Reduced Versus Complete Space Configurations in Total Information Analysis

  • José G. Clavel
  • Shizuhiko Nishisato
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


In most multidimensional analyses, the dimension reduction is a key concept and reduced space analysis is routinely used. Contrary to this traditional approach, total information analysis (TIA) (Nishisato and Clavel, Behaviormetrika 37:15–32, 2010) places its focal point on tapping every piece of information in data. The present paper is to demonstrate that the time-honored practice of reduced space analysis may have to be reconsidered as its grasp of data structure may be compromised by ignoring intricate details of data. The paper will present numerical examples to make our point.


Space Discrepancy Total Space Space Analysis Common Space Triangular Part 
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  1. Benzécri JP, et al. (1973) L’Analyse des Données: II. L’Analyse des correspondances. Dunod, PariszbMATHGoogle Scholar
  2. Clavel JG, Nishisato S (2008) Joint analysis of within-set and between-set distances. In: Shigemasu K, Okada A, Imaizumi T, Hoshino T (eds) New trends in psychometrics. Universal Academy Press, Tokyo, pp 41–50Google Scholar
  3. Garmize L, Rycklak J (1964) Role-play validation of socio-cultural theory of symbolism. J Consult Psychol 28:107–115CrossRefGoogle Scholar
  4. Gifi A (1990) Nonlinear multivariate analysis. Wiley, New YorkzbMATHGoogle Scholar
  5. Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic Press, LondonzbMATHGoogle Scholar
  6. Nishisato A (2007) Multidimensional nonlinear descriptive analysis. Chapman and Hall/CRC, Boca Raton, FloridazbMATHGoogle Scholar
  7. Nishisato S (1980) Analysis of categorical data: dual scaling and its applications. The University of Toronto Press, TorontozbMATHGoogle Scholar
  8. Nishisato S (1984) Elements of dual scaling: An introduction to practical data analysis. Lawrence Erlbaum Associates, Hilsdale, NJGoogle Scholar
  9. Nishisato S (2011) Quantification theory: Reminiscence and a step forward. In: Gaul W, Geyer-Schulz A, Schmidt-Thieme L, Kunze J (eds) Challenges at the interface of data analysis, computer science, and optimization, studies in classification, data analysis, and knowledge organization. Springer, Heidelberg, BerlinGoogle Scholar
  10. Nishisato S, Clavel J (2003) A note on between-set distances in dual scaling and correspondence analysis. Behaviormetrika 30:87–98MathSciNetzbMATHCrossRefGoogle Scholar
  11. Nishisato S, Clavel J (2008) Interpreting data in reduced space: A case of what is not what in multidimensional data analysis. In: Shigemasu K, Okada A, Imaizumi T, Hoshino T (eds) New trends in psychometrics. Universal Academy Press, Tokyo, pp 357–366Google Scholar
  12. Nishisato S, Clavel J (2010) Total information analysis: Comprehensive dual scaling. Behaviormetrika 37:15–32CrossRefGoogle Scholar
  13. Stebbins CL (1950) Variations and evolution. Columbus University Press, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Universidad de MurciaMurciaSpain
  2. 2.University of TorontoTorontoCanada

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