A new class of weighted similarity indices using polytomous variables

We introduce new similarity measures between two subjects, withreference to variables with multiple categories. In contrast totraditionally used similarity indices, they also consider thefrequency of the categories of each attribute in the sample. Thisfeature is useful when dealing with rare categories, since itmakes sense to differently evaluate the pairwise presence of arare category from the pairwise presence of a widespread one. Aweighting criterion for each category derived from Shannon'sinformation theory is suggested. There are two versions of theweighted index: one for independent categorical variables and onefor dependent variables. The suitability of the proposed indicesis shown in this paper using both simulated and real world datasets