Skip to main content

A Novel Method for Manifold Construction

  • Conference paper
  • 1657 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5507))

Abstract

This paper presents a distance invariance method to construct the low dimension manifold that preserves the neighborhood topological relations among data patterns. This manifold can display close relationships among patterns.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Balasubramanian, M., Schwartz, E.L.: The Isomap Algorithm and Topological Stability. Science 295, 7 (2002)

    Article  Google Scholar 

  2. Bishop, C.M., Svensen, M., Williams, C.K.I.: GTM: The Generative Topographic Mapping. NCRG/96/015 (1997)

    Google Scholar 

  3. Case, S.M.: Biochemical Systematics of Members of the Genus Rana Native to Western North America. Systematic Zoology 27, 299–311 (1978)

    Article  Google Scholar 

  4. Erwin, E., Obermayer, K., Schulten, K.: Self-Organizing Maps: Ordering, Convergence Properties and Energy Functions. Biological Cybernetics 67, 47–55 (1992)

    Article  MATH  Google Scholar 

  5. Kohonen, T.: Self-Organized Formation of Topologically Correct Feature Maps. Biological Cybernetics 43, 59–69 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kohonen, T.: Self-Organization and Associative Memory, 2nd edn., pp. 119–157. Springer, Berlin (1988)

    MATH  Google Scholar 

  7. Kohonen, T.: Comparison of SOM Point Densities Based on Different Criteria. Neural Computation 11, 2081–2095 (1999)

    Article  Google Scholar 

  8. Liou, C.-Y., Musicus, B.R.: Separable Cross-Entropy Approach to Power Spectrum Estimation. IEEE Transactions on Acoustics, Speech and Signal Processing 38, 105–113 (1990)

    Article  Google Scholar 

  9. Liou, C.-Y., Tai, W.-P.: Conformality in the Self-Organization Network. Artificial Intelligence 116, 265–286 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Liou, C.-Y., Chen, H.-T., Huang, J.-C.: Separation of Internal Representations of the Hidden Layer. In: Proceedings of the International Computer Symposium, Workshop on Artificial Intelligence, pp. 26–34 (2000)

    Google Scholar 

  11. Liou, C.-Y., Musicus, B.R.: Cross Entropy Approximation of Structured Gaussian Covariance Matrices. IEEE Transaction on Signal Processing 56, 3362–3367 (2006)

    Article  MathSciNet  Google Scholar 

  12. Liou, C.-Y., Cheng, W.-C.: Manifold Construction by Local Neighborhood Preservation. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds.) ICONIP 2007, Part II. LNCS, vol. 4985, pp. 683–692. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Luttrell, S.: Code Vector Density in Topographic Mappings: Scalar Case. IEEE Transactions on Neural Networks 2, 427–436 (1991)

    Article  Google Scholar 

  14. Roweis, S.T., Saul, L.K.: Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  15. Sattath, S., Tversky, A.: Additive Similarity Trees. Psychometrika 42, 319–345 (1977)

    Article  Google Scholar 

  16. Sokal, R.R., Sneath, P.H.A.: Principles of Numerical Taxonomy. W. H. Freeman, San Francisco (1963)

    MATH  Google Scholar 

  17. Tenenbaum, J., Silva, V., Langford, J.C.: A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  18. Torgerson, W.S.: Multidimensional Scaling, I: Theory and Method. Psychometrika 17, 401–419 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  19. Wu, J.-M., Chiu, S.-J.: Independent Component Analysis Using Potts Models. IEEE Transactions on Neural Networks 12, 202–212 (2001)

    Article  Google Scholar 

  20. Wu, J.-M., Lu, C.-Y., Liou, C.-Y.: Independent Component Analysis of Correlated Neuronal Responses in Area MT. In: Proceedings of the International Conference on Neural Information Processing, pp. 639–642 (2005)

    Google Scholar 

  21. Wu, J.-M., Lin, Z.-H., Hsu, P.-H.: Function Approximation Using Generalized Adalines. IEEE Transactions on Neural Networks 17, 541–558 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cheng, WC., Liou, CY. (2009). A Novel Method for Manifold Construction. In: Köppen, M., Kasabov, N., Coghill, G. (eds) Advances in Neuro-Information Processing. ICONIP 2008. Lecture Notes in Computer Science, vol 5507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03040-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03040-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03039-0

  • Online ISBN: 978-3-642-03040-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics