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Given a p-dimensional 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 two-dimensional 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.
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