Deep clustering can optimize representations of instances (i.e., representation learning) and explore the inherent data distribution (i.e., clustering) simultaneously, which demonstrates a superior performance over conventional clustering methods with given features. However, the coupled objective implies a trivial solution that all instances collapse to the uniform features. To tackle the challenge, a two-stage training strategy is developed for decoupling, where it introduces an additional pre-training stage for representation learning and then fine-tunes the obtained model for clustering. Meanwhile, one-stage methods are developed mainly for representation learning rather than clustering, where various constraints for cluster assignments are designed to avoid collapsing explicitly. Despite the success of these methods, an appropriate learning objective tailored for deep clustering has not been investigated sufficiently. In this work, we first show that the prevalent discrimination task in supervised learning is unstable for one-stage clustering due to the lack of ground-truth labels and positive instances for certain clusters in each mini-batch. To mitigate the issue, a novel stable cluster discrimination (SeCu) task is proposed and a new hardness-aware clustering criterion can be obtained accordingly. Moreover, a global entropy constraint for cluster assignments is studied with efficient optimization. Extensive experiments are conducted on benchmark data sets and ImageNet. SeCu achieves state-of-the-art performance on all of them, which demonstrates the effectiveness of one-stage deep clustering. Code is available at \url{https://github.com/idstcv/SeCu}.

通过提出一种稳定的聚类判别任务和全局熵约束优化方法，实现一阶深度聚类并在基准数据集和ImageNet上达到了最先进性能。

深度聚类的稳定簇划分