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Dichotomy Algorithms in the Multi-class Problem of Pattern Recognition

In: Advances in Operational Research in the Balkans

Author

Listed:
  • Damir N. Gainanov

    (Ural Federal University)

  • Nenad Mladenović

    (Khalifa University)

  • Berenov Dmitriy

    (Ural Federal University)

Abstract

Pattern recognitionPattern recognition problem in geometric state with solutions in the class of decision trees is discussed. In each node, the partition of the corresponding subsample of objects is performed using a linear function (hyperplane). In this paper, for the node of the decision tree we state the problem of the dichotomy of a set of classes into 2 subsets of classes for 2 different definitions of the distance function between such subsets. This problem is considered in relation to the projection of the initial sample on the direction connecting 2 most remote points. For any 2 variants of the partition of a set of classes, the concept of closeness is introduced on the basis of the distance between the corresponding binary tuples. For 4 different algorithms for partition of a set of classes, computational experiments are conducted for a series of 100 random sets. The results of computational experiments and the complexity of these algorithms are presented.

Suggested Citation

  • Damir N. Gainanov & Nenad Mladenović & Berenov Dmitriy, 2020. "Dichotomy Algorithms in the Multi-class Problem of Pattern Recognition," Springer Proceedings in Business and Economics, in: Nenad Mladenović & Angelo Sifaleras & Marija Kuzmanović (ed.), Advances in Operational Research in the Balkans, pages 3-14, Springer.
    • Handle: RePEc:spr:prbchp:978-3-030-21990-1_1
    DOI: 10.1007/978-3-030-21990-1_1
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