The classical deep clustering optimization methods basically leverage information such as clustering centers, mutual information, and distance metrics to construct implicit generalized labels to establish information feedback (weak supervision) and thus optimize the deep model. However, the resulting generalized labels have different degrees of errors in the whole clustering process due to the limitation of clustering accuracy, which greatly interferes with the clustering process. To this end, this paper proposes a general deep clustering optimization method from the perspective of empirical risk minimization, using the correlation relationship between the samples. Experiments on two classical deep clustering methods demonstrate the necessity and effectiveness of the method. Code is available at https://github.com/yangzonghao1024/DCGLU.