Manifold Learning of Vector Fields

  • Hongyu Li
  • I-Fan Shen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)


In this paper, vector field learning is proposed as a new application of manifold learning to vector field. We also provide a learning framework to extract significant features from vector data. Vector data containing position, direction and magnitude information is different from common point data only containing position information. The algorithm of locally linear embedding (LLE) is extended to deal with vector data. The learning ability of the extended version has been tested on synthetic data sets and experimental results demonstrate that the method is very helpful and promising. Manifold features of vector data obtained by learning methods can be used for next work such as classification, clustering, visualization, or segmentation of vectors.


Vector Data Locally Linear Embedding Manifold Learn Discrete Vector Magnitude Information 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Telea, A.C., Wijk, J.J.V.: Simplified representation of vector fields. In: Ebert, D., Gross, M., Hamann, B. (eds.) Proc. of IEEE Visualization 1999, pp. 35–42 (1999)Google Scholar
  2. 2.
    Heckel, B., Weber, G., Hamann, B., Joy, K.I.: Construction of vector field hierarchies. In: Proc. of IEEE Visualization 1999, pp. 19–25 (1999)Google Scholar
  3. 3.
    Garcke, H., Preusser, T., Rumpf, M., Telea, A., Weikard, U., Wijk, J.J.V.: A phase field model for continuous clustering on vector fields. IEEE Trans. Visualization and Computer Graphics, 230–241 (2001)Google Scholar
  4. 4.
    Chen, J.L., Bai, Z., Hamann, B., Ligocki, T.J.: A normalized-cut algorithm for hierachical vector field data segmentation. In: Proc. of Visualization and Data Analysis 2003 (2003)Google Scholar
  5. 5.
    Li, H., Chen, W., Shen, I.F.: Segmentation of discrete vector fields. IEEE Transaction on Visualization and Computer Graphics (2006) (to appear)Google Scholar
  6. 6.
    Li, H., Chen, W., Shen, I.F.: Supervised learning for classification. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS (LNAI), vol. 3614, pp. 49–57. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Li, H., Shen, I.F.: Similarity measure for vector field learning. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 436–441. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Roweis, S., Saul, L.: Nonlinear dimension reduction by locally linear embedding. Science 290, 2323–2326 (2000)CrossRefGoogle Scholar
  9. 9.
    Borg, I., Groenen, P.: Modern Multidimensional Scaling. Springer, Heidelberg (1997)MATHGoogle Scholar
  10. 10.
    Tipping, M.E., Bishop, C.: Mixtures of probabilistic principal component analyzers. Neural Computation 11, 443–482 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hongyu Li
    • 1
  • I-Fan Shen
    • 1
  1. 1.Department of Computer Science and EngineeringFudan UniversityShanghaiChina

Personalised recommendations