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Inverse correspondence analysis

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  • Groenen, P.J.F.
  • van de Velden, M.

Abstract

In correspondence analysis, rows and columns of a data matrix are depicted as points in low-dimensional space. The row and column profiles are approximated by minimizing the so-called weighted chi squared distance between the original profiles and their approximations, see or example, Greenacre (1984). In this paper, we will study the inverse correspondence analysis solution. We will show that there exists a nonempty closed and bounded polyhedron of such matrices. We also present an algorithm to find the vertices of the polyhedron. A proof that the maximum of the Pearson chi-squared statistic is attained at one of the vertices is given. In addition, it is discussed how extra equality constraints on some elements of the data matrix can be imposed on the inverse correspondence analysis problem. As a special case, we present a method for imposing integer restrictions on the data matrix as well. The approach to inverse correspondence analysis followed here is similar to the one employed by De Leeuw and Groenen (1997) in their inverse multidimensional scaling problem.

Suggested Citation

  • Groenen, P.J.F. & van de Velden, M., 2002. "Inverse correspondence analysis," Econometric Institute Research Papers EI 2002-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:550
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    References listed on IDEAS

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    1. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
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