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1 results

  • The Approximation of Two-Mode Proximity Matrices by Sums of Order-Constrained Matrices

  • Lawrence Hubert, Phipps Arabie
  • Journal:
    Psychometrika / Volume 60 / Issue 4 / December 1995
    Published online by Cambridge University Press:
    01 January 2025, pp. 573-605

  • A least-squares strategy is proposed for representing a two-mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries. The primary class of constraints considered define Q-forms (or anti-Q-forms) for a two-mode matrix, where after suitable and separate row and column reorderings, the entries within each row and within each column are nondecreasing (or nonincreasing) to a maximum (or minimum) and thereafter nonincreasing (or nondecreasing). Several other types of order constraints are also mentioned to show how alternative structures can be considered using the same computational strategy.