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Clustering

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Support Vector Machines for Pattern Classification

Part of the book series: Advances in Pattern Recognition ((ACVPR))

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Abstract

Unlike multilayer neural networks, support vector machines can be formulated for one-class problems. This technique is called domain description or one-class classification and is applied to clustering and detection of outliers for both pattern classification and function approximation [1].

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Notes

  1. 1.

    When kernels, such as RBF kernels, that depend only on \(\textbf{x}-\textbf{x}^\prime\) are used, the linear term in (8.22) is constant from (8.23). Then it is shown that the problem is equivalent to maximizing the margin in separating data from the origin by the hyperplane [5, pp. 230–234].

References

  1. J. Ma and S. Perkins. Time-series novelty detection using one-class support vector machines. In Proceedings of International Joint Conference on Neural Networks (IJCNN 2003), volume 3, pages 1741–1745, Portland, OR, 2003.

    Google Scholar 

  2. D. M. J. Tax and R. P. W. Duin. Support vector domain description. Pattern Recognition Letters, 20(11–13):1191–1199, 1999.

    Article  Google Scholar 

  3. D. M. J. Tax and R. P. W. Duin. Outliers and data descriptions. In Proceedings of the Seventh Annual Conference of the Advanced School for Computing and Imaging (ASCI 2001), pages 234–241, Heijen, The Netherlands, 2001.

    Google Scholar 

  4. D. M. J. Tax and R. P. W. Duin. Support vector data description. Machine Learning, 54(1):45–66, 2004.

    Article  MATH  Google Scholar 

  5. B. Schölkopf and A. J. Smola. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge, MA, 2002.

    Google Scholar 

  6. D. M. J. Tax and P. Juszczak. Kernel whitening for one-class classification. In S.-W. Lee and A. Verri, editors, Pattern Recognition with Support Vector Machines: Proceedings of First International Workshop, SVM 2002, Niagara Falls, Canada, pages 40–52, Springer-Verlag, Berlin, Germany, 2002.

    Google Scholar 

  7. I. W. Tsang, J. T. Kwok, and S. Li. Learning the kernel in Mahalanobis one-class support vector machines. In Proceedings of the 2006 International Joint Conference on Neural Networks (IJCNN 2006), pages 2148–2154, Vancouver, Canada, 2006.

    Google Scholar 

  8. T. Ban and S. Abe. Implementing multi-class classifiers by one-class classification methods. In Proceedings of the 2006 International Joint Conference on Neural Networks (IJCNN 2006), pages 719–724, Vancouver, Canada, 2006.

    Google Scholar 

  9. D. Lee and J. Lee. Domain described support vector classifier for multi-classification problems. Pattern Recognition, 40(1):41–51, 2007.

    Article  MATH  Google Scholar 

  10. C. Yuan and D. Casasent. Support vector machines for class representation and discrimination. In Proceedings of International Joint Conference on Neural Networks (IJCNN 2003), volume 2, pages 1611–1616, Portland, OR, 2003.

    Google Scholar 

  11. M. Girolami. Mercer kernel-based clustering in feature space. IEEE Transactions on Neural Networks, 13(3):780–784, 2002.

    Article  Google Scholar 

  12. S. Miyamoto and D. Suizu. Fuzzy c-means clustering using transformations into high dimensional spaces. In Proceedings of the First International Conference on Fuzzy Systems and Knowledge Discovery (FSKD '02), volume 2, pages 656–660, Singapore, 2002.

    Google Scholar 

  13. A. Ben-Hur, D. Horn, H. T. Siegelmann, and V. Vapnik. Support vector clustering. Journal of Machine Learning Research, 2:125–137, 2001.

    Article  Google Scholar 

  14. J. Yang, V. Estivill-Castro, and S. K. Chalup. Support vector clustering through proximity graph modelling. In Proceedings of the Ninth International Conference on Neural Information Processing (ICONIP '02), volume 2, pages 898–903, Singapore, 2002.

    Google Scholar 

  15. J. Lee and D. Lee. An improved cluster labeling method for support vector clustering. Pattern Analysis and Machine Intelligence, 27(3):461–464, 2005.

    Article  Google Scholar 

  16. T. Ban and S. Abe. Spatially chunking support vector clustering algorithm. In Proceedings of International Joint Conference on Neural Networks (IJCNN 2004), volume 1, pages 413–418, Budapest, Hungary, 2004.

    Google Scholar 

  17. C. S. Chu, I. W. Tsang, and J. T. Kwok. Scaling up support vector data description by using core-sets. In Proceedings of International Joint Conference on Neural Networks (IJCNN 2004), volume 1, pages 425–430, Budapest, Hungary, 2004.

    Google Scholar 

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Authors and Affiliations

  1. Graduate School of Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan

    Prof. Dr. Shigeo Abe

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  1. Prof. Dr. Shigeo Abe
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Correspondence to Shigeo Abe .

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Abe, S. (2010). Clustering. In: Support Vector Machines for Pattern Classification. Advances in Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-84996-098-4_8

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  • DOI: https://doi.org/10.1007/978-1-84996-098-4_8

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  • Print ISBN: 978-1-84996-097-7

  • Online ISBN: 978-1-84996-098-4

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