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Some new aspects of taxicab correspondence analysis

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  • Vartan Choulakian
  • Biagio Simonetti
  • Thu Pham Gia

Abstract

Correspondence analysis (CA) and nonsymmetric correspondence analysis are based on generalized singular value decomposition, and, in general, they are not equivalent. Taxicab correspondence analysis (TCA) is a $$\hbox {L}_{1}$$ L 1 variant of CA, and it is based on the generalized taxicab singular value decomposition (GTSVD). Our aim is to study the taxicab variant of nonsymmetric correspondence analysis. We find that for diagonal metric matrices GTSVDs of a given data set are equivalent; from which we deduce the equivalence of TCA and taxicab nonsymmetric correspondence analysis. We also attempt to show that TCA stays as close as possible to the original correspondence matrix without calculating a dissimilarity (or similarity) measure between rows or columns. Further, we discuss some new geometric and distance aspects of TCA. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Vartan Choulakian & Biagio Simonetti & Thu Pham Gia, 2014. "Some new aspects of taxicab correspondence analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(3), pages 401-416, August.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:3:p:401-416
    DOI: 10.1007/s10260-014-0259-6
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    References listed on IDEAS

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    1. Vartan Choulakian, 2003. "The optimality of the centroid method," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 473-475, September.
    2. Choulakian, Vartan, 2005. "Transposition invariant principal component analysis in L1 for long tailed data," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 23-31, January.
    3. Shizuhiko Nishisato, 1984. "Forced classification: A simple application of a quantification method," Psychometrika, Springer;The Psychometric Society, vol. 49(1), pages 25-36, March.
    4. Vartan Choulakian & Jules Tibeiro, 2013. "Graph Partitioning by Correspondence Analysis and Taxicab Correspondence Analysis," Journal of Classification, Springer;The Classification Society, vol. 30(3), pages 397-427, October.
    5. Yoshio Takane & Sunho Jung, 2009. "Tests of ignoring and eliminating in nonsymmetric correspondence analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 3(3), pages 315-340, December.
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