Application of the DIRECT algorithm to searching for an optimal k-partition of the set $$\mathcal {A}\subset \mathbb {R}^n$$ A ⊂ R n and its application to the multiple circle detection problem

Rudolf Scitovski () and Kristian Sabo ()
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Rudolf Scitovski: University of Osijek
Kristian Sabo: University of Osijek

Journal of Global Optimization, 2019, vol. 74, issue 1, No 4, 63-77

Abstract: Abstract In this paper, we propose an efficient method for searching for a globally optimal k-partition of the set $$\mathcal {A}\subset \mathbb {R}^n$$ A ⊂ R n . Due to the property of the DIRECT global optimization algorithm to usually quickly arrive close to a point of global minimum, after which it slowly attains the desired accuracy, the proposed method uses the well-known k-means algorithm with a initial approximation chosen on the basis of only a few iterations of the DIRECT algorithm. In case of searching for an optimal k-partition of spherical clusters, the method is not worse than other known methods, but in case of solving the multiple circle detection problem, the proposed method shows remarkable superiority.

Keywords: Globally optimal partition; k-means; Incremental algorithm; DIRECT; Multiple circles detection problem; 65K05; 90C26; 90C27; 90C56; 90C57; 05E05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10898-019-00743-8

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