Rank Properties for Centred Three-Way Arrays

  • Casper J. AlbersEmail author
  • John C. Gower
  • Henk A. L. Kiers
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


When analysing three-way arrays, it is a common practice to centre the arrays. Depending on the context, centring is performed over one, two or three modes. In this paper, we outline how centring affects the rank of the array; both in terms of maximum rank and typical rank.


Three-way analysis Multiway analysis Maximum rank Typical rank CANDECOMP/PARAFAC 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Casper J. Albers
    • 1
    Email author
  • John C. Gower
    • 2
  • Henk A. L. Kiers
    • 1
  1. 1.Department of Psychometrics & StatisticsUniversity of GroningenGroningenThe Netherlands
  2. 2.Department of Mathematics & StatisticsThe Open UniversityMilton KeynesUK

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