Abstract
In support vector data description (SVDD) a spherically shaped boundary around a normal data set is used to separate this set from abnormal data. The volume of this data description is minimized to reduce the chance of accepting abnormal data. However the SVDD does not guarantee that the single spherically shaped boundary can best describe the normal data set if there are some distinctive data distributions in this set. A better description is the use of multiple spheres, however there is currently no investigation available. In this paper, we propose a theoretical framework to multi-sphere SVDD in which an optimisation problem and an iterative algorithm are proposed to determine model parameters for multi-sphere SVDD to provide a better data description to the normal data set. We prove that the classification error will be reduced after each iteration in this learning process. Experimental results on 28 well-known data sets show that the proposed multi-sphere SVDD provides lower classification error rate comparing with the standard single-sphere SVDD.
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References
Bishop, C.M.: Novelty detection and neural network validation. In: IEE Proceedings of Vision, Image and Signal Processing, pp. 217–222 (1994)
Barnett, V., Lewis, T.: Outliers in statistical data, 3rd edn. Wiley, Chichester (1978)
Campbell, C., Bennet, K.P.: A linear programming approach to novelty detection. In: Advances in Neural Information Processing Systems, vol. 14 (2001)
Chang, C.-C., Lin, C.-J.: LIBSVM: A Library for Support Vector Machines, http://www.csie.ntu.edu.tw/~cjlinlibsvm
Hao, P.Y., Liu, Y.H.: A New Multi-class Support Vector Machine with Multi-sphere in the Feature Space. In: Okuno, H.G., Ali, M. (eds.) IEA/AIE 2007. LNCS (LNAI), vol. 4570, pp. 756–765. Springer, Heidelberg (2007)
Kubat, M., Matwin, S.: Addressing the curse of imbalanced training set: One-sided selection. In: Proc. 14th International Conference on Machine Learning, pp. 179–186 (1997)
Le, T., Tran, D., Ma, W., Sharma, D.: An Optimal Sphere and Two Large Margins Approach for Novelty Detection. In: Proc. IEEE World Congress on Computational Intelligence (WCCI) (accepted 2010)
Lin, Y., Lee, Y., Wahba, G.: Support vector machine for classification in nonstandard situations. Machine Learning 15, 1115–1148 (2002)
Moya, M.M., Koch, M.W., Hostetler, L.D.: One-class classifier networks for target recognition applications. In: Proceedings of World Congress on Neural Networks, pp. 797–801 (1991)
Mu, T., Nandi, A.K.: Multiclass Classification Based on Extended Support Vector Data Description. IEEE Transactions on Systems, Man, And Cybernetics Part B: Cybernetics 39(5), 1206–1217 (2009)
Parra, L., Deco, G., Miesbach, S.: Statistical independence and novelty detection with information preserving nonlinear maps. Neural Computation 8, 260–269 (1996)
Roberts, S., Tarassenko, L.: A Probabilistic Resource Allocation Network for Novelty Detection. Neural Computation 6, 270–284 (1994)
Schlkopf, B., Smola, A.J.: Learning with kernels. The MIT Press, Cambridge (2002)
Tax, D.M.J., Duin, R.P.W.: Support vector data description. Machine Learning 54, 45–56 (2004)
Tax, D.M.J.: Datasets (2009), http://ict.ewi.tudelft.nl/~davidt/occ/index.html
Towel, G.G.: Local expert autoassociator for anomaly detection. In: Proc. 17th International Conference on Machine Learning, pp. 1023–1030. Morgan Kaufmann Publishers Inc., San Francisco (2000)
Vapnik, V.: The nature of statistical learning theory. Springer, Heidelberg (1995)
Vert, J., Vert, J.P.: Consistency and convergence rates of one class svm and related algorithm. Journal of Machine Learning Research 7, 817–854 (2006)
Xiao, Y., Liu, B., Cao, L., Wu, X., Zhang, C., Hao, Z., Yang, F., Cao, J.: Multi-sphere Support Vector Data Description for Outliers Detection on Multi-Distribution Data. In: Proc. IEEE International Conference on Data Mining Workshops, pp. 82–88 (2009)
Yu, M., Ye, J.: A Small Sphere and Large Margin Approach for Novelty Detection Using Training Data with Outliers. IEEE Transaction on Pattern Analysis and Machine Intelligence 31, 2088–2092 (2009)
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Le, T., Tran, D., Ma, W., Sharma, D. (2010). A Theoretical Framework for Multi-sphere Support Vector Data Description. In: Wong, K.W., Mendis, B.S.U., Bouzerdoum, A. (eds) Neural Information Processing. Models and Applications. ICONIP 2010. Lecture Notes in Computer Science, vol 6444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17534-3_17
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DOI: https://doi.org/10.1007/978-3-642-17534-3_17
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