On the regularized Laplacian eigenmaps |
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Authors: | Ying Cao Di-Rong Chen |
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Affiliation: | Department of Mathematics, LMIB, Beijing University of Aeronautics and Astronautics, Beijing 100191, PR China |
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Abstract: | To find an appropriate low-dimensional representation for complex data is one of the central problems in machine learning and data analysis. In this paper, a nonlinear dimensionality reduction algorithm called regularized Laplacian eigenmaps (RLEM) is proposed, motivated by the method for regularized spectral clustering. This algorithm provides a natural out-of-sample extension for dealing with points not in the original data set. The consistency of the RLEM algorithm is investigated. Moreover, a convergence rate is established depending on the approximation property and the capacity of the reproducing kernel Hilbert space measured by covering numbers. Experiments are given to illustrate our algorithm. |
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Keywords: | Nonlinear dimensionality reduction Regularized Laplacian eigenmaps Graph Laplacian Learning rate |
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