
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.
