Adaptive Manifold Learning

Manifold learning algorithms seek to find a low-dimensional parameterization of high-dimensional data. They heavily rely on the notion of what can be considered as local, how accurately the manifold can be approximated locally, and, last but not least, how the local structures can be patched togethe...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2012-02, Vol.34 (2), p.253-265
Main Authors: Zhang, Zhenyue, Wang, Jing, Zha, Hongyuan
Format: Article
Language:English
Subjects:
Accuracy
Adaptive algorithms
Adaptive structures
Algorithm design and analysis
Algorithms
Applied sciences
Approximation algorithms
Artificial intelligence
bias reduction
classification
Computer science
control theory
systems
Curvature
Data processing. List processing. Character string processing
Density
dimensionality reduction
Estimation
Exact sciences and technology
Learning
Linear approximation
Manifold learning
Manifolds
Memory organisation. Data processing
neighborhood selection
Parametrization
Software
Studies
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Summary:Manifold learning algorithms seek to find a low-dimensional parameterization of high-dimensional data. They heavily rely on the notion of what can be considered as local, how accurately the manifold can be approximated locally, and, last but not least, how the local structures can be patched together to produce the global parameterization. In this paper, we develop algorithms that address two key issues in manifold learning: 1) the adaptive selection of the local neighborhood sizes when imposing a connectivity structure on the given set of high-dimensional data points and 2) the adaptive bias reduction in the local low-dimensional embedding by accounting for the variations in the curvature of the manifold as well as its interplay with the sampling density of the data set. We demonstrate the effectiveness of our methods for improving the performance of manifold learning algorithms using both synthetic and real-world data sets.
ISSN:0162-8828
1939-3539
2160-9292
DOI:10.1109/TPAMI.2011.115