Open Access
2008 A scale-based approach to finding effective dimensionality in manifold learning
Xiaohui Wang, J. S. Marron
Electron. J. Statist. 2: 127-148 (2008). DOI: 10.1214/07-EJS137


The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale space viewpoint is the key to our approach enabling us to meet the challenge of noisy data. Our approach finds the effective dimensionality of the data over all scale without any prior knowledge. It has better performance compared with other methods especially in the presence of relatively large noise and is computationally efficient.


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Xiaohui Wang. J. S. Marron. "A scale-based approach to finding effective dimensionality in manifold learning." Electron. J. Statist. 2 127 - 148, 2008.


Published: 2008
First available in Project Euclid: 17 March 2008

zbMATH: 1320.62115
MathSciNet: MR2386090
Digital Object Identifier: 10.1214/07-EJS137

Keywords: hypothesis test , intrinsic dimension , manifold learning , Multivariate analysis , scale space

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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