Dynamic clustering and strong patterns recognition: new tools in automatic classification

Abstract

The dynamic clustering method (D.C.M.) developed by Diday is a nonhierarchical classification procedure which can help the geologist who is faced with the problem of forming groups among a multidimensional population of chemical analyses. Instead of computing the similarity between every possible pair of elements of a population, the D.C.M. suggests the use of a set of nuclei which will act as a template in the process of grouping elements together to form a partition of the population. By using the concept of similarity between an element and a group of elements, called a nucleus, the D.C.M. will assign a group number to every individual of the original population.When the first partition has been completed, the more representative elements of the groups are chosen and combined into an improved set of nuclei. This set will then be used to perform a second grouping and the whole process will be repeated over and over until no improvement can be achieved by an other iteration. The result is a local optimum, i.e. a stable partition into a given number of groups. The D.C.M. can be applied several times to the same set of data to generate different local optima (the starting set of nuclei being different). By grouping the elements which were classified together for every local optimum, a partition into an equal or greater number of groups can result. This is the concept of strong patterns.Three hundred and thirty-three rocks of the Monteregian Hills petrogenetic suite were classified on the basis of their content in ten major elements. Five major groups, corresponding to five different rock types could be easily recognized and discriminated without any a priori assumptions. It is suggested that the algorithms presented here could be used to achieve more subtle partitioning problems, efficiently and economically, on larger sets of data.