title: Picture of all Solutions of Successive 2-Block Maxbet Problems.
abstract: The Maxbet method is a generalized principal components analysis of a data set, where the group structure of the variables is taken into account. Similarly, 3-block[12,13] partial Maxdiff method is a generalization of covariance analysis, where only the covariances between blocks (1, 2) and (1, 3) are taken into account. The aim of this paper is to give the global maximum for the 2-block Maxbet and 3-block[12,13] partial Maxdiff problems by picking the best solution from the complete solution set for the multivariate eigenvalue problem involved. To do this, we generalize the characteristic polynomial of a matrix to a system of two characteristic polynomials, and provide the complete solution set of the latter via Sylvester resultants. Examples are provided.
authors: Dépt. de Math./Statistique, Université de Moncton, Moncton, NB, E1A 3E9, Canada. vartan.choulakian@umoncton.ca.
authors: Vartan
authors: V
authors: Choulakian
keywords: Gröbner bases; Maxbet; Maxdiff; Sylvester resultant; algebraic statistics; centroid method; multi-block method; principal components analysis