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A nonlinear multi-classification knowledge-based kernel machine

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Abstract

This paper presents a knowledge-based nonlinear kernel classification model for multi-category discrimination of sets or objects with prior knowledge. A kernel function is employed to find a nonlinear classifier capable of discriminating future points into an appropriate class. The prior knowledge is in the form of multiple polyhedral sets belonging to one or more categories or classes, and it is introduced as additional constraints into the formulation of the regularized nonlinear kernel least squares multi-class support vector machine model. The resulting formulation leads to a linear system of equations that can be solved using matrix methods or iterative methods. This work extends previous work (Oladunni et al. in ICCS 2006, Lecture notes in Computer Science, Part I, LNCS, vol 3991. Springer, Berlin, pp 188–195, 2006) that incorporated similar prior knowledge into a regularized linear least squares multi-class model. To evaluate the model, data and prior knowledge from the two-phase flow regimes in pipes were used to train and test the proposed formulation.

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References

  • Bazaraa MS, Sherali HD and Shetty CM (1993). Nonlinear programming—theory and algorithms. Wiley, New York

    Google Scholar 

  • Burges CJC (1998). A tutorial on support vector machines for pattern classification. Data Mining KnowlDiscovery 2(2): 121–167

    Article  Google Scholar 

  • Cristianini N and Shawe-Taylor J (2000). Support vector machines and other kernel-based learning methods. Cambridge University Press, Cambridge

    Google Scholar 

  • Ding CHQ and Dubchak I (2001). Multi-class protein fold recognition using support vector machines and neural networks. Bioinformatics 17: 349–358

    Article  Google Scholar 

  • Fung G and Mangasarian OL (2005). Multicategory proximal support vector machine classifiers. Mach Learn 59: 77–97

    Article  Google Scholar 

  • Fung G, Mangasarian OL, Shavlik JW (2002) Knowledge-based support vector machine classifiers. In: Proceedings neural information processing systems (NIPS 2002), Vancouver, December 10–12

  • Fung G, Mangasarian OL, Shavlik JW (2003) Knowledge-based nonlinear kernel classifiers. In: Manfred W, Bernhard S (eds) Conference on learning theory (COLT 03) and workshop on kernel machines, Washington, D.C., August 24–27, 2003. Springer, Berlin, pp 102–113

  • Hsu C-W and Lin C-J (2002). A comparison of methods for multi-class support vector machines. IEEE Trans Neural Netw 13: 415–425

    Article  Google Scholar 

  • Lee Y-J, Mangasarian OL and Wolberg WH (2000). Breast cancer survival and chemotherapy: a support vector machine analysis. DIMACS Ser Discr Math Theor Comp Sci Am Math Soc 55: 1–10

    Google Scholar 

  • Mangasarian OL (1994). Nonlinear programming. SIAM, Philadelphia

    Google Scholar 

  • Mangasarian OL (2005). Knowledge-based linear programming. SIAM J Optim 15: 375–382

    Article  Google Scholar 

  • Mangasarian OL, Shavlik JW and Wild EW (2004). Knowledge-based kernel approximation. J Mach Learn Res 5: 1127–1141

    Google Scholar 

  • McQuillan KW and Whalley PB (1985). Flow patterns in vertical two-phase flow. Int J Multiphase Flow 11: 161–175

    Article  Google Scholar 

  • Oladunni OO (2006) Least square multi-class kernel machines with prior knowledge and applications. PhD Dissertation, University of Oklahoma

  • Oladunni OO, Trafalis TB, Papavassiliou DV (2006) Knowledge-based multiclass support vector machines applied to vertical two-phase flow. In: Alexandrov VN et al (eds) ICCS 2006, Lecture notes in Computer Science, Part I, LNCS, vol 3991. Springer, Berlin, pp 188–195

  • Rifkin R and Klautau A (2004). In defense of one-vs-all classification. J Mach Learn Res 5: 101–141

    Google Scholar 

  • Santosa B, Conway T and Trafalis TB (2002). Knowledge-based clustering and application of multi-class SVM for genes expression analysis. Intell Eng Syst Artif Neural Netw 12: 391–395

    Google Scholar 

  • Suykens JAK and Vandewalle J (1999a). Least squares support vector machine classifers. Neural Process Lett 9: 293–300

    Article  Google Scholar 

  • Suykens JAK, Vandewalle J (1999b) Multiclass least squares support vector machine classifers. In: Proc. of Joint Conf. on Neural Networks (IJCNN’99), Washington, DC

  • Trafalis TB, Oladunni O and Papavassiliou DV (2005). Two-phase flow regime identification with a multi- classification SVM model. Ind Eng Chem Res 44: 4414–4426

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Industrial Engineering, The University of Oklahoma, 202 West Boyd, CEC 124, Norman, OK, 73019, USA

    Olutayo O. Oladunni & Theodore B. Trafalis

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  1. Olutayo O. Oladunni
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  2. Theodore B. Trafalis
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Correspondence to Olutayo O. Oladunni.

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Oladunni, O.O., Trafalis, T.B. A nonlinear multi-classification knowledge-based kernel machine. Comput Manag Sci 6, 81–100 (2009). https://doi.org/10.1007/s10287-008-0073-4

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