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 c-means 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.