Using \(\epsilon \)-nets for Solving the Classification Problem

  • Maria A. IvanchukEmail author
  • Igor V. Malyk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)


We propose a new approach for solving the classification problem, which is based on the using \(\epsilon \)-nets theory. It is showed that for separating two sets one can use their \(\epsilon \)-nets, which considerably reduce the complexity of the separating algorithm for large sets’ sizes. The necessary and sufficient conditions of separable \(\epsilon \)-nets of two sets are proved. The algorithm of building separable \(\epsilon \)-nets is proposed. The \(\epsilon \)-nets, constructed according to this algorithm, have size \(O(1/\varepsilon )\), which does not depended on the size of set. The set of possible values of \(\epsilon \) for \(\epsilon \)-nets of both sets is considered. The properties of this set and the theorem of its convergence are proved. The proposed algorithm of solving the classification problem using the \(\epsilon \)-nets has the same computational complexity as Support Vector Machine \(O(n\ln n)\) and its accuracy is comparable with SVM results.


Epsilon-nets Sets’ separation VC-dimension 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Bukovinian State Medical UniversityChernivtsiUkraine
  2. 2.Yuriy Fedkovych Chernivtsi National UniversityChernivtsiUkraine

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