Abstract
To minimize the primal support vector machine (SVM) problem, we propose to use iterative majorization. To allow for nonlinearity of the predictors, we use (non)monotone spline transformations. An advantage over the usual kernel approach in the dual problem is that the variables can be easily interpreted. We illustrate this with an example from the literature.
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References
BORG, I. and GROENEN, P.J.F. (2005): Modern Multidimensional Scaling: Theory and applications (2nd edition). Springer, New York.
BURGES, C.J.C. (1998): A Tutorial on Support Vector Machines for Pattern Recognition. Knowledge Discovery and Data Mining, 2, 121–167.
DE LEEUW, J. (1994): Block Relaxation Algorithms in Statistics. In: H.-H. Bock, W. Lenski and M. M. Richter (Eds.): Information Systems and Data Analysis. Springer, Berlin, 308–324.
GIFI, A. (1990): Nonlinear Multivariate Analysis. Wiley, Chichester.
HASTIE, T., TIBSHIRANI, R. and FRIEDMAN, J. (2000): The Elements of Statistical Learning. Springer, New York.
HEISER, W.J. (1995): Convergent Computation by Iterative Majorization: Theory and Applications in Multidimensional Data Analysis. In: W.J. Krzanowski (Ed.): Recent Advances in Descriptive Multivariate Analysis. Oxford University Press, Oxford, 157–189.
HUBER, P.J. (1981): Robust Statistics. Wiley, New York.
HUNTER, D.R. and LANGE, K. (2004): A Tutorial on MM Algorithms. The American Statistician, 39, 30–37.
KIERS, H.A.L. (2002): Setting up Alternating Least Squares and Iterative Majorization Algorithms for Solving Various Matrix Optimization Problems. Computational Statistics and Data Analysis, 41, 157–170.
LANGE, K., HUNTER, D.R. and YANG, I. (2000): Optimization Transfer using Surrogate Objective Functions. Journal of Computational and Graphical Statistics, 9, 1–20.
RAMSAY, J.O. (1988): Monotone Regression Splines in Action. Statistical Science, 3,4, 425–461.
VAPNIK, V.N. (2000): The nature of statistical learning theory. Springer, New York.
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Groenen, P.J.F., Nalbantov, G., Bioch, J.C. (2007). Nonlinear Support Vector Machines Through Iterative Majorization and I-Splines. In: Decker, R., Lenz, H.J. (eds) Advances in Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70981-7_18
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DOI: https://doi.org/10.1007/978-3-540-70981-7_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70980-0
Online ISBN: 978-3-540-70981-7
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