7 Discussion


In the present study, many useful properties of the converging sequence of iteratively computed correlation matrices given a proximity matrix have been introduced. Structures in and mimic the effects in dimension reduction techniques such as factor analysis and multidimensional scaling. Near stationary iterations with the sorted colored maps can be employed to identify structural (clustering) information embedded in the data. A rank-two iteration finds the Robinson seriation in the proximity matrix while the converged rank-one structure splits a proximity matrix into two sets with the divisive clustering tree and the rank-one tree seriation. A non-rank-one converged pattern matrix can also be used to study the symmetry pattern exists in the proximity matrix. The whole converging process projected through the eigenvector plot with ellipse is a powerful and dynamic visualization environment for many faces of high-dimensional statistical data analysis.


The original purpose of this study was to investigate the general behavior of patient-clusters on symptom-groups for the psychosis disorder data set. Instead of using many of the available multivariate analysis methods, we have come up with the generalized association plots (GAP) for information visualization.


We have partially accomplished the goal. Through careful examination of the double sorted raw data matrix map with the sufficient graphs and the sequence of correlation maps for both the symptoms and the patients, we thoroughly understand the symptom-groups and the patient-clusters in detail. However, this is only the beginning of our effort for understanding the whole process of the development of psychosis disorder disease. The fifty SAPS and SANS symptoms used in this study is only part of the many rating scales in the MPGRP project. The complete data base comes with different rating scales (nominal, ordinal, and continuous) at different time points with biological background information of each patient in the study. It is an extremely difficult challenge to develop multiphase longitudinal and categorical versions of GAP to help in understanding this kind of large-scale study in a more thorough manner.



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