SVM-Maj: A majorization approach to linear support vector machines with different hinge errors

Advances in Data Analysis and Classification

Volumn 2, Issue 1, 2008, Pages 17-43

  Groenen, P J F ^a   Nalbantov, G ^a   Bioch, J C ^a  

^a ERASMUS UNIVERSITY ROTTERDAM   (Netherlands)

Author keywords

Absolute hinge error; Huber hinge error; Iterative majorization; Optimal scaling; Quadratic hinge error; Support vector machines

Indexed keywords

ALGORITHMS; BINARY SEQUENCES; COMPUTATIONAL EFFICIENCY; ERROR ANALYSIS; ITERATIVE METHODS; REGRESSION ANALYSIS;

ABSOLUTE HINGE ERRORS; HUBER HINGE ERRORS; ITERATIVE MAJORIZATION; OPTIMAL SCALING; QUADRATIC HINGE ERRORS;

SUPPORT VECTOR MACHINES;

EID: 42149193051     PISSN: 18625347     EISSN: 18625355     Source Type: Journal    
DOI: 10.1007/s11634-008-0020-9     Document Type: Article

References (28)

1. Borg I, Groenen PJF (2005) Modern multidimensional scaling: theory and applications, 2nd edn. Springer, New York
2. Burges CJC (1998) A tutorial on support vector machines for pattern recognition. Knowl Discov Data Min 2: 121-167
3. Chang C-C, Lin C-J (2006) LIBSVM: a library for support vector machines (Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm)
4. Chu W, Keerthi S, Ong C (2003) Bayesian trigonometric support vector classifier. Neural Comput 15(9): 2227-2254
5. Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines. Cambridge University Press, Cambridge
6. De Leeuw J (1994) Block relaxation algorithms in statistics. In: Bock H-H, Lenski W, Richter MM(eds) Information systems and data analysis. Springer, Berlin, pp 308-324
7. Gifi A (1990) Nonlinear multivariate analysis. Wiley, Chichester
8. Groenen PJF, Nalbantov G, Bioch JC (2007) Nonlinear support vector machines through iterative majorization. In: Decker R, Lenz H-J(eds) Advances in data analysis. Springer, Berlin, pp 149-162
9. Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning. Springer, New York
10. Heiser WJ (1995) Convergent computation by iterative majorization: theory and applications in multidimensional data analysis. In: Krzanowski WJ(eds) Recent advances in descriptive multivariate analysis. Oxford University Press, Oxford, pp 157-189
11. Hsu C-W, Lin C-J (2006) BSVM: bound-constrained support vector machines (Software available at http://www.csie.ntu.edu.tw/~cjlin/bsvm/index.html)
12. Huber PJ (1981) Robust statistics. Wiley, New York
13. Hunter DR, Lange K (2004) A tutorial on MM algorithms. Am Stat 39: 30-37
14. Joachims T (1999) Making large-scale SVM learning practical. In: Schölkopf B, Burges C, Smola A (eds) Advances in kernel methods-support vector learning. MIT-Press, Cambridge ( http://www-ai.cs.uni-dortmund.de/ DOKUMENTE/joachims_99a.pdf )
15. Joachims T (2006) Training linear SVMs in linear time. In: Proceedings of the ACM conference on knowledge discovery and data mining (KDD) ( http://www.cs.cornell.edu/People/tj/publications/joachims_06a.pdf )
16. Kiers HAL (2002) Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems. Comput Stat Data Anal 41: 157-170
17. Kruskal JB (1965) The analysis of factorial experiments by estimating monotone transformations of the data. J R Stat Soc Ser B 27: 251-263
18. Lange K, Hunter DR, Yang I (2000) Optimization transfer using surrogate objective functions. J Comput Graph Stat 9: 1-20
19. Newman D, Hettich S, Blake C, Merz C (1998) UCI repository of machine learning databases ( http://www.ics.uci.edu/~mlearn/MLRepository.html University of California, Irvine, Department of Information and Computer Sciences)
20. Rosset S, Zhu J (2007) Piecewise linear regularized solution paths. Ann Stat 35: 1012-1030
21. Rousseeuw PJ, Leroy AM (2003) Robust regression and outlier detection. Wiley, New York
22. Suykens JAK, Van Gestel T, De Brabanter J, De Moor B, Vandewalle J (2002) Least squares support vector machines. World Scientific, Singapore
23. Van der Kooij AJ (2007) Prediction accuracy and stability of regression with optimal scaling transformations. Unpublished doctoral dissertation, Leiden University
24. Van der Kooij AJ, Meulman JJ, Heiser WJ (2006) Local minima in categorical multiple regression. Comput Stat Data Anal 50: 446-462
25. Vapnik VN (2000) The nature of statistical learning theory. Springer, New York
26. Young FW (1981) Quantitative analysis of qualitative data. Psychometrika 46: 357-388
27. Young FW, De Leeuw J, Takane Y (1976) Additive structure in qualitative data: an alternating least squares method with optimal scaling features. Psychometrika 41: 471-503
28. Young FW, De Leeuw J, Takane Y (1976) Regression with qualitative and quantitative variables: an alternating least squares method with optimal scaling features. Psychometrika 41: 505-529