# Using $$\epsilon$$-nets for Solving the Classification Problem

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

## Abstract

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.

## Keywords

Epsilon-nets Sets’ separation VC-dimension

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© Springer International Publishing AG 2017

## Authors and Affiliations

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