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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Balasubramanian, M., Schwartz, E.L.: The Isomap Algorithm and Topological Stability. Science 295, 7 (2002)
Bishop, C.M., Svensen, M., Williams, C.K.I.: GTM: The Generative Topographic Mapping. NCRG/96/015 (1997)
Case, S.M.: Biochemical Systematics of Members of the Genus Rana Native to Western North America. Systematic Zoology 27, 299–311 (1978)
Erwin, E., Obermayer, K., Schulten, K.: Self-Organizing Maps: Ordering, Convergence Properties and Energy Functions. Biological Cybernetics 67, 47–55 (1992)
Kohonen, T.: Self-Organized Formation of Topologically Correct Feature Maps. Biological Cybernetics 43, 59–69 (1982)
Kohonen, T.: Self-Organization and Associative Memory, 2nd edn., pp. 119–157. Springer, Berlin (1988)
Kohonen, T.: Comparison of SOM Point Densities Based on Different Criteria. Neural Computation 11, 2081–2095 (1999)
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)
Liou, C.-Y., Tai, W.-P.: Conformality in the Self-Organization Network. Artificial Intelligence 116, 265–286 (2000)
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)
Liou, C.-Y., Musicus, B.R.: Cross Entropy Approximation of Structured Gaussian Covariance Matrices. IEEE Transaction on Signal Processing 56, 3362–3367 (2006)
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)
Luttrell, S.: Code Vector Density in Topographic Mappings: Scalar Case. IEEE Transactions on Neural Networks 2, 427–436 (1991)
Roweis, S.T., Saul, L.K.: Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290, 2323–2326 (2000)
Sattath, S., Tversky, A.: Additive Similarity Trees. Psychometrika 42, 319–345 (1977)
Sokal, R.R., Sneath, P.H.A.: Principles of Numerical Taxonomy. W. H. Freeman, San Francisco (1963)
Tenenbaum, J., Silva, V., Langford, J.C.: A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290, 2319–2323 (2000)
Torgerson, W.S.: Multidimensional Scaling, I: Theory and Method. Psychometrika 17, 401–419 (1952)
Wu, J.-M., Chiu, S.-J.: Independent Component Analysis Using Potts Models. IEEE Transactions on Neural Networks 12, 202–212 (2001)
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)
Wu, J.-M., Lin, Z.-H., Hsu, P.-H.: Function Approximation Using Generalized Adalines. IEEE Transactions on Neural Networks 17, 541–558 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)