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Analysis of Data Measured on a Lattice

  • Ulrich Halekoh
  • Paul O. Degens
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

A data vector z is additively decomposed into several components by minimizing a sum of quadratic forms in each component. The data may be measured on an arbitrary lattice but the quadratic forms have to be constructed according to the chosen lattice (here mainly in IR+). The decomposition method can be regarded as a spline approximation. The transformation of z to each component is linear, diagonalizable and its eigenvalues are contained in the unit interval. At first we introduce the concept of the detection of a structural change with this method. Then we concentrate on the analysis of two interdependent time series by the simultaneous decomposition of the two (coupled) series. For the application of the method the two series are best regarded as one datafield measured on a lattice with two directions, one direction representing the time and the other specifying the series. The concepts will be explained with data from a monitoring study in NRW on the influence of air pollution on vulnerable persons.

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1991

Authors and Affiliations

  • Ulrich Halekoh
    • 1
  • Paul O. Degens
    • 1
  1. 1.Medizinisches Institut für UmwelthygieneUniversität DüsseldorfDüsseldorfGermany

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