Optimal classification/Rypka

Rypka's Method
Rypka's method utilizes the theoretical and empirical separatory equations shown below to perform the task of optimal classification. The method finds the optimal order of the fewest attributes, which in combination define a bounded class of elements.

Application of the method begins with construction of an attribute-valued system in truth table or spreadsheet form with elements listed in the left most column beginning in the second row. Characteristics are listed in the first row beginning in the second column with the code name of the data in the upper left most cell. The values which connect each characteristic with each element are placed in the intersecting cells. Selecting appropriate characteristics to universally define the class of elements may be the most difficult part for the classifier of utilizing this method.

The elements are first sorted in descending order according to their truth table value, which is calculated from the existing sequence and value of characteristics for each element. Duplicate truth table values or multisets for the entire bounded class reveal either the need to eliminate duplicate elements or the need to include additional characteristics.

An empirical separatory value is calculated for each characteristic in the set and the characteristic with the greatest empirical separatory value is exchanged with the characteristic which occupies the most significant attribute position.

Next the second most significant characteristic is found by calculating an empirical separatory value for each remaining characteristic in combination with the first characteristic. The characteristic which produces the greatest separatory value is then exchanged with the characteristic which occupies the second most significant attribute position.

Next the third most significant characteristic is found by calculating an empirical separatory value for each remaining characteristic in combination with the first and second characteristics. The characteristic which produces the greatest empirical separatory value is then exchanged with the characteristic which occupies the third most significant attribute position. This procedure may continue until all characteristics have been processed or until one hundred percent separation of the elements has been achieved.

A larger radix will allow faster identification by excluding a greater percentage of elements per characteristic. A binary radix for instance excludes only fifty percent of the elements per characteristic whereas a five-valued radix excludes eighty percent of the elements per characteristic. What follows is an elucidation of the matrix and separatory equations.