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ICML
2007
IEEE

Robust non-linear dimensionality reduction using successive 1-dimensional Laplacian Eigenmaps

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Robust non-linear dimensionality reduction using successive 1-dimensional Laplacian Eigenmaps
Non-linear dimensionality reduction of noisy data is a challenging problem encountered in a variety of data analysis applications. Recent results in the literature show that spectral decomposition, as used for example by the Laplacian Eigenmaps algorithm, provides a powerful tool for non-linear dimensionality reduction and manifold learning. In this paper, we discuss a significant shortcoming of these approaches, which we refer to as the repeated eigendirections problem. We propose a novel approach that combines successive 1dimensional spectral embeddings with a data advection scheme that allows us to address this problem. The proposed method does not depend on a non-linear optimization scheme; hence, it is not prone to local minima. Experiments with artificial and real data illustrate the advantages of the proposed method over existing approaches. We also demonstrate that the approach is capable of correctly learning manifolds corrupted by significant amounts of noise.
Samuel Gerber, Tolga Tasdizen, Ross T. Whitaker
Added 17 Nov 2009
Updated 17 Nov 2009
Type Conference
Year 2007
Where ICML
Authors Samuel Gerber, Tolga Tasdizen, Ross T. Whitaker
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