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

In this paper, we propose an efficient method for searching for a globally optimal k- partition of the set 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.

globally optimal partition ; k-means ; Incremental algorithm ; DIRECT ; multiple circles detection problem ;

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