The Resolution of a Compositional Data Set into Mixtures of Fixed Source Compositions
针对成分数据来自物理混合过程的情况，提出在无先验知识下估计端元数量和成分的方法，这些端元构成解释所有观测的代数基。
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 x 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 endmembers. 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.