Exploiting order information embedded in ordered categories for ordinal data clustering

As a major type of categorical data, ordinal data are those with the attributes whose possible values (also called categories interchangeably) are naturally ordered. As far as we know, all the existing distance metrics proposed for categorical data do not take the underlying order information into account during the distance measurement. This will make the produced distance incorrect and will further influence the results of ordinal data clustering. We therefore propose a specially designed distance metric, which can exploit the order information embedded in the ordered categories for distance measurement. It quantifies the distance between two ordinal categories by accumulating the sub-entropies of all the categories ordered between them. Since the proposed distance metric takes the order information into account, distance produced by it will be more reasonable than the other metrics proposed for categorical data. Moreover, it is parameter-free and can be easily applied to different ordinal data clustering tasks. Experimental results show the promising advantages of the proposed distance metric.