Summary
We describe a variant of the Isomap manifold learning algorithm [1], called ‘C-Isomap’. Isomap was designed to learn non-linear mappings which are isometric embeddings of a flat, convex data set. C-Isomap is designed to recover mappings in the larger class of conformal embeddings, provided that the original sampling density is reasonably uniform. We compare the performance of both versions of Isomap and other algorithms for manifold learning (MDS, LLE, GTM) on a range of data sets.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The authors gratefully acknowledge the support of the DARPA Human ID project, the Office of Naval Research, and the National Science Foundation (grant DMS-Ol01364). The authors also thank Sam Roweis for stimulating discussions, and Larry Saul for suggesting the conformal fishbowl example as a test case.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J. B. Tenenbaum, V. de Silva and J. C. Langford. Science 290, 2319 (2000).
K. V. Mardia, J. T. Kent and J. M. Bibby. Multivariate Analysis, (Academic Press, London, 1979).
C. M. Bishop, M. Svensén, and C. K. I. Williams. Neural Computation 10, 215 (1998).
D. Beymer, T. Poggio, Science 272, 1905 (1996).
A. Hyvärinen and P. Pajunen (1998). Nonlinear Independent Component Analysis: Existence and Uniqueness Results. Neural Networks 12(3), 423 (1999).
S. Roweis and L. Saul. Science 290, 2323 (2000).
M. Bernstein, V. de Silva, J. C. Langford, and J. B. Tenenbaum. Preprint dated (12/20/2000) available at: http://isomap.Stanford.edu/BdSLT.pdf.
T. F. Cox and M. A. A. Cox, Multidimensional Scaling, (Chapman & Hall, London, 1994).
T. M. Mitchell, Machine Learning, (McGraw-Hill, New York, 1997).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
de Silva, V., Tenenbaum, J.B. (2003). Unsupervised Learning of Curved Manifolds. In: Denison, D.D., Hansen, M.H., Holmes, C.C., Mallick, B., Yu, B. (eds) Nonlinear Estimation and Classification. Lecture Notes in Statistics, vol 171. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21579-2_31
Download citation
DOI: https://doi.org/10.1007/978-0-387-21579-2_31
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95471-4
Online ISBN: 978-0-387-21579-2
eBook Packages: Springer Book Archive