Semi-supervised Fuzzy c-Means Clustering Using Clusterwise Tolerance Based Pairwise Constraints

Recently, semi-supervised clustering has been remarked and discussed in many research fields. In semi-supervised clustering, prior knowledge or information are often formulated as pairwise constraints, that is, must-link and cannot-link. Such pairwise constraints are frequently used in order to improve clustering properties. In this paper, we will propose a new semi-supervised fuzzy c-means clustering by using clusterwise tolerance and pairwise constraints. First, the concept of clusterwise tolerance and pairwise constraints are introduced. Second, the optimization problem of fuzzy cmeans clustering using clusterwise tolerance based pairwise constraint is formulated. Especially, must-link constraint is considered and introduced as pairwise constraints. Third, a new clustering algorithm is constructed based on the above discussions. Finally, the effectiveness of proposed algorithm is verified through numerical examples.