On the Number of Partitions of a Sample into Groups for the Stability Criterion

A new approach to solution of the problem of grouping of objects based on the stability criterion is presented. The stability is defined by the index of structural disposition of the object depending on the sample classification, on the introduced measures of closeness between objects, and specified transforms of the attribute space. A practical method is developed for determination of the maximum number of different partitions of the sample into two groups based on the stability criterion.

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