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.


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.


  • 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, 328-383.

  • McQuitty, L. L. (1968), "Multiple Clusters, Types, and Dimensions from Iterative Intercolumnar Correlational Analysis," Multivariate Behavioral Research, 3, 465-477.


[Prev] [Context] [Next]