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...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 34(2012), 2 vom: 13. Feb., Seite 253-65 |
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| Weitere Verfasser: | , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2012
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't Research Support, U.S. Gov't, Non-P.H.S. |
| Zusammenfassung: | 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 |
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| Beschreibung: | Date Completed 21.05.2012 Date Revised 01.03.2012 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |
| DOI: | 10.1109/TPAMI.2011.115 |