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Regularized Kernel Local Linear Embedding on Dimensionality Reduction for Non-vectorial Data

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AI 2009: Advances in Artificial Intelligence (AI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5866))

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Abstract

In this paper, we proposed a new nonlinear dimensionality reduction algorithm called regularized Kernel Local Linear Embedding (rKLLE) for highly structured data. It is built on the original LLE by introducing kernel alignment type of constraint to effectively reduce the solution space and find out the embeddings reflecting the prior knowledge. To enable the non-vectorial data applicability of the algorithm, a kernelized LLE is used to get the reconstruction weights. Our experiments on typical non-vectorial data show that rKLLE greatly improves the results of KLLE.

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References

  1. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(22), 2323–2326 (2000)

    Article  Google Scholar 

  2. Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15(6), 1373–1396 (2003)

    Article  MATH  Google Scholar 

  3. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(22), 2319–2323 (2000)

    Article  Google Scholar 

  4. Zhang, Z., Zha, H.: Principal manifolds and nonlinear dimensionality reduction via tangent space. SIAM Journal on Scientific Computing 26(1), 313–338 (2005)

    Article  MathSciNet  Google Scholar 

  5. Lawrence, N.: Probabilistic non-linear principal component analysis with gaussian process latent variable models. Journal of Machine Learning Research 6, 1783–1816 (2005)

    MathSciNet  Google Scholar 

  6. Jolliffe, M.: Principal Component Analysis. Springer, New York (1986)

    Google Scholar 

  7. Fisher, R.A.: The use of multiple measurements in taxonomic problems. Annals of Eugenics 7, 179–188 (1936)

    Google Scholar 

  8. Gärtner, T.: A survey of kernels for structured data. ACM SIGKDD Explorations Newsletter 5(1), 49–58 (2003)

    Article  Google Scholar 

  9. Schölkopf, B., Smola, A.J., Müller, K.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10, 1299–1319 (1998)

    Article  Google Scholar 

  10. Baudat, G., Anouar, F.: Generalized discriminant analysis using a kernel approach. Neural Computation 12(10), 2385–2404 (2000)

    Article  Google Scholar 

  11. Davison, M.L.: Multidimensional Scaling. Wiley series in probability and mathematical statistics. Applied probability and statistics. Wiley, New York (1983)

    Google Scholar 

  12. Guo, Y., Gao, J., Kwan, P.W.: Kernel Laplacian eigenmaps for visualization of non-vectorial data. In: Sattar, A., Kang, B.-h. (eds.) AI 2006. LNCS (LNAI), vol. 4304, pp. 1179–1183. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Schölkopf, B., Smola, A.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. The MIT Press, Cambridge (2002)

    Google Scholar 

  14. Nabney, I.T.: NETLAB: Algorithms for Pattern Recognition. Advances in Pattern Recognition. Springer, London (2004)

    Google Scholar 

  15. Jebara, T.: Images as bags of pixels. In: Ninth IEEE International Conference on Computer Vision (ICCV 2003), vol. 1, pp. 265–272 (2003)

    Google Scholar 

  16. Guo, Y., Gao, J.: An integration of shape context and semigroup kernel in image classification. In: International Conference on Machine Learning and Cybernetics (2007)

    Google Scholar 

  17. Qiu, J., Hue, M., Ben-Hur, A., Vert, J.P., Noble, W.S.: An alignment kernel for protein structures. Bioinformatics 23, 1090–1098 (2007)

    Article  Google Scholar 

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Guo, Y., Gao, J., Kwan, P.W. (2009). Regularized Kernel Local Linear Embedding on Dimensionality Reduction for Non-vectorial Data. In: Nicholson, A., Li, X. (eds) AI 2009: Advances in Artificial Intelligence. AI 2009. Lecture Notes in Computer Science(), vol 5866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10439-8_25

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  • DOI: https://doi.org/10.1007/978-3-642-10439-8_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10438-1

  • Online ISBN: 978-3-642-10439-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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