A quantitative measure of compactness and similarity in competitive space

We describe similarity measures among objects in metric and competitive spaces. We propose a competitive similarity function as a similarity measure used in classification and pattern recognition problems. This function enables us to construct some efficient algorithms for solving all main data mining problems, to obtain quantitative estimates for the compactness of images and the informativeness of trait spaces, and to construct easily interpretable decision rules. The method applies to problems with arbitrary numbers of images and characters of their distributions, and can also be used for solving poorly conditioned problems.