Abstract
Many data sets can be viewed as a collection of samples representing mixtures of a relatively small number of end members. When end members are present in the sample set, the algorithm QMODEL by Klovan and Miesch can efficiently determine proportionate contributions. EXTENDED QMODEL by Full, Ehrlich, and Klovan was designed to deduce the composition of realistic end members when the end members are not represented by samples. However, in the presence of high levels of random variation or outliers not belonging to the system of interest, EXTENDED QMODEL may not be reliable inasmuch as it is largely dependent on extreme values for definition of an initial mixing polyhedron. FUZZY QMODEL utilizes the fuzzy c-means algorithm of Bezdek to provide an alternative initial mixing polyhedron. This algorithm utilizes the collective property of all the data rather than outliers and so can produce suitable solutions in the presence of noisy or “messy” data points.
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References
Bezdek, J., 1974, Numerical taxonomy with fuzzy sets: Jour. Math. Bio., v. 1, p. 57–71.
Bezdek, J., 1981, Pattern recognition with fuzzy objective functions: Plenum Press, New York.
Bezdek, J. C., Ehrlich, R., Trivedi, M., and Full, W. E., 1982, Fuzzy clustering: A new tool for geostatistical analysis: Jour. Syst., Meas. Decis.
Bezdek, J. C., Ehrlich, R., and Full, W. E., in preparation, The fuzzyc-means clustering algorithms.
Duda, R. O. and Hart, P. E., 1973, Pattern classification and scene analysis: Wiley, New York.
Full, W. E., Ehrlich, R., and Klovan, J. E., 1981, EXTENDED QMODEL—Objective definition of external end members in the analysis of mixtures: Jour. Math. Geol., v. 13, no. 4, p. 331–344.
Hurdle, K. J., 1980, The evaluation of contour current contribution to the lower rise near the Norfolk—Washington canyon system: Unpublished masters thesis, University of South Carolina.
Klovan, J. E. and Imbrie, J., 1971, An algorithm and FORTRAN IV program for large scaleQ-mode factor analysis and calculation of factor scores: Jour. Math. Geol., v. 3, no. 1, p. 61–76.
Klovan, J. E. and Miesch, A. T., 1976, EXTENDED CABFAC and QMODEL Computer Programs forQ-mode factor analysis of compositional data: Comput. Geosci., v. 1, p. 161–178.
Miesch, A. T., 1976a,Q-mode factor analysis of geochemical and petrologic data matrices with constant row-sums: Geol. Surv. Prof. Paper 574-G, 47 p.
Miesch, A. T., 1976b, Interactive computer programs for petrologic modeling with extendedQ-mode factor analysis: Comput. Geosci., v. 2, p. 439–492.
Taylor, R. J., 1980, Provenance and paleoclimatic implications of Holocene-Pleistocene sands on the upper continental rise of the Hudson and Baltimore-Wilmington canyon systems—Fourier grain shape analysis: Unpublished masters thesis, University of South Carolina.
Zadeh, L., 1965, Fuzzy sets: Inform. Control, v. 8, p. 338–353.
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Full, W.E., Ehrlich, R. & Bezdek, J.C. FUZZY QMODEL—A new approach for linear unmixing. Mathematical Geology 14, 259–270 (1982). https://doi.org/10.1007/BF01032888
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DOI: https://doi.org/10.1007/BF01032888