The Resolution of a Compositional Data Set into Mixtures of Fixed Source Compositions

SUMMARY If a compositional data set is a realization of a physical mixing process, then within tolerable errors its observation vectors should be convex combinations of a fixed set of extreme source compositions called end‐members. Given a compositional data set x (n × p) consisting of the measurements on p variables for each of n specimens, but without any prior knowledge on the formation of X, this paper illustrates a solution to the problem of estimating the number and composition of such end‐members. These estimated compositions, in turn, form an algebraical basis for a mixing process which should account for each of the n observation vectors of X.