Two semi-supervised entropy regularized fuzzy c-means

In this paper, two semi-supervised clustering methods are proposed, which are based on entropy regularized fuzzy c-means algorithm. First, two fuzzy c-means algorithms are introduced. The one is the standard one and the other is the entropy regularized one. Second, two semi-supervised standard fuzzy c-means algorithms are introduced, which are derived from adding loss function of memberships to the original optimization problem. Third, two new optimization problems are proposed, in which one is derived from adding new loss function of memberships to the original optimization problem and the other is derived from adding the loss function used in the latter semisupervised standard fuzzy c-means algorithm. Last, two iterative algorithms are proposed by solving the optimization problems.