Abstract
If a geochemical compositional datasetX (n×p)is a realization of a physical mixing process, then each of its sample (row) vectors will approximately be a convex combination (mixture) of a fixed set of (l×p)extreme compositions termed endmembers. The kpoints in p-space corresponding to a specified set of k (k<p)linearly independent endmember estimates associated with a p-variate (n×p)compositional datasetX,define the vertices of a (k−1)dimensional simplexH.The nestimated mixturesX′ (n×p)which together account for the systematic variation in the datasetX,should each be convex combinations of the kfixed endmember estimates. Accordingly,the npoints in p-space which represent these mixtures should be interior points of the simplexH.Otherwise, for each sample point which lies outsideH,at least one of the mixture coefficients (endmember contributions) will be negative. The purpose of this paper is to describe procedures for expandingHin the situation that its vertices are not a set of extreme points for the set which represents the mixtures.
Published Version
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