Hierarchical and Reweighting Cluster Kernels for Semi-Supervised Learning

Zalán Bodó, Lehel Csató


Recently semi-supervised methods gained increasing attention and many novel semi-supervised learning algorithms have been proposed. These methods exploit the information contained in the usually large unlabeled data set in order to improve classification or generalization performance. Using data-dependent kernels for kernel machines one can build semi-supervised classifiers by building the kernel in such a way that feature space dot products incorporate the structure of the data set. In this paper we propose two such methods: one using specific hierarchical clustering, and another kernel for reweighting an arbitrary base kernel taking into account the cluster structure of the data.


Kernel methods, semi-supervised learning, clustering

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Mikhail Belkin, Partha Niyogi, and Vikas Sindhwani. Manifold regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples. Journal of Machine Learning Research, 7:2399–2434, 2006.

Ingwer Borg and Patrick J. F. Groenen. Modern Multidimensional Scaling, 2nd edition. Springer- Verlag, New York, 2005.

B. E. Boser, I. Guyon, and V. N. Vapnik. A Training Algorithm for Optimal Margin Classifiers. Computational Learning Theory, 5:144–152, 1992.

Chih-Chung Chang and Chih-Jen Lin. LIBSVM: a library for support vector machines, 2001.

Olivier Chapelle, Bernhard Schölkopf, and Alexander Zien. Semi-Supervised Learning. MIT Press, September 2006.

Olivier Chapelle, Jason Weston, and Bernhard Schölkopf. Cluster Kernels for Semi-Supervised Learning. In Suzanna Becker, Sebastian Thrun, and Klaus Obermayer, editors, NIPS, pages 585– 592. MIT Press, 2002.

Richard Duda, Peter Hart, and David Stork. Pattern Classification. John Wiley and Sons, 2001. 0-471-05669-3.

Bernd Fischer, Volker Roth, and Joachim M. Buhmann. Clustering with the Connectivity Kernel. In Sebastian Thrun, Lawrence K. Saul, and Bernhard Schölkopf, editors, NIPS. MIT Press, 2003.

Imre J. Rudas and János Fodor. Intelligent systems. Int. J. of Computers, Communication & Control, III(Suppl. issue: Proceedings of ICCCC 2008):132–138, 2008.

B. Schölkopf and A. J. Smola. Learning with Kernels. The MIT Press, Cambridge, MA, 2002.

J. B. Tenenbaum, V. de Silva, and J. C. Langford. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science, 290(5500):2319–2323, December 2000.

Jason Weston, Christina Leslie, Eugene Ie, and William Stafford Noble. Semi-Supervised Protein Classification Using Cluster Kernels. In Olivier Chapelle, Bernhard Schölkopf, and Alexander Zien, editors, Semi-Supervised Learning, chapter 19, pages 343–360. MIT Press, 2006.

Quan Yong and Yang Jie. Geodesic Distance for Support Vector Machines. Acta Automatica Sinica, 31(2):202–208, 2005.

DOI: https://doi.org/10.15837/ijccc.2010.4.2496

Copyright (c) 2017 Zalán Bodó, Lehel Csató

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