The dissimilarity matrix (also called distance matrix) describes pairwise distinction between M objects. It is a square symmetrical MxM matrix with the (ij)th element equal to the value of a chosen measure of distinction between the (i)th and the (j)th object. The diagonal elements are either not considered or are usually equal to zero - i.e. the distinction between an object and itself is postulated as zero.
A closely related and the opposite concept is the similarity matrix . Both types of description are often used for the same data.
Any reasonable measure of dissimilarity may be used, including subjective scores of dissimilarity. The only requirement is that the greter distinction between two objects, the greater the value the measure of dissimilarity.
As far as the dissimilarity matrix is specified, a corresponding similarity matrix can be calculated, e.g by transformations like
where Sij are pairwise values of a similarity measure, Dij - of a dissimilarity measure.
In many branches of multivariate statistical analysis the initial data are represented as the dissimilarity (or distance) matrices, and/or as similarity matrices, e.g. in multidimensional scaling , correspondence analysis , cluster analysis .