Out-of-sample extrapolation of learned manifolds.

Full Abstract

We investigate the problem of extrapolating the embedding of a manifold learned from finite samples to novel out-of-sample data. We concentrate on the manifold learning method called Maximum Variance Unfolding (MVU) for which the extrapolation problem is still largely unsolved. Taking the perspective of MVU learning being equivalent to Kernel PCA, our problem reduces to extending a kernel matrix generated from an unknown kernel function to novel points. Leveraging on previous developments, we propose a novel solution which involves approximating the kernel eigenfunction using Gaussian basis functions. We also show how the width of the Gaussian can be tuned to achieve extrapolation. Experimental results which demonstrate the effectiveness of the proposed approach are also included.

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Author information

Author/s: Chin, Tat-Jun (TJ); Suter, David (D);

Affiliation: Institute for Infocomm Research, Agency for Science, Technology, and Research, Singapore. tjchin(-atsign-)i2r.a-star.edu.sg

Journal and publication information

Publication Type: Journal Article

Journal: IEEE transactions on pattern analysis and machine intelligence (IEEE Trans Pattern Anal Mach Intell), published in United States. (Language: eng)

Reference: 2008-Sep; vol 30 (issue 9) : pp 1547-56

Dates: Created 2008/07/11; Completed 2008/09/23;

PMID: 18617714, status: MEDLINE (last retrieval date: 11/6/2008)

Sourced from the National Library of Medicine. Abstract text and other information may be subject to copyright.

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MeSH headings (categories)

This article was linked to the MESH Headings shown below.

Algorithms
Artificial Intelligence
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods

Image Interpretation, Computer-Assisted - methods
Pattern Recognition, Automated - methods
Reproducibility of Results
Sensitivity and Specificity

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