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Algorithm for one classification problem

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Conclusions

We have examined a class of optimal classification problems with an objective function based on a loss functional defined directly on the set of all subsets of the given set of objects without resorting to distance between objects.

A “fast” algorithm MATCHING was proposed for approximate solution of the optimal class fication problem. The algorithm is iterative, and the number of partitioning classes analyzed is roughly halved from iteration to iteration. The assignment problem is solved in each iteration.

Computer experiments have shown that in many cases (over 75% for problems of dimension from 4 to 15) a symmetric initial matrix in the assignment problem produces a symmetric optimal assignment.

The relative error of the proposed algorithm investigated for some model problems does not exceed 12% in most of the cases (Figs. 4 and 5) and, in general, depends on the dimension of the problem (n) and the location of k* on the interval [1, n], where k* is the number of classes in the optimal classification.

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Additional information

Translated from Kibernetika, No. 6, pp. 90–95, November–December, 1988.

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Kolesnik, N.N., Rudnev, Y.P. Algorithm for one classification problem. Cybern Syst Anal 24, 788–795 (1988). https://doi.org/10.1007/BF01079153

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Keywords

  • Objective Function
  • Operating System
  • Artificial Intelligence
  • Relative Error
  • Approximate Solution