Abstract: Given a-dimensional proximity matrix
, a sequence of correlation matrices,
, is iteratively formed from it. Here
is the correlation matrix of the original proximity matrix
and
is the correlation matrix of
,
. This sequence was first introduced by McQuitty (1968), Breiger, Boorman and Arabie (1975) developed an algorithm, CONCOR, based on their rediscovery of its convergence. The sequence
often converges to a matrix
whose elements are
or
. This special pattern of
partitions the
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
reaches two, the column vectors of
fall on an ellipse in a two-dimensional subspace. The unique order of relative positions for the
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.
Key words and phrases: Data visualization, divisive clustering tree, latent structure, perfect symmetry, proximity matrices, seriation.