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The Resolution of a Compositional Data Set into Mixtures of Fixed Source Compositions
Author(s) -
Renner Ross M.
Publication year - 1993
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2986179
Subject(s) - data set , resolution (logic) , set (abstract data type) , mathematics , statistics , computer science , programming language
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.