THE APPROXIMATION OF 2-MODE PROXIMITY MATRICES BY SUMS OF ORDER-CONSTRAINED MATRICES

A least-squares strategy is proposed for representing a two-mode proxi mity matrix as an approximate sum of a small number of matrices that s atisfy 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 reo rderings, the entries within each row and within each column are nonde creasing (or nonincreasing) to a maximum (or minimum) and thereafter n onincreasing (or nondecreasing). Several other types of order constrai nts are also mentioned to show how alternative structures can be consi dered using the same computational strategy.