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...
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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 fuzzyclustering could be one of the best solutions. In the following order we used different fuzzyclustering algorithms, namely, the fuzzyc-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 fuzzyc-varieties (FcV) algorithm, which was developed for recognition of r-dimensional linear varieties in high-dimensional data (lines, planes or hyperplanes). fuzzyclustering 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.
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