Algorithm BIDIMS for Automated Systematization of Data Array. Case Study: Rediscovering Mendeleev’s Periodic Table of Chemical Elements

The method (algorithm BIDIMS) of multivariate objects display to bidimensional structure in which the sum of differences of objects properties and their nearest neighbors is minimal is being described. The basic regularities on the set of objects at this ordering become evident. Besides, such structures (tables) have high inductive opportunities: many latent properties of objects may be predicted on their coordinates in this table. Opportunities of a method are illustrated on an example of bidimentional ordering of chemical elements. The table received in result practically coincides with the periodic Mendeleev table.

Matrixes of Relations between Pairs Objects and Transformations between Various Kinds

Ways of representation of relations between pair's objects are described at a complete choice. Methods of revealing and kinds of relations between objects are considered. The table of conformity between various forms of representation of relations is resulted.

Cluster Analysis of Some Clases of Objects by Application of the Test Recognition Algorithms

The paper treats the task for cluster analysis of a given assembly of objects on the basis of the information contained in the description table of these objects. Various methods of cluster analysis are briefly considered. Heuristic method and rules for classification of the given assembly of objects are presented for the cases when their division into classes and the number of classes is not known. The algorithm is checked by a test example and two program products (PP) – learning systems and software for company management. Analysis of the results is presented.