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The here applied objective function for clustering consists of two parts, where the first one takes into account intra-cluster relations, and the second – inter-cluster ones. In the case of k -means algorithm, such bi-partial objective function combines cluster dispersions with inter-cluster similarity, to be jointly minimized.  The first part only of such objective function provides the “standard” quality of clustering based on distances between objects (the well-known classical k -means). To improve the clustering quality based on the bi-partial objective function, we need to develop the permutable version of k -means algorithm. This paper shows the permutable k -means that appears to be a new type of clustering procedure.

The Permutable k-means for the Bi-Partial Criterion