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A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain
Fuzzy quadratic surface support vector machine based on fisher discriminant analysis
1. | School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian 116025, China |
2. | Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27695-7906 |
3. | Department of Mathematics, Shanghai University, Shanghai 200444 |
4. | School of Management, University of Chinese Academy of Sciences, Beijing, 100190 |
References:
[1] |
L. T. H. An and P. D. Tao, A continuous approach for the concave cost supply problem via DC programming and DCA, Discrete Applied Mathematics, 156 (2008), 325-338.
doi: 10.1016/j.dam.2007.03.024. |
[2] |
W. An and M. Liang, Fuzzy support vector machine based on within-class scatter for classification problems with outliers or noises, Neurocomputing, 110 (2013), 101-110.
doi: 10.1016/j.neucom.2012.11.023. |
[3] |
K. Bache and M. Lichman, UCI Machine Learning Repository, Irvine, CA: University of California, School of Information and Computer Science, 2013. Available from: http://archive.ics.uci.edu/ml. |
[4] |
M. Bicego and M. A. Figueiredo, Soft clustering using weighted one-class support vector machines, Pattern Recognition, 42 (2009), 27-32.
doi: 10.1016/j.patcog.2008.07.004. |
[5] |
J. P. Brooks, Support vector machines with the ramp loss and the hard margin loss, Operations Research, 59 (2011), 467-479.
doi: 10.1287/opre.1100.0854. |
[6] |
H.-G. Chew and C.-C. Lim, On regularisation parameter transformation of support vector machines, Journal of Industrial and Management Optimization, 5 (2009), 403-415.
doi: 10.3934/jimo.2009.5.403. |
[7] |
I. Dagher, Quadratic kernel-free non-linear support vector machine, Journal of Global Optimization, 41 (2008), 15-30.
doi: 10.1007/s10898-007-9162-0. |
[8] |
R. A. Fisher, The use of multiple measurements in taxonomic problems, Annals of Human Genetics, 7 (1936), 179-188.
doi: 10.1111/j.1469-1809.1936.tb02137.x. |
[9] |
X. Jiang, Y. Zhang and J. C. Lv, Fuzzy SVM with a new fuzzy membership function, Neural Computing and Applications, 15 (2006), 268-276.
doi: 10.1007/s00521-006-0028-z. |
[10] |
T. Joachims, Text categorization with support vector machines: learning with many relevant features, Machine Learning: ECML-98, Lecture Notes in Computer Science, 1398 (1998), 137-142.
doi: 10.1007/BFb0026683. |
[11] |
S. B. Kazmi, Q. Ain and M. A. Jaffar, Wavelets-based facial expression recognition using a bank of support vector machines, Soft Computing, 16 (2012), 369-379.
doi: 10.1007/s00500-011-0721-4. |
[12] |
C. F. Lin and S. D. Wang, Fuzzy support vector machines, IEEE Transactions on Neural Networks, 13 (2002), 464-471. |
[13] |
Y. Liu and M. Yuan, Reinforced multicategory support vector machines, Journal of Computational and Graphical Statistics, 20 (2011), 901-919.
doi: 10.1198/jcgs.2010.09206. |
[14] |
J. Luo, Z. Deng, D. Bulatov, J. E. Lavery and S.-C. Fang, Comparison of an $l_1$-regression-based and a RANSAC-based planar segmentation procedure for urban terrain data with many outliers, Image and Signal Processing for Remote Sensing XIX, 8892 (2013), p889209.
doi: 10.1117/12.2028627. |
[15] |
J. Luo, S.-C. Fang, Z. Deng and X. Guo, Quadratic Surface Support Vector Machine for Binary Classification, Submitted to Neurocomputing, 2014. |
[16] |
K. Schittkowski, Optimal parameter selection in support vector machines, Journal of Industrial and Management Optimization, 1 (2005), 465-476.
doi: 10.3934/jimo.2005.1.465. |
[17] |
F. E. H. Tay and L. Cao, Application of support vector machines in financial time series forecasting, Omega, 29 (2001), 309-317.
doi: 10.1016/S0305-0483(01)00026-3. |
[18] |
V. N. Vapnik, The Nature of Statistical Learning Theory, $2^{nd}$ edition, Springer-Verlag, New York, 2000.
doi: 10.1007/978-1-4757-3264-1. |
[19] |
C. Wu, C. Li and Q. Long, A DC programming approach for sensor network localization with uncertainties in archor positions, Journal of Industrial and Management Optimization, 10 (2014), 817-826.
doi: 10.3934/jimo.2014.10.817. |
[20] |
Y. Wu and Y. Liu, Robust truncated hinge loss support vector machines, Journal of the American Statistical Association, 102 (2007), 974-983.
doi: 10.1198/016214507000000617. |
[21] |
X. Zhang, X. Xiao and G. Xu, Fuzzy support vector machine based on affinity among samples, Journal of Software, 17 (2006), 951-958.
doi: 10.1360/jos170951. |
[22] |
G. Zhang, S. Wang, Y. Wang and W. Liu, LS-SVM approximate solution for affine nonlinear systems with partially unknown systems, Journal of Industrial and Management Optimization, 10 (2014), 621-636.
doi: 10.3934/jimo.2014.10.621. |
show all references
References:
[1] |
L. T. H. An and P. D. Tao, A continuous approach for the concave cost supply problem via DC programming and DCA, Discrete Applied Mathematics, 156 (2008), 325-338.
doi: 10.1016/j.dam.2007.03.024. |
[2] |
W. An and M. Liang, Fuzzy support vector machine based on within-class scatter for classification problems with outliers or noises, Neurocomputing, 110 (2013), 101-110.
doi: 10.1016/j.neucom.2012.11.023. |
[3] |
K. Bache and M. Lichman, UCI Machine Learning Repository, Irvine, CA: University of California, School of Information and Computer Science, 2013. Available from: http://archive.ics.uci.edu/ml. |
[4] |
M. Bicego and M. A. Figueiredo, Soft clustering using weighted one-class support vector machines, Pattern Recognition, 42 (2009), 27-32.
doi: 10.1016/j.patcog.2008.07.004. |
[5] |
J. P. Brooks, Support vector machines with the ramp loss and the hard margin loss, Operations Research, 59 (2011), 467-479.
doi: 10.1287/opre.1100.0854. |
[6] |
H.-G. Chew and C.-C. Lim, On regularisation parameter transformation of support vector machines, Journal of Industrial and Management Optimization, 5 (2009), 403-415.
doi: 10.3934/jimo.2009.5.403. |
[7] |
I. Dagher, Quadratic kernel-free non-linear support vector machine, Journal of Global Optimization, 41 (2008), 15-30.
doi: 10.1007/s10898-007-9162-0. |
[8] |
R. A. Fisher, The use of multiple measurements in taxonomic problems, Annals of Human Genetics, 7 (1936), 179-188.
doi: 10.1111/j.1469-1809.1936.tb02137.x. |
[9] |
X. Jiang, Y. Zhang and J. C. Lv, Fuzzy SVM with a new fuzzy membership function, Neural Computing and Applications, 15 (2006), 268-276.
doi: 10.1007/s00521-006-0028-z. |
[10] |
T. Joachims, Text categorization with support vector machines: learning with many relevant features, Machine Learning: ECML-98, Lecture Notes in Computer Science, 1398 (1998), 137-142.
doi: 10.1007/BFb0026683. |
[11] |
S. B. Kazmi, Q. Ain and M. A. Jaffar, Wavelets-based facial expression recognition using a bank of support vector machines, Soft Computing, 16 (2012), 369-379.
doi: 10.1007/s00500-011-0721-4. |
[12] |
C. F. Lin and S. D. Wang, Fuzzy support vector machines, IEEE Transactions on Neural Networks, 13 (2002), 464-471. |
[13] |
Y. Liu and M. Yuan, Reinforced multicategory support vector machines, Journal of Computational and Graphical Statistics, 20 (2011), 901-919.
doi: 10.1198/jcgs.2010.09206. |
[14] |
J. Luo, Z. Deng, D. Bulatov, J. E. Lavery and S.-C. Fang, Comparison of an $l_1$-regression-based and a RANSAC-based planar segmentation procedure for urban terrain data with many outliers, Image and Signal Processing for Remote Sensing XIX, 8892 (2013), p889209.
doi: 10.1117/12.2028627. |
[15] |
J. Luo, S.-C. Fang, Z. Deng and X. Guo, Quadratic Surface Support Vector Machine for Binary Classification, Submitted to Neurocomputing, 2014. |
[16] |
K. Schittkowski, Optimal parameter selection in support vector machines, Journal of Industrial and Management Optimization, 1 (2005), 465-476.
doi: 10.3934/jimo.2005.1.465. |
[17] |
F. E. H. Tay and L. Cao, Application of support vector machines in financial time series forecasting, Omega, 29 (2001), 309-317.
doi: 10.1016/S0305-0483(01)00026-3. |
[18] |
V. N. Vapnik, The Nature of Statistical Learning Theory, $2^{nd}$ edition, Springer-Verlag, New York, 2000.
doi: 10.1007/978-1-4757-3264-1. |
[19] |
C. Wu, C. Li and Q. Long, A DC programming approach for sensor network localization with uncertainties in archor positions, Journal of Industrial and Management Optimization, 10 (2014), 817-826.
doi: 10.3934/jimo.2014.10.817. |
[20] |
Y. Wu and Y. Liu, Robust truncated hinge loss support vector machines, Journal of the American Statistical Association, 102 (2007), 974-983.
doi: 10.1198/016214507000000617. |
[21] |
X. Zhang, X. Xiao and G. Xu, Fuzzy support vector machine based on affinity among samples, Journal of Software, 17 (2006), 951-958.
doi: 10.1360/jos170951. |
[22] |
G. Zhang, S. Wang, Y. Wang and W. Liu, LS-SVM approximate solution for affine nonlinear systems with partially unknown systems, Journal of Industrial and Management Optimization, 10 (2014), 621-636.
doi: 10.3934/jimo.2014.10.621. |
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