Self-Organizing Maps and Learning. AISC, vol. 295, pp. 109–118. Springer, Heidelberg (2014)
Fumera, G., Roli, F., Giacinto, G.: Reject option with multiple thresholds. Pattern Recogn. 33, 2099–2101 (2000)
Hansen, L.K., Liisberg, C., Salamon, P.: The error-reject tradeoff. Open Syst. Inf. Dynamics 4(2), 159–184 (1997)
Herbei, R., Wegkamp, M.H.: Classification with reject option. Can. J. Stat. 34(4), 709–721 (2006)
Hsu, C.-W., Lin, C.-J.: A comparison of methods for multiclass support vector machines. Trans. Neur. Netw. 13(2), 415–425 (2002)
Koltchinskii, V., Panchenko, D., Lozano, F.: Some new bounds on the generalization error of combined classifiers. In: Advances in Neural Information Processing Systems 13, Papers from Neural Information Processing Systems (NIPS) 2000, Denver, CO, USA, pp. 245–251 (2000)
Lei, Y., Dogan, Ü., Binder, A., Kloft, M.: Multi-class SVMs: from tighter data-dependent generalization bounds to novel algorithms. CoRR, abs/1506.04359 (2015)
Maximov, Y., Reshetova, D.: Tight risk bounds for multi-class margin classifiers. CoRR, abs/1507.03040 (2015)
Platt, J.C.: Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In: Advances in Large Margin Classifiers, pp. 61–74. MIT Press (1999)
Ramaswamy, H.G., Tewari, A., Agarwal, S.: Consistent algorithms for multiclass classification with a reject option. CoRR, abs/1505.04137 (2015)
Villmann, T., Kaden, M., Bohnsack, A., Villmann, J.-M., Drogies, T., Saralajew, S., Hammer, B.: Self-adjusting reject options in prototype based classification. In: Workshop on Self-Organizing Maps (2015)
Wu, T.-F., Lin, C.-J., Weng, R.C.: Probability estimates for multi-class classification by pairwise coupling. J. Mach. Learn. Res. 5, 975–1005 (2004)
Yuan, M., Wegkamp, M.H.: Classification methods with reject option based on convex risk minimization. J. Mach. Learn. Res. 11, 111–130 (2010)
Acknowledgement
Funding by the CITEC centre of excellence is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Kummert, J., Paassen, B., Jensen, J., Göpfert, C., Hammer, B. (2016). Local Reject Option for Deterministic Multi-class SVM. In: Villa, A., Masulli, P., Pons Rivero, A. (eds) Artificial Neural Networks and Machine Learning – ICANN 2016. ICANN 2016. Lecture Notes in Computer Science(), vol 9887. Springer, Cham. https://doi.org/10.1007/978-3-319-44781-0_30
Download citation
DOI: https://doi.org/10.1007/978-3-319-44781-0_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-44780-3
Online ISBN: 978-3-319-44781-0
eBook Packages: Computer ScienceComputer Science (R0)