Study of traffic-emitted lead pollution of soil and plants using different fuzzy clustering algorithms |
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Authors: | Costel Sârbu Jürgen W Einax |
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Institution: | 1.Department of Analytical Chemistry,Faculty of Chemistry and Chemical Engineering, “Babe?-Bolyai” University,Cluj-Napoca,Romania;2.Department of Environmental Analysis, Institute of Inorganic and Analytical Chemistry,Friedrich Schiller University of Jena,Jena,Germany |
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Abstract: | We discuss the clustering of 234 environmental samples resulting from an extensive monitoring program concerning soil lead
content, plant lead content, traffic density, and distance from the road at different sampling locations in former East Germany.
Considering the structure of data and the unsatisfactory results obtained applying classical clustering and principal component
analysis, it appeared evident that fuzzy clustering could be one of the best solutions. In the following order we used different
fuzzy clustering algorithms, namely, the fuzzy c-means (FCM) algorithm, the Gustafson–Kessel (GK) algorithm, which may detect
clusters of ellipsoidal shapes in data by introducing an adaptive distance norm for each cluster, and the fuzzy c-varieties
(FCV) algorithm, which was developed for recognition of r-dimensional linear varieties in high-dimensional data (lines, planes or hyperplanes). Fuzzy clustering with convex combination
of point prototypes and different multidimensional linear prototypes is also discussed and applied for the first time in analytical
chemistry (environmetrics). The results obtained in this study show the advantages of the FCV and GK algorithms over the FCM
algorithm. The performance of each algorithm is illustrated by graphs and evaluated by the values of some conventional cluster
validity indices. The values of the validity indices are in very good agreement with the quality of the clustering results.
Figure Projection of all samples on the plane defined by the membership degrees to cluster A2, and A4 obtained using Fuzzy c-varieties (FCV) algorithm (expression of objective function and distance enclosed) |
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Keywords: | Fuzzy c-means algorithm Gustafson– Kessel algorithm Fuzzy c-varieties algorithm Clustering validity Soil and plant samples Traffic-emitted lead pollution |
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