Abstract
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.
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References
Scheuermann, G., Hamann, B., Joy, K.I., Kollmann, W.: Visualizing local vector field topology. SPIE Journal of Electronic Imaging 9, 356–367 (2000)
Tipping, M.E., Bishop, C.: Mixtures of probabilistic principal component analyzers. Neural Computation 11, 443–482 (1999)
Roweis, S., Saul, L.: Nonlinear dimension reduction by locally linear embedding. Science 290, 2323–2326 (2000)
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)
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)
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)
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)
Li, H., Chen, W., Shen, I.-F.: Segmentation of discrete vector fields. IEEE Transaction on Visualization and Computer Graphics (2006) (to appear)
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)
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)
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)
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Li, H., Shen, IF. (2006). Similarity Measure for Vector Field Learning. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_65
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DOI: https://doi.org/10.1007/11759966_65
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34439-1
Online ISBN: 978-3-540-34440-7
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