Similarity Measure for Vector Field Learning

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


Vector data containing direction and magnitude information other than position information is different from common point data only containing position information. Those general similarity measures for point data such as Euclidean distance are not suitable for vector data. Thus, a novel measure must be proposed to estimate the similarity between vectors. The similarity measure defined in this paper combines Euclidean distance with angle and magnitude differences. Based on this measure, we construct a vector field space on which a modified locally linear embedding (LLE) algorithm is used for vector field learning. Our experimental results show that the proposed similarity measure works better than traditional Euclidean distance.


Euclidean Distance Similarity Measure Vector Data Position Information Locally Linear Embedding 
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.
    Scheuermann, G., Hamann, B., Joy, K.I., Kollmann, W.: Visualizing local vector field topology. SPIE Journal of Electronic Imaging 9, 356–367 (2000)CrossRefGoogle Scholar
  2. 2.
    Tipping, M.E., Bishop, C.: Mixtures of probabilistic principal component analyzers. Neural Computation 11, 443–482 (1999)CrossRefGoogle Scholar
  3. 3.
    Roweis, S., Saul, L.: Nonlinear dimension reduction by locally linear embedding. Science 290, 2323–2326 (2000)CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    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
  6. 6.
    Garcke, H., Preusser, T., Rumpf, M., Telea, A., Weikard, U., Wijk, J.J.V.: A continuous clustering method for vector fields. In: Ertl, T., Hamann, B., Varshney, A. (eds.) Proc. of IEEE Visualization 2000, pp. 351–358 (2000)Google Scholar
  7. 7.
    Heckel, B., Uva, A.E., Hamann, B.: Clustering-based generation of hierarchical surface models. In: Wittenbrink, C., Varshney, A. (eds.) Proc. of IEEE Visualization 1998 (Hot Topics), pp. 50–55 (1998)Google Scholar
  8. 8.
    Li, H., Chen, W., Shen, I.-F.: Segmentation of discrete vector fields. IEEE Transaction on Visualization and Computer Graphics (2006) (to appear)Google Scholar
  9. 9.
    Tricoche, X., Scheuermann, G., Hagen, H.: A topology simplification method for 2d vector fields. In: Ertl, T., Hamann, B., Varshney, A. (eds.) Proc. of IEEE Visualization 2000, pp. 359–366 (2000)Google Scholar
  10. 10.
    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
  11. 11.
    Li, H., Shen, I.F.: Manifold learning of vector fields. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 430–435. Springer, Heidelberg (2006)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 Engineering, Shanghai Key Laboratory of Intelligent Information ProcessingFudan UniversityShanghaiChina

Personalised recommendations