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Learning Geometry-Aware Kernels in a Regularization Framework

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Computer Analysis of Images and Patterns (CAIP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8047))

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Abstract

In this paper, we propose a regularization framework for learning geometry-aware kernels. Some existing geometry-aware kernels can be viewed as instances in our framework. Moreover, the proposed framework can be used as a general platform for developing new geometry-aware kernels. We show how multiple sources of information can be integrated in our framework, allowing us to develop more flexible kernels. We present some new kernels based on our framework. The performance of the kernels is evaluated on classification and clustering tasks. The empirical results show that our kernels significantly improve the performance.

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References

  1. Kondor, R.I., Lafferty, J.: Diffusion kernels on graphs and other discrete input spaces. In: Proceedings of the 19th Annual International Conference on Machine Learning, pp. 315–322 (2002)

    Google Scholar 

  2. Smola, A.J., Kondor, R.: Kernels and regularization on graphs. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT/Kernel 2003. LNCS (LNAI), vol. 2777, pp. 144–158. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Ham, J., Lee, D., Mika, S., Schölkopf, B.: A kernel view of the dimensionality reduction of manifolds. In: Proceedings of the 21st Annual International Conference on Machine Learning, pp. 47–54 (2004)

    Google Scholar 

  4. Weinberger, K., Sha, F., Saul, L.: Learning a kernel matrix for nonlinear dimensionality reduction. In: Proceedings of the 21st Annual International Conference on Machine Learning, pp. 839–846 (2004)

    Google Scholar 

  5. Lawrence, N.D.: A unifying probabilistic perspective for spectral dimensionality reduction: Insights and new models. The Journal of Machine Learning Research 12, 1609–1638 (2012)

    MathSciNet  Google Scholar 

  6. Sindhwani, V., Niyogi, P., Belkin, M.: Beyond the point cloud: from transductive to semi-supervised learning. In: Proceedings of the 22nd International Conference on Machine Learning, pp. 824–831 (2005)

    Google Scholar 

  7. Song, L., Smola, A., Borgwardt, K., Gretton, A.: Colored maximum variance unfolding. Advances in Neural Information Processing Systems 20, 1385–1392 (2008)

    Google Scholar 

  8. Zhu, X., Kandola, J., Ghahramani, Z., Lafferty, J.: Nonparametric transforms of graph kernels for semi-supervised learning. Advances in Neural Information Processing Systems 17, 1641–1648 (2005)

    Google Scholar 

  9. Zhuang, J., Tsang, I., Hoi, S.: A family of simple non-parametric kernel learning algorithms. The Journal of Machine Learning Research 12, 1313–1347 (2011)

    MathSciNet  Google Scholar 

  10. Belkin, M., Niyogi, P., Sindhwani, V.: Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. The Journal of Machine Learning Research 7, 2399–2434 (2006)

    MathSciNet  MATH  Google Scholar 

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Pan, B., Chen, WS. (2013). Learning Geometry-Aware Kernels in a Regularization Framework. In: Wilson, R., Hancock, E., Bors, A., Smith, W. (eds) Computer Analysis of Images and Patterns. CAIP 2013. Lecture Notes in Computer Science, vol 8047. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40261-6_42

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  • DOI: https://doi.org/10.1007/978-3-642-40261-6_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40260-9

  • Online ISBN: 978-3-642-40261-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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