A new measure of groups perturbation

Defining a proper measure of proximity (or remoteness) between two groups of objects is of crucial importance in applied research. Much attention has been paid to consideration of continuous-valued attributes while nominal-valued attributes seems to be more difficult to handle. In this paper we defined non empty groups of objects, and each group is described as K-tuple sets of attributes values. Next, we defined interactions between two groups and description of the groups interactions. Instead of considering dissimilarities between groups, we introduced a measure of perturbation of one group by another. The introduced measure is in general asymmetrical, and therefore cannot be considered as the distance between the groups. The measure of perturbation one group by another group can be applied to e.g. clustering problems. The proposed method is both hierarchical and agglomerative, and is characterized by high speed of computation as well as surprising good accuracy of grouping.