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A nonlinear multi-classification knowledge-based kernel machine
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Original Paper
A nonlinear multi-classification knowledge-based kernel machine
Olutayo O. Oladunni1  and Theodore B. Trafalis1
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School of Industrial Engineering, The University of Oklahoma, 202 West Boyd, CEC 124, Norman, OK 73019, USA |
Published online: 21 March 2008
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.
Keywords Knowledge-based model - Multi-classification - Kernel - Prior knowledge - Tikhonov regularization
References
| Bazaraa MS, Sherali HD and Shetty CM (1993). Nonlinear programming—theory and algorithms. Wiley, New York
|
| |
Burges CJC (1998). A tutorial on support vector machines for pattern classification. Data Mining KnowlDiscovery 2(2): 121–167
|
| |
| Cristianini N and Shawe-Taylor J (2000). Support vector machines and other kernel-based learning methods. Cambridge University
Press, Cambridge
|
| |
Ding CHQ and Dubchak I (2001). Multi-class protein fold recognition using support vector machines and neural networks. Bioinformatics 17: 349–358
|
| |
Fung G and Mangasarian OL (2005). Multicategory proximal support vector machine classifiers. Mach Learn 59: 77–97
|
| |
| 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
|
| |
| 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
|
| |
| Mangasarian OL (1994). Nonlinear programming. SIAM, Philadelphia
|
| |
Mangasarian OL (2005). Knowledge-based linear programming. SIAM J Optim 15: 375–382
|
| |
| Mangasarian OL, Shavlik JW and Wild EW (2004). Knowledge-based kernel approximation. J Mach Learn Res 5: 1127–1141
|
| |
McQuillan KW and Whalley PB (1985). Flow patterns in vertical two-phase flow. Int J Multiphase Flow 11: 161–175
|
| |
| 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
|
| |
| 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
|
| |
Suykens JAK and Vandewalle J (1999a). Least squares support vector machine classifers. Neural Process Lett 9: 293–300
|
| |
| 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
|
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