# The use of nonmetric multidimensional scaling for the analysis of chromosomal associations

## Abstract

Methods are presented for the statistical analysis of the patterns of association among metaphase chromosomes in the conventional cytogenetic preparation of human peripheral lymphocytes. For each cell midpoints of the p and q ends and the centromere of each chromosome were digitized, these coordinates were used to compute a 138 by 138 matrix of distances between points, and the distances were then transformed to ranks. A separation matrix, Δ, was then computed by averaging the matrices of ranks across the replicate cells for each individual subject. The Δ matrix was then subjected to a two-dimensional nonmetric multidimensional scaling analysis. Plots of the resulting two-dimensional coordinates of the chromosomes represent summary metaphases. Comparative analyses of patterns of association found in the separation matrices and in the plots were carried out. Consistent patterns of association between groups of chromosomes were obtained for four human subjects in both Δ matrices and plots. The larger chromosomes (1-12, and X) were peripheral while the smaller chromosomes (13-22, and Y) were central and clustered. The acrocentric chromosomes (13, 14, 15, 21, 22) were especially clustered. The q points of most chromosomes were more peripheral than either the p or the c points. The summary plot seems to be a more idealized representation of the expected characteristics of the intact metaphase cell than is any single metaphase of the set from which the summary was derived. © 1980.