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Principal Curves of Oriented Points: theoretical and computational improvements

Author

Listed:
  • Pedro Delicado

    (Universitat Politècnica de Catalunya)

  • Mario Huerta

    (Universitat Politècnica de Catalunya)

Abstract

Summary Principal curves where introduced by Hastie & Stuetzle (1989) as smooth parametric curves passing through the middle of a multidimensional data set. Delicado (2001) defines Principal Curves of Oriented Points, based on the fixed points of a function from ℝp into itself. This definition is nonparametric and smoothing methods are used to find principal curves of a data set. Here we extend this work in two directions. First, we propose a bandwidth choice method based on the Minimum Spanning Tree of the data set. Second, we present an object oriented application that implements the principal curves computation for any dimension in a flexible recursive way. Examples on synthetic and real data are included.

Suggested Citation

  • Pedro Delicado & Mario Huerta, 2003. "Principal Curves of Oriented Points: theoretical and computational improvements," Computational Statistics, Springer, vol. 18(2), pages 293-315, July.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:2:d:10.1007_s001800300145
    DOI: 10.1007/s001800300145
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    References listed on IDEAS

    as
    1. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    2. Delicado, Pedro, 2001. "Another Look at Principal Curves and Surfaces," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 84-116, April.
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    Cited by:

    1. Pulkkinen, Seppo, 2015. "Ridge-based method for finding curvilinear structures from noisy data," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 89-109.
    2. Haonan Wang & Hari Iyer, 2007. "Application of local linear embedding to nonlinear exploratory latent structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 199-225, June.
    3. Delicado, P., 2011. "Dimensionality reduction when data are density functions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 401-420, January.

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