**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30840

##### Motivated Support Vector Regression using Structural Prior Knowledge

**Authors:**
Wei Zhang,
Yao-Yu Li,
Yi-Fan Zhu,
Qun Li,
Wei-Ping Wang

**Abstract:**

**Keywords:**
admissible support vector kernel,
reproducing kernel,
structural prior knowledge,
motivated support vector regression

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1328496

**References:**

[1] V. Vapnik, The Nature of Statistical Learning Theory. New York: Springer-Verlag, 1995.

[2] G. Bloch, F. Lauer, G. Colin, and Y. Chamaillard, "Support vector regression from simulation data and few experimental samples," Information Sciences, vol. 178, pp. 3813-3827, 2008.

[3] J.-B. Gao, S. R. Gunn, and C. J. Harris, "Mean field method for the support vector machine regression," Neurocomputing, vol. 50, pp. 391- 405, 2003.

[4] M. A. Mohandes, T. O. Halawani, S. Rehman, and A. A. Hussain, "Support vector machines for wind speed prediction," Renewable Energy, vol. 29, no. 6, pp. 939-947, 2004.

[5] W.-W. He, Z.-Z. Wang, and H. Jiang, "Model optimizing and feature selecting for support vector regression in time series forecasting," Neurocomputing, vol. 73, no. 3, pp. 600-611, 2008.

[6] F. Pan, P. Zhu, and Y. Zhang, "Metamodel-based lightweight design of b-pillar with twb structure via support vector regression," Computers and Structures, vol. 88, pp. 36-44, 2010.

[7] A. J. Smola, T. Friess, and K.-R. Mller, "Semiparametric support vector and linear programming machines," Advances in neural information processing systems, vol. 11, pp. 585-591, 1998.

[8] O. L. Mangasarian, J. Shavlik, and E. W. Wild, "Knowledge-based kernel approximation," Journal of Machine Learning Research, vol. 5, pp. 1127-1141, 2004.

[9] M. Lzaro, F. Prez-Cruz, and A. Arts-Rodriguez, "Learning a function and its derivative forcing the support vector expansion," IEEE Signal Processing Letters, vol. 12, pp. 194-197, 2005.

[10] F. Lauer and G. Bloch, "Incorporating prior knowledge in support vector regression," Mach. Learn., vol. 70, pp. 89-118, 2008.

[11] O. L. Mangasarian and E. W. wild, "Nonlinear knowledge in kernel approximation," IEEE Transactions on Neural Networks, vol. 18, pp. 300-306, 2007.

[12] B. Sch┬¿olkopf, P. Simard, A. J. Smola, and V. Vapnik, "Prior knowledge in support vector kernels," in Advanced in Kernel Method-Support Vector Learning, C. B. A. S. Sch┬¿olkopf, B., Ed. Cambridge, England: MIT Press, 1998.

[13] A. J. Smola and B. Sch┬¿olkopf, "A tutorial on support vector regression," Statistics and Computing, vol. 14, no. 3, pp. 199-222, 2004.

[14] P. K. Davis and J. H. Bigelow, "Motivated metamodels: Synthesis of cause-effect reasoning and statistical metamodeling," RAND, Tech. Rep. MR-1570, 2003.

[15] W. Zhang, X. Zhao, Y.-F. Zhu, and X.-J. Zhang, "A new composition method of admissible support vector kernel based on reproducing kernel," in International Conference on Computer and Applied Mathematics, Rio de Janeiro, March 2010.

[16] N. Aronszajn, "Theory of reproducing kernels," Transactions of the American Mathematical Society, vol. 68, no. 3, pp. 337-404, 1950.

[17] D. Haussler, "Convolution kernels on discrete structures," University of California, Sana Cruz, CA,, Tech. Rep. UCSC-CRL-99-10, 1999.

[18] G. F. Smits and E. M. Jondaan, "Improved svm regression using mixtures of kernels," in Proceeding of the 2002 international joint conference on neural networks, vol. 3. Honolulu, Hawaii, USA: IEEE, 2002.

[19] Y. Tan and J. Wang, "A support vector machine with a hybrid kernel and minimal vapnik-chervonenkis dimension," IEEE Transactions on Knowledge and Data Engineering, vol. 16, pp. 385-395, 2004.

[20] B. Sch┬¿olkopf, K.-K. Sung, C. J. Burges, F. Girosi, P. Niyogi, T. Poggio, and V. Vapnik, "Comparing support vector machines with gaussian kernels to radial basis function classifiers," IEEE Transactions on Signal Processing, vol. 45, pp. 2758-2765, 1997.

[21] G. Wahba, Spline Models for Observational Data, SIAM, Philadephia, 1990.

[22] J. St┬¿ockler, "Multivariate bernoulli splines and the periodic interpolation problem," Constr. Approx., vol. 7, pp. 105-120, 1991.

[23] G. Wahba, "Support vector machines,reproducing kernel hilbert spaces and randomized gacv," in Advances in Kernel Methods - Support Vector Learning, B. Sch┬¿olkopf, C. J. Burges, and A. J. Smola, Eds. Cambridge, England: MIT Press, 1999, pp. 69-88.

[24] A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics. Boston, Dordrecht, London: Kluwer Academic Publishers Group, 2003.

[25] R. Schaback, "A unified theory of radial basis functions native hilbert spaces for radial basis functions ii," Journal of Computational and Applied Mathematics, vol. 121, pp. 165-177, 2000.

[26] J. Mercer, Ed., Functions of positive and negative type and their connection with the theory of integral equations, ser. Philosophical Transactions of the Royal Society, London, 1909, vol. A, 209.

[27] P. K. Davis, "Introduction to multiresolution, multiperspective modeling (mrmpm) and exploratory analysis," RAND, Tech. Rep. WR-224, 2005.

[28] R. Horn, Topics in Matrix Analysis. Cambridge, MA: Cambridge University Press, 1994.

[29] C. J. Burges, "A tutorial on support vector machines for pattern recognition," Data Mining and Knowledge Discovery, vol. 2, pp. 121-167, 1998.

[30] Y.-J. Park, "Application of genetic algorithms in response surface optimization problems," Doctor of Philosophy, Arizona State University, December 2003.

[31] S. S. Chaudhry and W. Luo, "Application of genetic algorithms in production and operations management: A review," International Journal of Production Research, vol. 43, pp. 4083-4101, 2005.

[32] C. R. Houck, J. A. Joines, and M. G. Kay, "A genetic algorithm for function optimization: A matlab implementation," Tech. Rep. NCSU-IE TR 95-09, 1995.

[33] B. P. Zeigler, H. Praehofer, and T. G. Kim, Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems, second edition ed. CA, USA: Academic Press, 2000.