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Classification — the Ubiquitous Challenge pp 256–263Cite as

Exploring Multivariate Data Structures with Local Principal Curves

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Abstract

A new approach to find the underlying structure of a multidimensional data cloud is proposed, which is based on a localized version of principal components analysis. More specifically, we calculate a series of local centers of mass and move through the data in directions given by the first local principal axis. One obtains a smooth “local principal curve” passing through the “middle” of a multivariate data cloud. The concept adopts to branched curves by considering the second local principal axis. Since the algorithm is based on a simple eigendecomposition, computation is fast and easy.

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Author information

Authors and Affiliations

  1. Institut für Statistik, Ludwig-Maximilians-Universität München, Akademiestr.1, D-80799, München, Germany

    Jochen Einbeck, Gerhard Tutz & Ludger Evers

Authors
  1. Jochen Einbeck
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  2. Gerhard Tutz
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  3. Ludger Evers
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Editor information

Editors and Affiliations

  1. Fachbereich Statistik, Universität Dortmund, 44221, Dortmund

    Claus Weihs

  2. Institut für Entscheidungstheorie und Unternehmensforschung, Universität Karlsruhe (TH), 76128, Karlsruhe

    Wolfgang Gaul

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© 2005 Springer-Verlag Berlin · Heidelberg

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Einbeck, J., Tutz, G., Evers, L. (2005). Exploring Multivariate Data Structures with Local Principal Curves. In: Weihs, C., Gaul, W. (eds) Classification — the Ubiquitous Challenge. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28084-7_28

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