One-Class Classification (OCC) is a supervised learning technique for classification whereby the classifier is obtained only by training the objects from the target class and identifying whether new observations belong to the class or not. In this paper, we propose a novel approach to OCC, which is based on optimal covering of the target objects by ‘good’ norm balls. The proposed classifier consists of the selected norm balls from an integer programming model where the finite norm ball candidates from the target objects are used. Computational experiments were carried out to examine the performance and characteristics of the proposed classifier using artificial and real data from the UCI Repository. The results showed that the proposed model was comparable to existing OCC methods in the comparison group. In addition, the proposed model demonstrated high sparsity leading to low testing burden and robustness to noises.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Beck, M. T., Werner, M., Feld, S., & Schimper, T. (2014). Mobile edge computing: A taxonomy
Bishop, C. M. (1994). Novelty detection and neural network validation. IEE Proceedings-Vision, Image and Signal processing, 141, 217–222.
Bishop, C. M. (1995). Neural networks for pattern recognition. Oxford: Oxford University Press.
Cabral, G. G., Oliveira, A. L., & Cahu, C. B. (2009). Combining nearest neighbor data description and structural risk minimization for one-class classification. Neural Computing and Applications, 18, 175–183.
Chen, H. S., & Becerra, V. M. (2016). Sparse density estimator with tunable kernels. Neurocomputing, 173, 1976–1982.
Conforti, M., Cornuejols, G., & Zambelli, G. (2014). Integer programming (Vol. 271). Berlin: Springer.
Duda, R. O., Hart, P. E., & Stork, D. G. (2012). Pattern classification. New Jersy: John Wiley and Sons.
Eckstein, J., Hammer, P. L., Liu, Y., Nediak, M., & Simeone, B. (2002). The maximum box problem and its application to data analysis. Computational Optimization and Applications, 23, 285–298.
Gaber, M. M., Gomes, J. B., & Stahl, F. (2014). Pocket data mining, big data on small devices. Series: Studies in big data
Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical learning with sparsity. Boca Raton: CRC Press.
Japkowicz, N., Myers, C., Gluck, M., et al. (1995). A novelty detection approach to classification. IJCAI, 1, 518–523.
Jeong, K., & Choi, J. Y. (2015). Design of one-class classifier using hyper-rectangles. Journal of Korean Institute of Industrial Engineers, 41, 439–446.
Letouzey, F., Denis, F., & Gilleron, R. (2000). Learning from positive and unlabeled examples, in Algorithmic Learning Theory (pp. 71–85). Berlin: Springer.
Li, C., Zhang, Y., & Li, X. (2009). Ocvfdt: one-class very fast decision tree for one-class classification of data streams, In Proceedings of the Third International Workshop on Knowledge Discovery from Sensor Data, ACM, pp. 79–86.
Lichman, M. (2013). UCI machine learning repository, http://archive.ics.uci.edu/ml
Manevitz, L., & Yousef, M. (2007). One-class document classification via neural networks. Neurocomputing, 70, 1466–1481.
Nguyen, G.H., Bouzerdoum, A., & Phung, S.L. (2009). Learning pattern classification tasks with imbalanced data sets, in Pattern Recognition, InTCH
Parzen, E. (1962). On estimation of a probability density function and mode. The annals of mathematical statistics, 33, 1065–1076.
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., et al. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12, 2825–2830.
Ritter, G., & Gallegos, M. T. (1997). Outliers in statistical pattern recognition and an application to automatic chromosome classification. Pattern Recognition Letters, 18, 525–539.
Schölkopf, B., Williamson, R. C., Smola, A. J., Shawe-Taylor, J., Platt, J. C., et al. (1999). Support vector method for novelty detection. NIPS, 12, 582–588.
Serafini, P. (2014). Classifying negative and positive points by optimal box clustering. Discrete Applied Mathematics, 165, 270–282.
Skabar, A. (2003). Single-class classifier learning using neural networks: An application to the prediction of mineral deposits. In Machine Learning and Cybernetics, 2003 International Conference on, IEEE, Vol. 4, pp. 2127–2132.
Tax, D.M. (2001) One-class classification, Ph.D Thesis, Delft University of Technology
Tax, D. M., & Duin, R. P. (1999). Data domain description using suppor vectors. ESANN, 99, 251–256.
Tax, D. M., & Duin, R. P. (2000). Data description in subspaces, in Pattern Recognition, 2000. Proceedings. 15th International Conference on, vol. 2, IEEE, pp. 672–675.
Tax, D. M., & Duin, R. P. (2004). Support vector data description. Machine learning, 54, 45–66.
Thornhill, N. F., Patwardhan, S. C., & Shah, S. L. (2008). A continuous stirred tank heater simulation model with applications. Journal of Process Control, 18, 347–360.
Thornhill, N. F., Patwardhan, S. C., & Shah, S. L. (2013). The continuous stirred tank heater simulation, http://personalpages.ps.ic.ac.uk/~nina/CSTHSimulation/index.htm.
Tsai, C. F., Hsu, Y. F., Lin, C. Y., & Lin, W. Y. (2009). Intrusion detection by machine learning: A review. Expert Systems with Applications, 36, 11994–12000.
Xpress, (2017). Xpress 8.0, http://www.fico.com/en.
Yu, H., Han, J., & Chang, K.-C. (2004). Pebl: Web page classification without negative examples. IEEE Transactions on Knowledge and Data Engineering, 16, 70–81.
Yu, H., Zhai, C., & Han, J. (2003). Text classification from positive and unlabeled documents, In Proceedings of the twelfth international conference on Information and knowledge management, ACM, pp. 232–239.
Zhou, J., Chan, K., Chong, V., & Krishnan, S. M. (2006). Extraction of brain tumor from mri images using one-class support vector machine, in Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference of the, IEEE, pp. 6411-6414
The authors are grateful for the valuable comments from anonymous reviewers. This work was supported in part by the National Research Foundation of Korea Grant (No. NRF-2019R1F1A1042307) and in part by the National Research Foundation of Korea Grant (No. NRF-2018R1A2B2003227). In addition, this work was supported in part by BK21 FOUR (Brain Korea 21 Fostering Outstanding Universities for Research) in Interdisciplinary Program of Arts & Design Technology, Chonnam National University.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Kim, S., Lee, K. & Jeong, YS. Norm ball classifier for one-class classification. Ann Oper Res (2021). https://doi.org/10.1007/s10479-021-03964-x
- Norm ball
- One-class classification
- Integer programming
- Set covering problem