{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T02:45:17Z","timestamp":1772333117740,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2005,5,1]],"date-time":"2005-05-01T00:00:00Z","timestamp":1114905600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2005,5]]},"DOI":"10.1007\/s10994-005-0463-6","type":"journal-article","created":{"date-parts":[[2005,6,9]],"date-time":"2005-06-09T09:02:36Z","timestamp":1118307756000},"page":"77-97","source":"Crossref","is-referenced-by-count":250,"title":["Multicategory Proximal Support Vector Machine Classifiers"],"prefix":"10.1007","volume":"59","author":[{"given":"Glenn M.","family":"Fung","sequence":"first","affiliation":[]},{"given":"O. L.","family":"Mangasarian","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"463_CR1","doi-asserted-by":"crossref","unstructured":"Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., & Sorensen, D. (1999). LAPACK User\u2019s Guide, third edition. Philadelphia, Pennsylvania: SIAM. http:\/\/www.netlib.org\/lapack\/.","DOI":"10.1137\/1.9780898719604"},{"key":"463_CR2","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1080\/10556789408805554","volume":"3","author":"K. P. Bennett","year":"1993","unstructured":"Bennett, K. P. & Mangasarian, O. L. (1993). Multicategory separation via linear programming. Optimization Methods and Software, 3, 27\u201339.","journal-title":"Optimization Methods and Software"},{"key":"463_CR3","doi-asserted-by":"crossref","unstructured":"Bottou, L., Cortes, C., Denker, J., Drucker, H., Guyon, I., Jackel, L., LeCun, Y., Muller, U., Sackinger, E., Simard, P., & Vapnik, V. (1994). Comparison of classifier methods: A case study in handwriting digit recognition. International Conference on Pattern Recognition (pp. 77\u201387). IEEE Computer Society Press.","DOI":"10.1109\/ICPR.1994.576879"},{"key":"463_CR4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10556780008805771","volume":"13","author":"P. S. Bradley","year":"2000","unstructured":"Bradley, P. S. & Mangasarian, O. L. (2000). Massive data discrimination via linear support vector machines. Optimization Methods and Software, 13, 1\u201310. ftp:\/\/ftp.cs.wisc.edu\/math-prog\/tech-reports\/98-03.ps.","journal-title":"Optimization Methods and Software"},{"key":"463_CR5","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1023\/A:1008663629662","volume":"12","author":"E. J. Bredensteiner","year":"1999","unstructured":"Bredensteiner, E. J. & Bennett, K. P. (1999). Multicategory classification by support vector machines. Computational Optimization and Applications, 12, 53\u201379.","journal-title":"Computational Optimization and Applications"},{"issue":"2","key":"463_CR6","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1023\/A:1009715923555","volume":"2","author":"C. J. C. Burges","year":"1998","unstructured":"Burges, C. J. C. (1998).Atutorial on support vectormachines for pattern recognition. Data Mining and Knowledge Discovery, 2:2, 121\u2013167.","journal-title":"Data Mining and Knowledge Discovery"},{"issue":"2","key":"463_CR7","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/BF02124738","volume":"5","author":"C. Chen","year":"1996","unstructured":"Chen, C. & Mangasarian, O. L. (1996). Hybrid misclassification minimization. Advances in Computational Mathematics, 5:2, 127\u2013136. ftp:\/\/ftp.cs.wisc.edu\/math-prog\/tech-reports\/95-05.ps.","journal-title":"Advances in Computational Mathematics"},{"key":"463_CR8","volume-title":"Learning from Data\u2014Concepts, Theory and Methods","author":"V. Cherkassky","year":"1998","unstructured":"Cherkassky, V. & Mulier, F. (1998). Learning from Data\u2014Concepts, Theory and Methods. New York: JohnWiley & Sons."},{"key":"463_CR9","unstructured":"CPLEX Optimization Inc., Incline Village, Nevada. (1992). Using the CPLEX(TM) Linear Optimizer and CPLEX(TM) Mixed Integer Optimizer (Version 2.0)."},{"key":"463_CR10","unstructured":"Dasgupta, S. (2000). Experiments with random projection. Uncertainty in Artificial Intelligence: Proceedings of the Sixteenth Conference (UAI-2000) (pp. 143\u2013151). San Francisco, CA: Morgan Kaufmann Publishers."},{"key":"463_CR11","doi-asserted-by":"crossref","first-page":"171","DOI":"10.7551\/mitpress\/1113.003.0014","volume-title":"Advances in large margin classifiers","author":"T. Evgeniou","year":"2000","unstructured":"Evgeniou, T., Pontil, M., & Poggio, T. (2000). Regularization networks and support vector machines. In A. Smola, P. Bartlett, B. Sch\u00f6lkopf, & D. Schuurmans (Eds.), Advances in large margin classifiers (pp. 171\u2013203). Cambridge, MA: MIT Press."},{"key":"463_CR12","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/0167-6377(94)00059-F","volume":"17","author":"F. Facchinei","year":"1995","unstructured":"Facchinei, F. (1995). Minimization of SC1 functions and the Maratos effect. Operations Research Letters, 17, 131\u2013137.","journal-title":"Operations Research Letters"},{"key":"463_CR13","doi-asserted-by":"crossref","unstructured":"Fung, G. & Mangasarian, O. L. (2001). Proximal support vector machine classifiers. In F. Provost & R. Srikant (Eds.), Proceedings KDD-2001: Knowledge discovery and data mining (pp. 77\u201386). San Francisco, CA, New York: Asscociation for Computing Machinery. ftp:\/\/ftp.cs.wisc.edu\/pub\/ dmi\/tech-reports\/01-02.ps.","DOI":"10.1145\/502512.502527"},{"issue":"10","key":"463_CR14","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1093\/bioinformatics\/16.10.906","volume":"16","author":"T. S. Furey","year":"2000","unstructured":"Furey, T. S., Duffy, N., Cristianini, N., Bednarski, D., Schummer, M., & Haussler, D. (2000). Support vector machine classification and validation of cnacer tissue samples usingmicroarray expression data. Bioinformatics, 16:10, 906\u2013914.","journal-title":"Bioinformatics"},{"issue":"1","key":"463_CR15","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1023\/A:1013815310229","volume":"15","author":"T. Van Gestel","year":"2002","unstructured":"Van Gestel, T., Suykens, J., Lanckriet, G., Lambrechts, A., De Moor, B., & Vandewalle, J. (2002). Multiclass ls-svms: moderated outputs and coding-decoding schemes. Neural Processing Letters, 15:1, 45\u201348.","journal-title":"Neural Processing Letters"},{"key":"463_CR16","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF01442169","volume":"11","author":"J.-B. Hiriart-Urruty","year":"1984","unstructured":"Hiriart-Urruty, J.-B., Strodiot, J. J., & Nguyen, V. H. (1984). Generalized hessian matrix and second-order optimality conditions for problems with CL1 data. Applied Mathematics and Optimization, 11, 43\u201356.","journal-title":"Applied Mathematics and Optimization"},{"key":"463_CR17","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","volume":"12","author":"A. E. Hoerl","year":"1952","unstructured":"Hoerl, A. E. & Kennard, R.W. (1952). Biased estimation for nonorthogonal problems. Technometrics, 12, 55\u201367.","journal-title":"Technometrics"},{"key":"463_CR18","unstructured":"Hsu, C.-W. & Lin, C.-J. (2001). A comparison on methods for multi-class support vector machines. http:\/\/www.csie.ntu.edu.tw\/cjlin\/papers.html."},{"key":"463_CR19","unstructured":"Kanzow, C., Qi, H., & Qi, L. (2001). On the minimum norm solution of linear programs. Preprint, University of Hamburg, Hamburg. Journal of Optimization Theory and Applications, to appear. http:\/\/www.math.uni-hamburg.de\/home\/kanzow\/paper.html."},{"key":"463_CR20","unstructured":"Lee, Y.-J. & Mangasarian, O. L. (2001). RSVM: Reduced support vector machines. Proceedings of the First SIAM International Conference on Data Mining, Chicago, April 5-7, CD-ROM. ftp:\/\/ftp.cs.wisc.edu\/ pub\/dmi\/tech-reports\/00-07.ps."},{"key":"463_CR21","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1011215321374","volume":"20","author":"Y.-J. Lee","year":"2001","unstructured":"Lee, Y.-J. & Mangasarian, O. L. (2001). SSVM: A smooth support vector machine. Computational Optimization and Applications, 20, 5\u201322. Data Mining Institute, University of Wisconsin, Technical Report 99-03. ftp:\/\/ftp.cs.wisc.edu\/pub\/dmi\/tech-reports\/99-03.ps.","journal-title":"Computational Optimization and Applications"},{"key":"463_CR22","doi-asserted-by":"crossref","unstructured":"Mangasarian, O. L. (1994). Nonlinear Programming. Philadelphia, PA: SIAM.","DOI":"10.1137\/1.9781611971255"},{"key":"463_CR23","doi-asserted-by":"crossref","first-page":"135","DOI":"10.7551\/mitpress\/1113.003.0012","volume-title":"Advances in large margin classifiers","author":"O. L. Mangasarian","year":"2000","unstructured":"Mangasarian, O. L. (2000). Generalized support vector machines. In A. Smola, P. Bartlett, B. Sch\u00f6lkopf, & D. Schuurmans (Eds.), Advances in large margin classifiers (pp. 135\u2013146). Cambridge, MA: MIT Press. ftp:\/\/ftp.cs.wisc.edu\/math-prog\/tech-reports\/98-14.ps."},{"key":"463_CR24","unstructured":"MATLAB. (1994\u20132001). User\u2019s Guide. The MathWorks, Inc., Natick, MA 01760. http:\/\/www.mathworks.com."},{"key":"463_CR25","unstructured":"Murphy, P. M. & Aha, D. W. (1992). UCI machine learning repository. http:\/\/www.ics.uci.edu\/~mlearn\/MLRepository.html."},{"key":"463_CR26","unstructured":"Polyak, B. T. (1987). Introduction to Optimization. New York: Optimization Software, Inc., Publications Division."},{"key":"463_CR27","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis Princeton","author":"R. T. Rockafellar","year":"1970","unstructured":"Rockafellar, R. T. (1970). Convex Analysis Princeton. New Jersey: Princeton University Press."},{"key":"463_CR28","unstructured":"Roth, V. V. & Steinhage, V. (1999). Nonlinear discriminant analysis using kernel function. In S. A. Solla, T. K. Leen, & K.-R. Mueller (Eds.), Advances in neural information processing systems\u2013NIPS*99 (pp. 568\u2013574)."},{"key":"463_CR29","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1109\/72.788641","volume":"10","author":"B. Sch\u00f6lkopf","year":"1999","unstructured":"Sch\u00f6lkopf, B., Mika, S., Burges, C. J. C., Knirsch, P., M\u00fcller, K.-R., R\u00e4tsch, G., & Smola, A. J. (1999). Input space versus feature space in kernel-based methods. IEEE Transactions on Neural Networks, 10, 1000\u20131017.","journal-title":"IEEE Transactions on Neural Networks"},{"key":"463_CR30","unstructured":"Smola, A. J. & Sch\u00f6lkopf, B. (2000). Sparse greedy matrix approximation for machine learning. Proc. 17th International Conf. on Machine Learning (pp. 911\u2013918). San Francisco, CA: Morgan Kaufmann."},{"key":"463_CR31","doi-asserted-by":"crossref","DOI":"10.1142\/5089","volume-title":"Least Squares Support Vector Machines","author":"J. A. K. Suykens","year":"2002","unstructured":"Suykens, J. A. K., Van Gestel, T., De Brabanter, J., De Moor, B., & Vandewalle, J. (2002). Least Squares Support Vector Machines. Singapore: World Scientific Publishing Co.."},{"key":"463_CR32","unstructured":"Suykens, J. A. K., Lukas, L., Van Dooren, P., De Moor, B., & Vandewalle, J. (1999). Least squares support vector machine classifiers: A large scale algorithm. European Conference on Circuit Theory and Design, ECCTD\u201999 (pp. 839\u2013842). Stresa, Italy."},{"issue":"3","key":"463_CR33","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1023\/A:1018628609742","volume":"9","author":"J. A. K. Suykens","year":"1999","unstructured":"Suykens, J. A. K. & Vandewalle, J. (1999). Least squares support vector machine classifiers. Neural Processing Letters, 9:3, 293\u2013300.","journal-title":"Neural Processing Letters"},{"key":"463_CR34","doi-asserted-by":"crossref","unstructured":"Suykens, J. A. K. & Vandewalle, J. (1999). Multiclass least squares support vector machines. Proceedings of IJCNN\u201999 (pp. CD-ROM). Washington, DC.","DOI":"10.1109\/IJCNN.1999.831072"},{"key":"463_CR35","volume-title":"Solutions of Ill\u2013Posed Problems","author":"A. N. Tikhonov","year":"1977","unstructured":"Tikhonov, A. N. & Arsenin, V. Y. (1977). Solutions of Ill\u2013Posed Problems. New York: John Wiley & Sons."},{"key":"463_CR36","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3264-1","volume-title":"The Nature of Statistical Learning Theory","author":"V. N. Vapnik","year":"2000","unstructured":"Vapnik, V. N. (2000). The Nature of Statistical Learning Theory. New York: Springer.","edition":"second"},{"key":"463_CR37","unstructured":"Weston, J. & Watkins, C. (1998). Multi-class support vector machines. Technical report csd-tr-98-04, Royal Holloway, University of London, Surrey, England."},{"key":"463_CR38","unstructured":"Williams, C. K. I. & Seeger, M. (2000). Using the Nystr\u00f6m method to speed up kernel machines. Advances in Neural Information Processing Systems (NIPS2000). http:\/\/www.kernel-machines.org."}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-005-0463-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10994-005-0463-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-005-0463-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T13:20:43Z","timestamp":1706275243000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10994-005-0463-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,5]]},"references-count":38,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2005,5]]}},"alternative-id":["463"],"URL":"https:\/\/doi.org\/10.1007\/s10994-005-0463-6","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"value":"0885-6125","type":"print"},{"value":"1573-0565","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,5]]}}}