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A nonconvergent example for the iterative water-filling algorithm
Performance evaluation of multiobjective multiclass support vector machines maximizing geometric margins
1. | Graduate School of Engineering, Osaka University, Yamada-Oka 1-2, Suita, Osaka 565-0871, Japan, Japan, Japan, Japan |
References:
[1] |
S. Abe, "Support Vector Machines for Pattern Classification," Springer-Verlag, New York, 2005. |
[2] |
F. Alizadeh and D. Goldfarb, Second-order cone programming, Mathematical Programming, Ser. B, 95 (2003), 3-51. |
[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), 77-87. |
[4] |
E. J. Bredensteiner and K. P. Bennett, Multicategory classification by support vector machines, Computational Optimization and Applications, 12 (1999), 53-79.
doi: 10.1023/A:1008663629662. |
[5] |
M. Ehrgott, "Multicriteria Optimization,'' 2nd edition, Springer-Verlag, 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), 255-268. |
[8] |
C. W. Hsh and C. J. Lin, A comparison of methods for multiclass support vector machines, IEEE Trans. Neural Networks, 13 (2) (2002), 181-201. |
[9] |
H. D. Mittelmann, An independent benchmarking of SDP and SOCP solvers, Mathematical Programming, Ser. B, 95 (2003), 407-430. |
[10] |
K. R. Müller, S. Mika, G. Rätsch, K. Tsuda and B. Shölkopf, An introduction to kernel-based learning algorithms, IEEE Trans. Neural Networks, 12 (2), (2001), 181-201.
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), 45-54.
doi: 10.1109/TNN.2003.820841. |
[12] |
J. C. Platt, N. Cristianini and J. Shawe-Taylor, Large margin DAG's for multiclass classification, in "Advances in Neural Information Processing Systems,'' Cambridge, MA: MIT Press, 12 (2000), 547-553. |
[13] |
K. Tatsumi, K. Hayashida, H. Higashi and T. Tanino, Multi-objective multiclass support vector machine for pattern recognition, in "Proc. SICE Annual Conference 2007,'' 1095-1098.
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), 115-140. |
[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: http://www.ics.uci.edu/~mlearn/databases/ |
[17] |
J. Weston and C. Watkins, Multi-class support vector machines, Technical report CSD-TR-98-04, Univ. London, Royal Holloway, (1998). |
[18] |
V. N. Vapnik, "Statistical Learning Theory,'' A Wiley-Interscience Publication, 1998. |
show all references
References:
[1] |
S. Abe, "Support Vector Machines for Pattern Classification," Springer-Verlag, New York, 2005. |
[2] |
F. Alizadeh and D. Goldfarb, Second-order cone programming, Mathematical Programming, Ser. B, 95 (2003), 3-51. |
[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), 77-87. |
[4] |
E. J. Bredensteiner and K. P. Bennett, Multicategory classification by support vector machines, Computational Optimization and Applications, 12 (1999), 53-79.
doi: 10.1023/A:1008663629662. |
[5] |
M. Ehrgott, "Multicriteria Optimization,'' 2nd edition, Springer-Verlag, 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), 255-268. |
[8] |
C. W. Hsh and C. J. Lin, A comparison of methods for multiclass support vector machines, IEEE Trans. Neural Networks, 13 (2) (2002), 181-201. |
[9] |
H. D. Mittelmann, An independent benchmarking of SDP and SOCP solvers, Mathematical Programming, Ser. B, 95 (2003), 407-430. |
[10] |
K. R. Müller, S. Mika, G. Rätsch, K. Tsuda and B. Shölkopf, An introduction to kernel-based learning algorithms, IEEE Trans. Neural Networks, 12 (2), (2001), 181-201.
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), 45-54.
doi: 10.1109/TNN.2003.820841. |
[12] |
J. C. Platt, N. Cristianini and J. Shawe-Taylor, Large margin DAG's for multiclass classification, in "Advances in Neural Information Processing Systems,'' Cambridge, MA: MIT Press, 12 (2000), 547-553. |
[13] |
K. Tatsumi, K. Hayashida, H. Higashi and T. Tanino, Multi-objective multiclass support vector machine for pattern recognition, in "Proc. SICE Annual Conference 2007,'' 1095-1098.
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), 115-140. |
[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: http://www.ics.uci.edu/~mlearn/databases/ |
[17] |
J. Weston and C. Watkins, Multi-class support vector machines, Technical report CSD-TR-98-04, Univ. London, Royal Holloway, (1998). |
[18] |
V. N. Vapnik, "Statistical Learning Theory,'' A Wiley-Interscience Publication, 1998. |
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