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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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)
Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(22), 2319–2323 (2000)
Zhang, Z., Zha, H.: Principal manifolds and nonlinear dimensionality reduction via tangent space. SIAM Journal on Scientific Computing 26(1), 313–338 (2005)
Lawrence, N.: Probabilistic non-linear principal component analysis with gaussian process latent variable models. Journal of Machine Learning Research 6, 1783–1816 (2005)
Jolliffe, M.: Principal Component Analysis. Springer, New York (1986)
Fisher, R.A.: The use of multiple measurements in taxonomic problems. Annals of Eugenics 7, 179–188 (1936)
Gärtner, T.: A survey of kernels for structured data. ACM SIGKDD Explorations Newsletter 5(1), 49–58 (2003)
Schölkopf, B., Smola, A.J., Müller, K.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10, 1299–1319 (1998)
Baudat, G., Anouar, F.: Generalized discriminant analysis using a kernel approach. Neural Computation 12(10), 2385–2404 (2000)
Davison, M.L.: Multidimensional Scaling. Wiley series in probability and mathematical statistics. Applied probability and statistics. Wiley, New York (1983)
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)
Schölkopf, B., Smola, A.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. The MIT Press, Cambridge (2002)
Nabney, I.T.: NETLAB: Algorithms for Pattern Recognition. Advances in Pattern Recognition. Springer, London (2004)
Jebara, T.: Images as bags of pixels. In: Ninth IEEE International Conference on Computer Vision (ICCV 2003), vol. 1, pp. 265–272 (2003)
Guo, Y., Gao, J.: An integration of shape context and semigroup kernel in image classification. In: International Conference on Machine Learning and Cybernetics (2007)
Qiu, J., Hue, M., Ben-Hur, A., Vert, J.P., Noble, W.S.: An alignment kernel for protein structures. Bioinformatics 23, 1090–1098 (2007)
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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
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