Abstract
In this paper, we propose the Kernel Laplacian Eigenmaps for nonlinear dimensionality reduction. This method can be extended to any structured input beyond the usual vectorial data, enabling the visualization of a wider range of data in low dimension once suitable kernels are defined. Comparison with related methods based on MNIST handwritten digits data set supported the claim of our approach. In addition to nonlinear dimensionality reduction, this approach makes visualization and related applications on non-vectorial data possible.
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References
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(22), 2323–2326 (2000)
Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15(6), 1373–1396 (2003)
He, X., Niyogi, P.: Locality preserving projections. In: Thrun, S., Saul, L., Schölkopf, B. (eds.) Advances in Neural Information Processing Systems, vol. 16, MIT Press, Cambridge (2004)
Schölkopf, B., Smola, A.J., Müller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10, 1299–1319 (1998)
Ham, J., Lee, D.D., Mika, S., Schölkopf, B.: A kernel view of the dimensionality reduction of manifolds. In: ICML 2004: Proceedings of the twenty-first international conference on Machine learning, pp. 47–54. ACM Press, New York (2004)
Chung, F.R.K.: Spectral Graph Theory. Regional Conference Series in Mathmatics, vol. 92. AMS (1997)
Guo, Y., Gao, J.: An integration of shape context and semigroup kernel in image classification. Pattern Recognition Letters (submitted, 2006)
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Guo, Y., Gao, J., Kwan, P.W.H. (2006). Kernel Laplacian Eigenmaps for Visualization of Non-vectorial Data. In: Sattar, A., Kang, Bh. (eds) AI 2006: Advances in Artificial Intelligence. AI 2006. Lecture Notes in Computer Science(), vol 4304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11941439_144
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DOI: https://doi.org/10.1007/11941439_144
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49787-5
Online ISBN: 978-3-540-49788-2
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