Dichotomy Algorithms in the Multi-class Problem of Pattern Recognition

Damir N. Gainanov (), Nenad Mladenović () and Berenov Dmitriy ()
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Damir N. Gainanov: Ural Federal University
Nenad Mladenović: Khalifa University
Berenov Dmitriy: Ural Federal University

A chapter in Advances in Operational Research in the Balkans, 2020, pp 3-14 from Springer

Abstract: 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.

Keywords: Pattern recognition; Algorithm; Partition function; Hamming distance (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:prbchp:978-3-030-21990-1_1

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DOI: 10.1007/978-3-030-21990-1_1

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