Classification of normalized cluster methods in an order theoretic model

An interesting class of cluster methods in the Janowitz model for cluster analysis is explored. Normalized cluster methods, those which produce splitting levels between 0 and 1 inclusive, are defined. A Galois connection is examined, and the eleven closed classes of normalized cluster methods produced are completely characterized in two ways, one easily applied, and one in terms of residuated maps with which the class of cluster methods is compatible.