Statistica Sinica 12(2002), 7-29 GENERALIZED ASSOCIATION PLOTS: INFORMATION VISUALIZATION VIA ITERATIVELY GENERATED CORRELATION MATRICES

Given a p-dimensional proximity matrix Dp p, a sequence of correlation matrices, R = (R; R; : : :), is iteratively formed from it. Here R is the correlation matrix of the original proximity matrix D and R is the correlation matrix of R , n > 1. This sequence was rst introduced by McQuitty (1968), Breiger, Boorman and Arabie (1975) developed an algorithm, CONCOR, based on their rediscovery of its convergence. The sequence R often converges to a matrix R (1) whose elements are +1 or 1. This special pattern of R partitions the p objects into two disjoint groups and so can be recursively applied to generate a divisive hierarchical clustering tree. While convergence is itself useful, we are more concerned with what happens before convergence. Prior to convergence, we note a rank reduction property with elliptical structure: when the rank of R reaches two, the column vectors of R fall on an ellipse in a two-dimensional subspace. The unique order of relative positions for the p points on the ellipse can be used to solve seriation problems such as the reordering of a Robinson matrix. A software package, Generalized Association Plots (GAP), is developed which utilizes computer graphics to retrieve important information hidden in the data or proximity matrices.