Planar classification of objects (Q921779)

So-called structural methods provide one of the effective tools of empirical data analysis. An important category among structural methods are automatic classification methods, which perform data aggregation by splitting the observed objects into several classes. The classes are generated so that one class contains ``similar'' objects that do not differ much from one another. We show that this substantive formulation of the classification problem is not always compatible with the goals of data analysis. We accordingly propose a new formulation of the classification problem that does not invoke ``similarity'' of objects in one class. This problem is called the planar classification problem. A recursive solution algorithm is proposed and its convergence is proved.