A scale-based approach to finding effective dimensionality in manifold learning
Xiaohui Wang and J. S. Marron
Source: Electron. J. Statist. Volume 2
(2008), 127-148.
Abstract
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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Keywords: manifold learning; intrinsic dimension; scale space; hypothesis test; multivariate analysis
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ejs/1205761031
Digital Object Identifier: doi:10.1214/07-EJS137
Mathematical Reviews number (MathSciNet): MR2386090
Zentralblatt MATH identifier: 05274639
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