Constraint K-Segment Principal Curves

  • Junping Zhang
  • Dewang Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4113)


To represent the intrinsic regularity of data, one way is to compute the “middle” curves or principal curves (PCs) across the data. However, there are difficulties for current PCs algorithms to discover some known positions that are out of the sampled range of data (Henceforth, out-of-the-samples). Based on principal curves with length constraint proposed by kégl (KPCs), we propose constraint K-segment principal curves (CKPCs) with two refinements. First, out-of-the-samples are introduced as endpoints to improve the performance of the KPCs algorithm. Second, a constraint term is proposed for removing some unexpected vertices and enhancing the stability of the KPCs algorithm. Experiments in three set of practical traffic stream data show that both the stability and the shape of the proposed CKPCs algorithm are better than those of the KPCs algorithm.


Stream Data Principal Curve Length Constraint Neighboring Segment Abnormal Data 
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  1. 1.
    Hastie, T., Stuetzle, W.: Principal curves. J. A. Stat. A. 84, 502–516 (1988)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Zhang, J., Wang, J.: An overview of principal curves. Chinese J. Computer 26, 1–18 (2003)zbMATHGoogle Scholar
  3. 3.
    Kégl, B., Krzyzak, A., et al.: Learning and design of principal curves. IEEE Trans. on PAMI 22, 281–297 (2000)Google Scholar
  4. 4.
    Chen, D., Zhang, J., Tang, S., Wang, J.: Freeway Traffic Stream Modeling Based on Principal Curves and Its Analysis. IEEE Trans. on ITS 5, 246–258 (2004)Google Scholar
  5. 5.
    Chen, D., Gong, X., Zheng, C.H.: A wireless traffic information collection system in Beijing urban freeways. In: IEEE on ITS. Conf., Singapore, pp. 387–391 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Junping Zhang
    • 1
    • 3
  • Dewang Chen
    • 1
    • 2
  1. 1.Shanghai Key Lab of Intelligent Information Processing, China, Department of Computer Science and EngineeringFudan UniversityShanghaiChina
  2. 2.School of Electronics and Information EngineeringBeijing Jiaotong UniversityChina
  3. 3.The Key Laboratory of Complex Systems and Intelligence ScienceChinese Academy of SciencesBeijingChina

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