Abstract
Rough Sets (RS) and Support Vector Machine (SVM) are the two big and independent research areas in AI. Originally, rough set theory is dealing with the concept approximation problem under uncertainty. The basic idea of RS is related to lower and upper approximations, and it can be applied in classification problem. At the first sight RS and SVM offer different approaches to classification problem. Most RS methods are based on minimal decision rules, while SVM converts the linear classifiers into instance based classifiers. This paper presents a comparison analysis between these areas and shows that, despite differences, there are quite many analogies in the two approaches. We will show that some rough set classifiers are in fact the SVM with Boolean kernel and propose some hybrid methods that combine the advantages of those two great machine learning approaches.
Research supported by Polish National Science Centre (NCN) grants DEC-2011/01/B/ST6/03867 and DEC-2012/05/B/ST6/03215, and the grant SYNAT - SP/I/1/77065/10 in frame of strategic scientific research and experimental development program: “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information” founded by Polish National Centre for Research and Development (NCBiR).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Asharaf, S., Shevade, S.K., Murty, N.M.: Rough support vector clustering. Pattern Recognition 38(10), 1779–1783 (2005)
Bazan, J.: A Comparison of Dynamic and non-Dynamic Rough Set Methods for Extracting Laws from Decision Tables. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1: Methodology and Applications. STUDFUZZ, vol. 18, pp. 321–365. Springer, Heidelberg (1998)
Chen, H.-L., Yang, B., Liu, J., Liu, D.-Y.: A support vector machine classifier with rough set-based feature selection for breast cancer diagnosis. Expert Systems with Applications 38(7), 9014–9022 (2011)
Honghai, F., Baoyan, L., Cheng, Y., Ping, L., Bingru, Y., Yumei, C.: Using Rough Set to Reduce SVM Classifier Complexity and Its Use in SARS Data Set. In: Khosla, R., Howlett, R.J., Jain, L.C. (eds.) KES 2005. LNCS (LNAI), vol. 3683, pp. 575–580. Springer, Heidelberg (2005)
Khardon, R., Servedio, R.A.: Maximum margin algorithms with boolean kernels. J. of Machine Learning Res. 6, 1405–1429 (2005)
Kryszkiewicz, M.: Maintenance of reducts in the variable precision rough set model. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining – Analysis of Imperfect Data, pp. 355–372. Kluwer Academic Publishers, Boston (1997)
Li, Y., Cai, Y., Li, Y., Xu, X.: Rough sets method for SVM data preprocessing. In: Proceedings of the 2004 IEEE Conference on Cybernetics and Intelligent Systems, pp. 1039–1042 (2004)
Lingras, P., Butz, C.J.: Interval set classifiers using support vector machines. In: Proc. the North American Fuzzy Inform. Processing Society Conference, pp. 707–710 (2004)
Lingras, P., Butz, C.J.: Rough set based 1-v-1 and 1-v-r approaches to support vector machine multi-classification. Information Sciences 177, 3782–3798 (2007)
Lingras, P., Butz, C.J.: Rough support vector regression. European Journal of Operational Research 206, 445–455 (2010)
Nguyen, H.S.: Approximate boolean reasoning: foundations and applications in data mining. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 334–506. Springer, Heidelberg (2006)
Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)
Sadohara, K.: Learning of boolean functions using support vector machines. In: Abe, N., Khardon, R., Zeugmann, T. (eds.) ALT 2001. LNCS (LNAI), vol. 2225, pp. 106–118. Springer, Heidelberg (2001)
Skowron, A., Rauszer, C.: The Discernibility Matrices and Functions in Information Systems. In: Słowiński, R. (ed.) Intelligent Decision Support – Handbook of Applications and Advances of the Rough Sets Theory, ch. 3, pp. 331–362. Kluwer Academic Publishers, Dordrecht (1992)
Ślęzak, D.: Approximate Entropy Reducts. Fundamenta Informaticae 53, 365–387 (2002)
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, NY (1995)
Zhang, J., Wang, Y.: A rough margin based support vector machine. Inf. Sci. 178(9), 2204–2214 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Nguyen, S.H., Nguyen, H.S. (2014). Applications of Boolean Kernels in Rough Sets. In: Kryszkiewicz, M., Cornelis, C., Ciucci, D., Medina-Moreno, J., Motoda, H., Raś, Z.W. (eds) Rough Sets and Intelligent Systems Paradigms. Lecture Notes in Computer Science(), vol 8537. Springer, Cham. https://doi.org/10.1007/978-3-319-08729-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-08729-0_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08728-3
Online ISBN: 978-3-319-08729-0
eBook Packages: Computer ScienceComputer Science (R0)