A New Method for Modeling Principal Curve

  • Hao JiSheng
  • He Qing
  • Shi Zhongzhi
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 228)


Principal curve pass through the middle of a multidimensional data set, to express the distributing shape of the points in the data set, we model principal curve for it. The new method of modeling the complex principal curve, based on B-spline network, is proposed. This method combines the polygonal line algorithm of learning principal curve with B-spline network. At one time, the algorithm finding a bifurcate point of the complex principal curve is presented. Our experimental results on simulate data demonstrate that it is feasible and effective.

Key words

Principal Curve The Polygonal Line Algorithm B-spline Network Bifurcate Point 


  1. 1.
    Hastie T. Principal Curves and surfaces. Laboratory for Computational Statistics, Stanford University, Department of Statistics: Technical Report 11, 1984.Google Scholar
  2. 2.
    Hastie T and Stuetzle W. Principal Curves. Journal of the American Statistical Association. 1989, 84: 502–516.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Moody J. Fastiearning in multi-resolution hierarchies. Advances in Neural information Processing System, vol. 1, 1989; 29–39.Google Scholar
  4. 4.
    Kégl B, Krzyzak A, Linder T and Zeger K. Learning and design of principal curves. IEEE Trans. On Pattern Analysis and Machine Intelligence. 2000, 22(3): 281–297.CrossRefGoogle Scholar
  5. 5.
    Martin Brown, Chris Harris. Neurofuzzy adaptive modeling and control. Prentice Hall International (UK) Limited, 1994: 89–100.Google Scholar
  6. 6.
    Stanford D. and Raftery A.E. Finding Curvilinear Features in Spatial Point Patterns; Principal Curve Clustering with Noise. IEEE Trans. on Pattern Analysis and Machine Intelligence. 2000,22(6): 601–609.CrossRefGoogle Scholar
  7. 7.
    Kegl B and Krzyzak A. Piecewise linear skeletonization using principal curves. IEEE Trans on Pattern Analysis and Machine Intelligence 2002,24(1): 59–74.CrossRefGoogle Scholar
  8. 8.
    Hemann T, Meinicke P, and Ritter H. Principal curve sonification. International Conference on Auditory Display 2000: 81–86.Google Scholar
  9. 9.
    Einbeck J, Tutz G, and Evers L, Exploring Multivariate Data Structures with Local Principal Curves”. In: C. Weihs and W. Gaul (Eds.): Classification-The Ubiquitous Challenge, Springer, Heidelberg2005: 256–263.CrossRefGoogle Scholar

Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • Hao JiSheng
    • 1
    • 2
  • He Qing
    • 2
  • Shi Zhongzhi
    • 2
  1. 1.College of Computer ScienceYanan UniversityShanxi YananChina
  2. 2.Key Laboratory of Intelligence Information Processing, Institute of Computing TechnologyChinese Academy of ScienceBeijingChina

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