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A nonconvergent example for the iterative waterfilling algorithm
Performance evaluation of multiobjective multiclass support vector machines maximizing geometric margins
1.  Graduate School of Engineering, Osaka University, YamadaOka 12, Suita, Osaka 5650871, Japan, Japan, Japan, Japan 
References:
[1] 
S. Abe, "Support Vector Machines for Pattern Classification," SpringerVerlag, New York, 2005. 
[2] 
F. Alizadeh and D. Goldfarb, Secondorder cone programming, Mathematical Programming, Ser. B, 95 (2003), 351. 
[3] 
L. Bottou, C. Cortes, J. Denker, H. Drucker, I. Guyon, L. Jackel, Y. LeCun, U. Muller, E. Sackinger, P. Simard and V. Vapnik, Comparison of classifier methods: A case study in handwriting digit recognition, in "Proc. Int. Conf. Pattern Recognition,'' (1994), 7787. 
[4] 
E. J. Bredensteiner and K. P. Bennett, Multicategory classification by support vector machines, Computational Optimization and Applications, 12 (1999), 5379. doi: 10.1023/A:1008663629662. 
[5] 
M. Ehrgott, "Multicriteria Optimization,'' 2^{nd} edition, SpringerVerlag, Berlin, 2005. 
[6] 
Y. Guermeur, Combining discriminant models with new multiclass SVMs, Neuro COLT2 Technical Report Series, 2000. 
[7] 
U. Kressel, Pairwise classification and support vector machines, in "Advances in kernel methods  Support vector learning'' (eds. B. Schölkopf, C. Burges, and A. J. Smola), MIT Press, Cambridge, (1999), 255268. 
[8] 
C. W. Hsh and C. J. Lin, A comparison of methods for multiclass support vector machines, IEEE Trans. Neural Networks, 13 (2) (2002), 181201. 
[9] 
H. D. Mittelmann, An independent benchmarking of SDP and SOCP solvers, Mathematical Programming, Ser. B, 95 (2003), 407430. 
[10] 
K. R. Müller, S. Mika, G. Rätsch, K. Tsuda and B. Shölkopf, An introduction to kernelbased learning algorithms, IEEE Trans. Neural Networks, 12 (2), (2001), 181201. doi: 10.1109/72.914517. 
[11] 
A. Passerini, M. Pontil and P. Frasconi, New results on error correcting output codes of kernel machines, IEEE Trans. Neural Networks, 14 (1), (2004), 4554. doi: 10.1109/TNN.2003.820841. 
[12] 
J. C. Platt, N. Cristianini and J. ShaweTaylor, Large margin DAG's for multiclass classification, in "Advances in Neural Information Processing Systems,'' Cambridge, MA: MIT Press, 12 (2000), 547553. 
[13] 
K. Tatsumi, K. Hayashida, H. Higashi and T. Tanino, Multiobjective multiclass support vector machine for pattern recognition, in "Proc. SICE Annual Conference 2007,'' 10951098. doi: 10.1109/SICE.2007.4421147. 
[14] 
K. Tatsumi, R. Kawachi, K. Hayashida and T. Tanino, Multiobjective multiclass support vector machines maximizing geometric margins, Pacific Journal of Optimization, 6 (1), (2000), 115140. 
[15] 
J. S. Taylor and N. Cristianini, "Kernel Methods for Pattern Analysis,'' Cambridge University Press, 2004. 
[16] 
, UCI benchmark repository of artificial and real data sets, University of California Irvine,, Available from: , (). 
[17] 
J. Weston and C. Watkins, Multiclass support vector machines, Technical report CSDTR9804, Univ. London, Royal Holloway, (1998). 
[18] 
V. N. Vapnik, "Statistical Learning Theory,'' A WileyInterscience Publication, 1998. 
show all references
References:
[1] 
S. Abe, "Support Vector Machines for Pattern Classification," SpringerVerlag, New York, 2005. 
[2] 
F. Alizadeh and D. Goldfarb, Secondorder cone programming, Mathematical Programming, Ser. B, 95 (2003), 351. 
[3] 
L. Bottou, C. Cortes, J. Denker, H. Drucker, I. Guyon, L. Jackel, Y. LeCun, U. Muller, E. Sackinger, P. Simard and V. Vapnik, Comparison of classifier methods: A case study in handwriting digit recognition, in "Proc. Int. Conf. Pattern Recognition,'' (1994), 7787. 
[4] 
E. J. Bredensteiner and K. P. Bennett, Multicategory classification by support vector machines, Computational Optimization and Applications, 12 (1999), 5379. doi: 10.1023/A:1008663629662. 
[5] 
M. Ehrgott, "Multicriteria Optimization,'' 2^{nd} edition, SpringerVerlag, Berlin, 2005. 
[6] 
Y. Guermeur, Combining discriminant models with new multiclass SVMs, Neuro COLT2 Technical Report Series, 2000. 
[7] 
U. Kressel, Pairwise classification and support vector machines, in "Advances in kernel methods  Support vector learning'' (eds. B. Schölkopf, C. Burges, and A. J. Smola), MIT Press, Cambridge, (1999), 255268. 
[8] 
C. W. Hsh and C. J. Lin, A comparison of methods for multiclass support vector machines, IEEE Trans. Neural Networks, 13 (2) (2002), 181201. 
[9] 
H. D. Mittelmann, An independent benchmarking of SDP and SOCP solvers, Mathematical Programming, Ser. B, 95 (2003), 407430. 
[10] 
K. R. Müller, S. Mika, G. Rätsch, K. Tsuda and B. Shölkopf, An introduction to kernelbased learning algorithms, IEEE Trans. Neural Networks, 12 (2), (2001), 181201. doi: 10.1109/72.914517. 
[11] 
A. Passerini, M. Pontil and P. Frasconi, New results on error correcting output codes of kernel machines, IEEE Trans. Neural Networks, 14 (1), (2004), 4554. doi: 10.1109/TNN.2003.820841. 
[12] 
J. C. Platt, N. Cristianini and J. ShaweTaylor, Large margin DAG's for multiclass classification, in "Advances in Neural Information Processing Systems,'' Cambridge, MA: MIT Press, 12 (2000), 547553. 
[13] 
K. Tatsumi, K. Hayashida, H. Higashi and T. Tanino, Multiobjective multiclass support vector machine for pattern recognition, in "Proc. SICE Annual Conference 2007,'' 10951098. doi: 10.1109/SICE.2007.4421147. 
[14] 
K. Tatsumi, R. Kawachi, K. Hayashida and T. Tanino, Multiobjective multiclass support vector machines maximizing geometric margins, Pacific Journal of Optimization, 6 (1), (2000), 115140. 
[15] 
J. S. Taylor and N. Cristianini, "Kernel Methods for Pattern Analysis,'' Cambridge University Press, 2004. 
[16] 
, UCI benchmark repository of artificial and real data sets, University of California Irvine,, Available from: , (). 
[17] 
J. Weston and C. Watkins, Multiclass support vector machines, Technical report CSDTR9804, Univ. London, Royal Holloway, (1998). 
[18] 
V. N. Vapnik, "Statistical Learning Theory,'' A WileyInterscience Publication, 1998. 
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