Robust kernel Isomap |
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Authors: | Heeyoul Choi Author Vitae] Seungjin Choi [Author Vitae] |
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Affiliation: | Department of Computer Science, Pohang University of Science and Technology, San 31 Hyoja-dong, Nam-gu, Pohang 790-784, Korea |
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Abstract: | Isomap is one of widely used low-dimensional embedding methods, where geodesic distances on a weighted graph are incorporated with the classical scaling (metric multidimensional scaling). In this paper we pay our attention to two critical issues that were not considered in Isomap, such as: (1) generalization property (projection property); (2) topological stability. Then we present a robust kernel Isomap method, armed with such two properties. We present a method which relates the Isomap to Mercer kernel machines, so that the generalization property naturally emerges, through kernel principal component analysis. For topological stability, we investigate the network flow in a graph, providing a method for eliminating critical outliers. The useful behavior of the robust kernel Isomap is confirmed through numerical experiments with several data sets. |
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Keywords: | Isomap Kernel PCA Manifold learning Multidimensional scaling (MDS) Nonlinear dimensionality reduction |
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