Abstract
This paper presents a knowledge-based kernel classification model for binary classification of sets or objects with prior knowledge. The prior knowledge is in the form of multiple polyhedral sets belonging to one or two classes, and it is introduced as additional constraints into a regularized knowledge-based optimization problem. The resulting formulation leads to a least squares problem that can be solved using matrix or iterative methods. To evaluate the model, the experimental laminar & turbulent flow data and the Reynolds number equation used as prior knowledge were used to train and test the proposed model.
Chapter PDF
Similar content being viewed by others
Keywords
- Support Vector Machine
- Tikhonov Regularization
- Kernel Matrix
- Linear Programming Formulation
- Drill Collar
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995)
Fung, G., Mangasarian, O.L., Shavlik, J.W.: Knowledge-based Support Vector Machine Classifiers. In: Neural Information Processing Systems 2002 (NIPS 2002), Vancouver, BC, December 10-12 (2002)
Fung, G.M., Mangasarian, O.L., Shavlik, J.W.: Knowledge-Based Nonlinear Kernel Classifiers. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT/Kernel 2003. LNCS (LNAI), vol. 2777, pp. 102–113. Springer, Heidelberg (2003)
Oladunni, O.O., Trafalis, T.B., Papavassiliou, D.V.: Knowledge-based multiclass support vector machines applied to vertical two-phase flow. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2006. LNCS, vol. 3991, pp. 188–195. Springer, Heidelberg (2006)
Suykens, J.A.K., Vandewalle, J.: Least Squares Support Vector Machine Classifiers. Neural Processing Letters 9, 293–300 (1999b)
Pelckmans, K., Suykens, J.A.K., De Moor, B.: Morozov, Ivanov and Tikhonov Regularization Based LS-SVMs. In: Pal, N.R., Kasabov, N., Mudi, R.K., Pal, S., Parui, S.K. (eds.) ICONIP 2004. LNCS, vol. 3316, pp. 1216–1222. Springer, Heidelberg (2004)
Mangasarian, O.L.: Generalized Support Vector Machines. In: Smola, A., Bartlett, P., Schölkopf, B., Schuurmans, D. (eds.) Advances in Large Margin Classifiers, MIT Press, Cambridge (2000), ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/99-14.ps
Mangasarian, O.L.: Nonlinear Programming. SIAM, Philadelphia (1994)
Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming – Theory and Algorithms. John Wiley & Sons, Chichester (1993)
Burges, C.J.C.: A Tutorial on Support Vector Machines for Pattern Classification. Data Mining and Knowledge Discovery 2(2), 121–167 (1998)
Cristianini, N., Shawe-Taylor, J.: Support Vector Machines and other Kernel-based Learning Methods. Cambridge University Press, Cambridge (2000)
Tikhonov, A.N., Arsenin, V.Y.: Solution of Ill-Posed Problems. Winston, Washington (1977)
Lewis, J.M., Lakshmivarahan, S., Dhall, S.: Dynamic Data Assimilation. Cambridge University Press, Cambridge (2006)
Trafalis, T.B., Oladunni, O.: Single Phase Fluid Flow Classification via Neural Networks & Support Vector Machine. In: Dagli, C.H., Buczak, A.L., Enke, D.L., Embrechts, M.J., Ersoy, O. (eds.) Intelligent Engineering Systems Through Artificial Neural Networks, vol. 14, pp. 427–432. ASME Press, New York (2004)
Oladunni, O., Trafalis, T.B.: Mixed-Integer Programming Kernel-Based Classification. WSEAS Transactions on Computers 4(7), 671–678 (2005)
Oladunni, O., Trafalis, T.B.: Single Phase Laminar & Turbulent Flow Classification in Annulus via a Knowledge-Based Linear Model. In: Dagli, H., Buczak, A.L., Enke, D.L., Embrechts, M.J., Ersoy, O. (eds.) Intelligent Engineering Systems Through Artificial Neural Networks, vol. 16, pp. 599–604. ASME Press, New York (2006)
Bourgoyne Jr., A.T., Chenevert, M.E., Millheim, K.K., Young Jr., F.S.: Applied Drilling Engineering. SPE Textbook Series, vol. 2, p. 155. SPE, Richardson (1991)
MATLAB User’s Guide.: The Math-Works, Inc., Natwick (1994-2003), http://www.mathworks.com
Gunn, S.T.: Support Vector Machine for Classification and Regression. Technical Report, Department of Electronic and Computer Science, University of Southampton (1998)
ILOG OPL STUDIO 3.7.: Language Manual, ILOG, S.A. Gentily, France and ILOG, Inc., Mountain View California, USA (2003), http://www.ilog.com/products/oplstudio/
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Oladunni, O.O., Trafalis, T.B. (2007). Regularized Knowledge-Based Kernel Machine. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2007. ICCS 2007. Lecture Notes in Computer Science, vol 4487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72584-8_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-72584-8_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72583-1
Online ISBN: 978-3-540-72584-8
eBook Packages: Computer ScienceComputer Science (R0)