Multiscale manifold representation and modeling

Many real world data sets can be viewed as points in a higher-dimensional space that lie concentrated around a lower-dimensional manifold structure. We propose a new multiscale representation for such point clouds based on lifting and perfect matching. The result is an adaptive wavelet transform tha...

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Bibliographic Details
Main Authors: Hyeokho Choi, Baraniuk, R.
Format: Conference Proceeding
Language:English
Subjects:
Application software
Biomedical computing
Clouds
Computer vision
Data mining
Information geometry
Manifolds
Signal processing algorithms
Wavelet coefficients
Wavelet transforms
Online Access:Request full text
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Summary:Many real world data sets can be viewed as points in a higher-dimensional space that lie concentrated around a lower-dimensional manifold structure. We propose a new multiscale representation for such point clouds based on lifting and perfect matching. The result is an adaptive wavelet transform that decomposes a point cloud into manifold approximations and details at multiple scales. We illustrate with several examples that the transform can extract an unknown smooth manifold from noisy point cloud samples using simple wavelet thresholding ideas.
ISSN:1520-6149
2379-190X
DOI:10.1109/ICASSP.2005.1416072