Summary
The paper first reviews a recently developed method called the Support Vector Machine. The main feature of the method is to transform the original input vectors into high-dimensional space, and then construct a linear regression function or hyperplane in that space. The transformation is usually done by applying the kernel technique. The paper then shows that the same kernel technique can be applied to classical algorithms such as Ridge Regression. In conclusion, we present a new transductive learning algorithm that also allows us to compute confidence levels.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
3Transduction is inference from particular to particular. Here we deal with a problem of transduction in the sense that we are interested only in the labelling of a particular example rather than in a general inductive rule for classifying future examples (3). Transduction is naturally related to a set of algorithms known as instance-based or case-based learning. Perhaps the most well-known algorithm in this class is k-nearest neighbour algorithm. The transductive algorithm described in this paper, however, is not based on similarities between examples (as are most of the instance-based techniques), but relies on selection of support vectors. Using the support vectors allows us to deal with high-dimensional problems, and to introduce the confidence and credibility measures.
References
Vapnik, V. N. (1998), Statistical Learning Theory. Wiley, New York.
Saunders, C., Gammerman, A. & Vovk, V. (1998), Ridge Regression Learning Algorithm in Dual Variables. Machine Learning, Proceedings of the Fifteenth International Conference (ICML’98), pp. 515–521, edited by Jude Shavlik, Morgan Kaufmann Publishers, San Francisco.
Gammerman, A. J. (1996), Machine Learning: progress and prospects. ISBN 0 0900145 93 5, University of London, 1996.
Gammerman, A., Vovk, V, & Vapnik, V. (1998), Learning by Transduction. Uncertainty in Artificial Intelligence, Proceedings of the Fourteenth Conference, pp.148–155, edited by G.F. Cooper and S. Moral, Morgan Kaufmann Publishers, San Francisco.
Vovk, V, Gammerman, A. & Saunders, C. (1999), Machine Learning Applications of Algorithmic Randomness. Machine Learning, Proceedings of the Sixteenth International Conference (ICML ’99), pp.444–453, edited by I. Bratko and S. Dzeroski, Morgan Kaufmann Publishers, San Francisco.
Wahba, G. (1978), Improper priors, spline smoothing and the problem of guarding against model errors in regression. J.Roy.Stat.Soc. Ser.B, 40:364–372, 1978.
Li, M. and Vitanyi, P. (1997), An introduction to Kolmogorov complexity and its applications. Springer, New York, 2nd edition, 1997.
Author information
Authors and Affiliations
Additional information
This work is partially supported by EPSRC through grants GR/L35812 (“Support Vector and Bayesian learning algorithms”), GR/M14937 (“Predictive complexity: recursion-theoretic variants”) and GR/M16856 (“Comparison of Support Vector Machine and Minimum Message Length methods for induction and prediction”)
Rights and permissions
About this article
Cite this article
Gammermann, A. Support vector machine learning algorithm and transduction. Computational Statistics 15, 31–39 (2000). https://doi.org/10.1007/s001800050034
Published:
Issue Date:
DOI: https://doi.org/10.1007/s001800050034