Abstract
Given a pdimensional proximity matrix
, a sequence^{*} of correlation matrices,
=(,,…), is iteratively formed from it. Here
is the correlation matrix of the original proximity matrix D and
is the correlation matrix of
, n > 1. The sequence R often converges to a matrix
whose elements are +1 or 1. This special pattern of
partitions the p objects into two disjoint groups and it can be recursively applied to generate a divisive hierarchical clustering tree. While convergence is itself useful, we are even more concerned with what happens before convergence. We discover that before convergence, there is a rank reduction property with elliptical structure. When rank of
reaches two, the column vectors on
fall on an ellipse on a twodimensional subspace. This 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 modern computer's graphic ability to retrieve important information hidden in the data or proximity matrices.
KEY WORDS: Data visualization, Divisive clustering tree, Latent structure; Perfect symmetry; Proximity matrices,
Seriation.
* This correlation sequence was first introduced by McQuitty (1968).
Breiger, Boorman & Arabie (1975) also developed an algorithm, CONCOR, based on their rediscovery of the convergence of this sequence.
Reference:

Breiger, R. L.,
Boorman, S. A. and Arabie, P (1975), "An Algorithm for Clustering Relational Data with Applications to Social Network Analysis and Comparison with Multidimensional Scaling," Journal of Mathematical Psychology, 12, 328383.

McQuitty, L. L. (1968), "Multiple Clusters, Types, and Dimensions from Iterative Intercolumnar Correlational Analysis," Multivariate Behavioral Research, 3, 465477.
