Lars Carlsen* and Rainer Bruggemann Pages 349 - 357 ( 9 )
Aim and Objective: In chemistry, there is a long tradition in classification. Usually, methods are adopted from the wide field of cluster analysis. The present study focusses on the application of partial ordering methodology for the classification of 21 alkyl substituted anilines.
Materials and Methods: The analyses are based on the concepts from partial order methodology and cluster analyses. Here, with the example of 21 alkyl anilines, we show that concepts taken out from the mathematical discipline of partially ordered sets may be applied for classification. The chemical compounds are described by a multi-indicator system. For the present study four indicators, mainly taken from the field of environmental chemistry were applied and a graph of the ordering (Hasse diagram) was constructed.
Results: A Hasse diagram is an acyclic, transitively reduced, triangle-free graph that may have several graph-theoretical components. The Hasse diagram has been directed from a structural chemical point of view. Two cluster analysis methods are applied (K-means and a hierarchical cluster method) and compared with the results from the Hasse diagram. In both cases, the partitioning of the set of 21 compounds by the component structure of the Hasse diagram appears to be better interpretable.
Conclusion: It is shown that the partial ordering approach indeed can be used for classification in the present case. However, it must be clearly stated that a guarantee for meaningful results, in general, cannot be given. For that, further theoretical work is needed.
Alkyl anilines, environmental chemistry, classification, partial ordering, indicator importance, tripartite graphs, dominance, separability, cluster analyses.
Awareness Center, Linkøpingvej 35, Trekroner, DK-4000 Roskilde, Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Department Ecohydrology, Müggelseedamm 310, D-12587 Berlin