A scale-based approach to finding effective dimensionality in manifold learning

Details A scale-based approach to finding effective dimensionality in manifold learning A scale-based approach to finding effective dimensionality in manifold learning

2007-10-29

arxiv.org/abs/0710.5349v2

Electronic Journal of Statistics 2008, Vol. 2, 127-148

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-EJS137 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

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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