Skip to main content
SpringerLink
Log in

Correspondence Analysis

  • Reference work entry
  • First Online:
Encyclopedia of Social Network Analysis and Mining

Synonyms

Dual scaling; Homogeneity analysis; Optimal scaling

Glossary

CA:

Correspondence analysis

Component:

A linear combination of the variables of a data table

Dimension:

See component

Factor:

See component

GSVD:

Generalized singular value decomposition

PCA:

Principal component analysis

SVD:

Singular value decomposition

Introduction

Correspondence analysis (CA;Benzécri 1973; Lebart and Fénelon 1975; Lebart et al. 1984; Escofier and Pagès 1990; Greenacre 1984, 2007; Abdi and Valentin 2007; Hwang et al. 2010; Abdi 2003; Abdi and Williams 2010b) is an extension of principal component analysis (pca; for details, see Abdi and Williams 2010a) tailored to handle nominal variables. Originally, ca was developed to analyze contingency tables in which a sample of observations is described by two nominal variables, but it was rapidly extended to the analysis of any data matrices with nonnegative entries. The origin of ca can be traced to the early work of Pearson (1901) or Fisher, but the...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,500.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Abdi H (2003) Multivariate analysis. In: Lewis-Beck M, Bryman A, Futing T (eds) Encyclopedia for research methods for the social sciences. Sage, Thousand Oaks, pp 699–702

    Google Scholar 

  • Abdi H (2007a) Singular value decomposition (SVD) and generalized singular value decomposition(GSVD). In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 907–912

    Google Scholar 

  • Abdi H (2007b) Eigen-decomposition: eigenvalues and eigenvectors. In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 304–308

    Google Scholar 

  • Abdi H (2007d) Discriminant correspondence analysis. In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 270–275

    Google Scholar 

  • Abdi H (2007e) Metric multidimensional scaling. In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 598–605

    Google Scholar 

  • Abdi H (2007f) Z-scores. In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 1057–1058

    Google Scholar 

  • Abdi H, Valentin D (2007) Multiple correspondence analysis. In Salkind, NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 651–657

    Google Scholar 

  • Abdi H, Williams LJ (2010a) Principal component analysis. Wiley Interdiscip Rev Comput Stat 2:433–459

    Google Scholar 

  • Abdi H, Williams LJ (2010b) Correspondence analysis. In: Salkind NJ (ed) Encyclopedia of research design. Sage, Thousand Oaks

    Google Scholar 

  • Abdi H, Williams LJ, Valentin D (2013) Multiple factor analysis: Principal component analysis for multi-table and multi-block data sets. Wiley Interdiscip Rev Comput Stat 5:149–179

    Google Scholar 

  • Benzécri J-P (1973) L'analyse des données, Vols 1 and 2. Dunod, Paris

    Google Scholar 

  • Eckart C, Young G (1936) The approximation of a matrix by another of a lower rank. Psychometrika 1:211–218

    MATH  Google Scholar 

  • Escofier B, Pagès J (1990) Analyses factorielles simples et multiples: objectifs, méthodes, interprétation. Dunod, Paris

    Google Scholar 

  • Escoufier Y (2007) Operators related to a data matrix: a survey. In: COMPSTAT: 17th symposium proceedings in computational statistics, Rome, Italy, 2006, pp 285–297. Physica Verlag, New York

    Google Scholar 

  • Good I (1969) Some applications of the singular value decomposition of a matrix. Technometrics 11:823–831

    MATH  Google Scholar 

  • Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic, London

    MATH  Google Scholar 

  • Greenacre MJ (2007) Correspondence analysis in practice, 2nd edn. Chapman & Hall/CRC, Boca Raton

    MATH  Google Scholar 

  • Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol 25:417–441

    Google Scholar 

  • Husson F, Lê S, Pagès J (2011) Exploratory multivariate analysis by example using R. Chapman & Hall/CRC, Boca Raton

    MATH  Google Scholar 

  • Hwang H, Tomiuk MA, Takane Y (2010) Correspondence analysis, multiple correspondence analysis and recent developments. In: Millsap R, Maydeu-Olivares A (eds) Handbook of quantitative methods in psychology. Sage, London

    Google Scholar 

  • Lebart L, Morineau A, Warwick KM (1984) Multivariate descriptive statistical analysis: correspondence analysis and related techniques for large matrices. Wiley, London

    MATH  Google Scholar 

  • Lebart L, Fénelon JP (1975) Statistique et informatique appliquées. Dunod, Paris

    Google Scholar 

  • Nakache JP, Lorente P, Benzécri JP, Chastang JF (1977) Aspect pronostics et thérapeutiques de l'infarctus myocardique aigu. Les Cahiers de l'Analyse des Données 2:415–534

    Google Scholar 

  • Pearson K (1901) On lines and planes of closest fit to systems of points in space. Philos Mag 6:559–572

    Google Scholar 

  • Saporta G, Niang N (2006) Correspondence analysis and classification. In: Greenacre M, Blasius J (eds) Multiple correspondence analysis and related methods. Chapman & Hall, Boca Raton, pp 371–392

    Google Scholar 

  • Stewart GW (1993) On the early history of the singular value decomposition. SIAM Rev 35:551–566

    MATH  MathSciNet  Google Scholar 

  • Takane Y (2002) Relationships among various kinds of eigenvalue and singular value decompositions. In: Yanai H, Okada A, Shigemasu K, Kano Y, Meulman J (eds) New developments in psychometrics. Springer, Tokyo, pp 45–56

    Google Scholar 

  • Williams LJ, Abdi H, French R, Orange JB (2010) A tutorial on multi-block discriminant correspondence analysis (MUDICA): a new method for analyzing discourse data from clinical populations. J Speech Lang Hear Res 53:1372–1393

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Behavioral and Brain Sciences, The University of Texas at Dallas, Richardson, TX, USA

    Hervé Abdi

  2. Centre d'Étude et de Recherche en Informatique et Communications, Conservatoire National des Arts et Métiers, Paris Cdex 03, France

    Michel Béra

Authors
  1. Hervé Abdi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michel Béra
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Calgary, Calgary, AB, Canada

    Reda Alhajj

  2. Department of Computer Science, University of Calgary, Calgary, AB, Canada

    Jon Rokne

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this entry

Cite this entry

Abdi, H., Béra, M. (2014). Correspondence Analysis. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6170-8_140

Download citation

Publish with us

Policies and ethics

Search

Navigation