The approximation of two-mode proximity matrices by sums of order-constrained matrices |
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Authors: | Lawrence Hubert Phipps Arabie |
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Affiliation: | (1) Department of Data Theory, University of Leiden, The Netherlands;(2) Faculty of Management, Rutgers University, USA;(3) Department of Psychology, The University of Illinois, 603 East Daniel Street, 61820 Champaign, IL |
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Abstract: | 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. |
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Keywords: | two-mode proximity matrices order constraints (anti-)Robinson form (anti-)Q-form least-squares matrix approximation |
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