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In this paper is presented a new method for clustering of objects described by nominal attributes. The method is based on the set theory. The similarities measures and distance measures between objects are attuned for nominal attributes and are based on the conditions’ dominance for each attribute. There are introduced a definition of conditions’ perturbation for each attribute and a measure of clusters’ perturbations. They allow us to describe in some sense clusters’ similarities and are used for coupling of clusters by twos. A pair ofclusters described by the lowest value of clusters’ perturbation measure is coupled creating a new cluster, and after removing this pair the number of clusters is decreased by one. Next, there is defined a measure ofclusters’ concentration as well as a measure of cluster’s distance. These two measures resorted to compute an evaluation of clusters’ set. This evaluation allows us to compare different sets of clusters which are obtained during clustering process. In the paper the new definitions are elucidated by examples, and there is considered a case of data series clustering problem as an illustrative example.
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Projects co-financed by:
Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.