GAP Families: GAP | DynaGAP | CateGAP | LongGAP | MissGAP | MDSGAP | CartoGAP
CanonicalGAP | ConditionalGAP | depGAP  



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.