On L1-Norm based tolerant fuzzy c-Means clustering

In this paper, we will propose two types of L₁-norm based tolerant fuzzy c-means clustering (TFCM) from the viewpoint of handling data more flexibly. One is based on the constraint for tolerance vector and the other is based on the regularization term. First, the concept of clusterwise tolerance is introduced into optimization problems. In these methods, a tolerance vector attributes not only to each data but also each cluster. First, the concept of clusterwise tolerance is introduced into optimization problems. Second, optimal solutions for these optimization problems are derived. Third, new clustering algorithms are constructed based on the explicit optimal solutions. Finally, effectiveness of proposed algorithms is verified through numerical examples.