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

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  • Ross M. Renner

Abstract

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.

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  • Ross M. Renner, 1993. "The Resolution of a Compositional Data Set into Mixtures of Fixed Source Compositions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(4), pages 615-631, December.
    • Handle: RePEc:bla:jorssc:v:42:y:1993:i:4:p:615-631
    DOI: 10.2307/2986179
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    Cited by:

    1. Mooijaart, Ab & van der Heijden, Peter G. M. & van der Ark, L. Andries, 1999. "A least squares algorithm for a mixture model for compositional data," Computational Statistics & Data Analysis, Elsevier, vol. 30(4), pages 359-379, June.

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