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That is, some special two-stage algorithms being the kinds of clustering with relational constraint are proposed. They optimize division of set of objects into clusters respecting the requirement that neighbours have to belong to the same cluster. In the case of the probabilistic<jats:italic>d<\/jats:italic>-clustering, relevant modification of its target function is suggested and studied. Versatile simulation study and empirical analysis verify the practical efficiency of these methods. The quality of clustering is assessed on the basis of indices of homogeneity, heterogeneity and correctness of clusters as well as the silhouette index. Using these tools and similarity indices (Rand, Peirce and Sokal and Sneath), it was shown that the probabilistic<jats:italic>d<\/jats:italic>-clustering can produce better results than Ward\u2019s algorithm. In comparison with the<jats:italic>k<\/jats:italic>-means approach, the probabilistic<jats:italic>d<\/jats:italic>-clustering\u2014although gives rather similar results\u2014is more robust to creation of trivial (of which empty) clusters and produces less diversified (in replications, in terms of correctness) results than<jats:italic>k<\/jats:italic>-means approach, i.e. is more predictable from the point of view of the clustering quality.<\/jats:p>","DOI":"10.1007\/s00357-020-09370-5","type":"journal-article","created":{"date-parts":[[2020,8,26]],"date-time":"2020-08-26T07:02:42Z","timestamp":1598425362000},"page":"313-352","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["k-Means, Ward and Probabilistic Distance-Based Clustering Methods with Contiguity Constraint"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6853-9163","authenticated-orcid":false,"given":"Andrzej","family":"M\u0142odak","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,8,26]]},"reference":[{"key":"9370_CR1","doi-asserted-by":"publisher","first-page":"2828","DOI":"10.1016\/j.jspi.2010.03.005","volume":"140","author":"AN Albatineh","year":"2010","unstructured":"Albatineh, A. 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