Chapter 15. Principal Component Analysis of Symbolic Data Described by Intervals

  1. Edwin Diday3,
  2. Monique Noirhomme-Fraiture4
  1. N. Carlo Lauro1,
  2. Rosanna Verde2,
  3. Antonio Irpino1

Published Online: 28 JAN 2008

DOI: 10.1002/9780470723562.ch15

Book Title

Symbolic Data Analysis and the SODAS Software

Symbolic Data Analysis and the SODAS Software

Additional Information

How to Cite

Lauro, N. C., Verde, R. and Irpino, A. (2008) Principal Component Analysis of Symbolic Data Described by Intervals, in Symbolic Data Analysis and the SODAS Software (eds E. Diday and M. Noirhomme-Fraiture), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470723562.ch15

Editor Information

  1. 3

    Université Paris IX-Dauphine, LISE-CEREMADE, Place du Marechal de Lattre de Tassigny, Paris Cedex 16, France F-75775

  2. 4

    Facultés Universitaires Notre-Dame de la Paix, Faculté d'Informatique, Rue Grandgagnage, 21, Namur, Belgium, B-5000

Author Information

  1. 1

    Universita Frederico II, Dipartimento di Mathematica e Statistica, Via Cinthia, Monte Sant'Angelo, Napoli, Italy I-80126

  2. 2

    Dipartimento di Studi Europei e Mediterranei, Seconda Universitádegli Studi di Napoli, Via del Setificio, 15 Complesso Monumentale Belvedere di S. Leucio, 81100 Caserta, Italy

Publication History

  1. Published Online: 28 JAN 2008
  2. Published Print: 18 JAN 2007

ISBN Information

Print ISBN: 9780470018835

Online ISBN: 9780470723562

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CHAPTER TOOLS

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Keywords:

  • symbolic data analysis (SDA);
  • interval algebra theorems;
  • interval data functions-computation;
  • midpoints radii principal component analysis (MRPCA);
  • classic linear algebra techniques;
  • orthogonal projector matrix;
  • factorial data analysis techniques;
  • symmetric coefficient matrix;
  • orthonormality constraints;
  • Euclidean distances

Summary

This chapter contains sections titled:

  • Introduction

  • Principal component analysis of interval data matrices: the input

  • Symbolic–numerical–symbolic PCAs

  • Interval algebra based methods

  • Visualizing PCA results on factor planes

  • A comparative example

  • Conclusion and perspectives

  • Appendix

  • References

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