Abstract
Due to the rapid development of information technology in recent years, it is common to encounter enormousamounts of data collected fromdiverse sources.This has led to a great demand for innovative analytic tools that can handle the kinds of complex data sets that cannot be tackled using traditional statistical methods. Modern data visualization techniques face a similar situation and must also provide adequate solutions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aizerman, M.A., Braverman, E.M. and Rozoner, L.I. (1964). Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821–837.
Akaho, S. (2001). A kernel method for canonical correlation analysis. In: International Meeting of Psychometric Society (IMPS2001), 15–19 July 2001, Osaka, Japan.
Alpaydin, E. (2004). Introduction to Machine Learning. MIT Press, Cambridge.
Aronszajn, N. (1950). Theory of reproducing kernels. Transactions of the American Mathematical Society, 68:337–404.
Bach, F. and Jordan, M.I. (2002). Kernel independent component analysis. Journal of Machine Learning Research, 3:1–48.
Ben-Hur, A., Horn, D., Siegelmann, H.T. and Vapnik, V. (2001). Support vector clustering. Journal of Machine Learning Research, 2:125–137.
Berlinet, A. and Thomas-Agnan, C. (2004). Reproducing Kernel Hilbert Spaces in Probability and Statistics. Kluwer, Boston, MA.
Boser, B.E., Guyon, I.M. and Vapnik, V.N. (1992). A training algorithm for optimal margin classifiers. In: Valient, L. and Warmuth, M. (eds) Proceedings of the 5th Annual ACM Workshop on Computational Learning Theory. ACM Press, Pittsburgh, PA, 5:144–152.
Hardoon, D.R., Szedmak, S. and Shawe-Taylor, J. (2004). Canonical correlation analysis: An overview with application to learning methods. Neural Computation, 16(12): 2639–2664.
Hein, M. and Bousquet, O. (2004). Kernels, associated structures and generalizations. Technical report, Max Planck Institute for Biological Cybernetics, Germany. http://www.kyb.tuebingen.mpg.de/techreports.html.
Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28:321–377.
Lee, Y.J., Hsieh, W.F. and Huang, C.M. (2005). ε-SSVR: A smooth support vector machine for ε-insensitive regression. IEEE Transactions on Knowledge and Data Engineering, 17(5): 678–685.
Lee, Y.J. and Huang, S.Y. (2007). Reduced support vector machines: a statistical theory. IEEE Transactions on Neural Networks, 18:1–13.
Lee, Y.J. and Mangasarian, O.L. (2001a). RSVM: Reduced support vector machines. In: Kumar, V. and Grossman, R. (eds) Proceedings of the First SIAM International Conference on Data Mining. SIAM, Philadephia, PA.
Lee, Y.J. and Mangasarian, O.L. (2001b). SSVM: A smooth support vector machine for classification. Computational Optimization and Applications, 20(1): 5–22.
MacQueen, J.B. (1967). Some methods for classification and analysis of multivariate observations. In: Le Cam, L. and Neyman, J. (eds) Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley, CA, 1:281–297.
Mardia, K.V., Kent, J.T. and Bibby, J.M. (1979). Multivariate Analysis. Probability and Mathematical Statistics: A Series of Monographs and Textbooks. Academic, New York.
Schölkopf, B., Burges, C. and Smola, A. (1999). Kernel principal component analysis. Advances in Kernel Methods – Support Vector Learning, 327–352. MIT Press, Cambridge, MA.
Schölkopf, B., Smola, A. and Müller, K. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5): 1299–1319.
Vapnik, V.N. (1995). The Nature of Statistical Learning Theory. Springer-Verlag, New York.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Chang, Yc., Lee, YJ., Pao, HK., Lee, MH., Huang, SY. (2008). Data Visualization via Kernel Machines. In: Handbook of Data Visualization. Springer Handbooks Comp.Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33037-0_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-33037-0_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33036-3
Online ISBN: 978-3-540-33037-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)