Abstract: Clustering is an effective technique in data mining to group a set of objects in terms of some attributes. However, most of existing K-Means based clustering algorithms cannot deal with outliers well and are difficult to efficiently solve the problem embedded the L0-norm constraint. To address the above issues and improve the performance of clustering significantly, we propose a novel clustering algorithm, named REFCMFS, which develops a L2,1-norm robust loss as the data-driven item and imposes a L0-norm constraint on the membership matrix to make the model more robust and sparse flexibly. In particular, REFCMFS designs a new way to simplify and solve the L0-norm constraint without any approximate transformation by absorbing 0 into the objective function through a ranking function. These improvements not only make REFCMFS efficiently obtain more promising performance but also provide a new tractable and skillful optimization method to solve the problem embedded the L0-norm constraint.