Algorithms of crisp, fuzzy, and probabilistic clustering with semi-supervision or pairwise constraints

An overview of several algorithms of semi-supervised clustering or constrained clustering based on crisp, fuzzy, or probabilistic framework is given with new results. First, equivalence between an EM algorithm for a semi-supervised mixture distribution model and an extended version of KL-information fuzzy c-means is shown. Second, algorithms of constrained clustering are compared, where an extended COP K-means is considered. Third class of algorithms is a two-stage version of a combination of COP K-means and agglomerative clustering. Numerical examples are shown to observe characteristics of the algorithms discussed herein.