Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Benzécri JP, et al. (1973) L’Analyse des Données: II. L’Analyse des correspondances. Dunod, Paris
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 41–50
Garmize L, Rycklak J (1964) Role-play validation of socio-cultural theory of symbolism. J Consult Psychol 28:107–115
Gifi A (1990) Nonlinear multivariate analysis. Wiley, New York
Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic Press, London
Nishisato A (2007) Multidimensional nonlinear descriptive analysis. Chapman and Hall/CRC, Boca Raton, Florida
Nishisato S (1980) Analysis of categorical data: dual scaling and its applications. The University of Toronto Press, Toronto
Nishisato S (1984) Elements of dual scaling: An introduction to practical data analysis. Lawrence Erlbaum Associates, Hilsdale, NJ
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, Berlin
Nishisato S, Clavel J (2003) A note on between-set distances in dual scaling and correspondence analysis. Behaviormetrika 30:87–98
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 357–366
Nishisato S, Clavel J (2010) Total information analysis: Comprehensive dual scaling. Behaviormetrika 37:15–32
Stebbins CL (1950) Variations and evolution. Columbus University Press, New York
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clavel, J.G., Nishisato, S. (2012). Reduced Versus Complete Space Configurations in Total Information Analysis. 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, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24466-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-24466-7_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24465-0
Online ISBN: 978-3-642-24466-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)