  Clustering is an effective technique in data mining to group a set of objects
in terms of some attributes. Among various clustering approaches, the family of
K-Means algorithms gains popularity due to simplicity and efficiency. However,
most of existing K-Means based clustering algorithms cannot deal with outliers
well and are difficult to efficiently solve the problem embedded the $L_0$-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 $L_{2,1}$-norm robust loss as the data-driven item
and imposes a $L_0$-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 $L_0$-norm constraint without any approximate
transformation by absorbing $\|\cdot\|_0$ 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 $L_0$-norm constraint.
Theoretical analyses and extensive experiments on several public datasets
demonstrate the effectiveness and rationality of our proposed REFCMFS method.
