Weighted Pivot Coordinates for Compositional Data and Their Application to Geochemical Mapping |
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Authors: | Karel Hron Peter Filzmoser Patrice de Caritat Eva Fišerová Alžběta Gardlo |
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Institution: | 1.Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science,Palacky University Olomouc,Olomouc,Czech Republic;2.Institute of Statistics and Mathematical Methods in Economics,Vienna University of Technology,Vienna,Austria;3.Research School of Earth Sciences,The Australian National University,Canberra,Australia;4.Institute of Molecular and Translational Medicine, Faculty of Medicine and Dentistry,Palacky University Olomouc,Olomouc,Czech Republic;5.Department of Clinical Biochemistry,University Hospital Olomouc,Olomouc,Czech Republic |
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Abstract: | The log ratio methodology converts compositional data, such as concentrations of chemical elements in a rock, from their original Aitchison geometry to interpretable real orthonormal coordinates, thereby allowing meaningful statistical processing and visualization. However, it must be taken into account that the original concentrations can be flawed by detection limit or imprecision problems that can severely affect the resulting coordinates. This paper aims to construct such orthonormal log ratio coordinates, called weighted pivot coordinates, that capture the relevant relative information about an original component and treat the redundant information in a controlled manner. Theoretical developments are supported by a thorough simulation study. Weighted pivot coordinates are then applied to the geochemical mapping of catchment outlet sediments from the National Geochemical Survey of Australia illustrating their advantage over possible alternatives. |
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