How to determine the number of clusters is an intractable problem in clustering analysis. In this paper, we propose a new learning paradigm named Maximum Weighted Likelihood (MwL), in which the weights are designable. Accordingly, we develop a novel Rival Penalized Expectation-Maximization (RPEM) algorithm, whose intrinsic rival penalization mechanism enables the redundant densities in the mixture to be gradually faded out during the learning. Hence, the RPEM can automatically select an appropriate number of densities in density mixture clustering. The experiments have shown the promising results.