Hard and fuzzy c-means clustering with mutual relation constraints

Recently, semi-supervised clustering attracts many researchers\´ interest. In particular, constraint-based semi-supervised clustering is focused and the constraints of must-link and cannot-link play very important role in the clustering. There are many kinds of relations as well as must-link or cannot-link and one of the most typical relations is the trade-off relation. Thus, in this paper we formulate the trade-off relation and propose a new "semi-supervised" concept called mutual relation. Moreover, we construct two types of new clustering algorithms with the mutual relation constraints based on the well-known and useful hard c-means (HCM) and fuzzy c-means (FCM), called hard c-means with the mutual relation constraints (HCMMR) and fuzzy c-means with the mutual relation constraints (FCMMR).