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}.

翻译：深度聚类能够同时优化实例的表示（即表示学习）并探索内在数据分布（即聚类），相比于使用给定特征的传统聚类方法表现出更优性能。然而，耦合的目标隐含着所有实例坍缩至统一特征的平凡解。为解决这一挑战，提出了一种两阶段训练策略进行解耦，其中额外引入预训练阶段进行表示学习，再微调所得模型用于聚类。与此同时，单阶段方法主要针对表示学习而非聚类开发，通过设计各种聚类分配约束显式避免坍缩。尽管这些方法取得了成功，但针对深度聚类的合适学习目标尚未得到充分研究。本文首先表明，由于缺乏真实标签且每个小批量中某些聚类缺少正实例，监督学习中广泛使用的判别任务在单阶段聚类中是不稳定的。为缓解该问题，提出一种新颖的稳定聚类判别（SeCu）任务，并据此获得新的难度感知聚类准则。此外，研究了带高效优化的聚类分配全局熵约束。在基准数据集和ImageNet上进行了广泛实验。SeCu在所有数据集上均达到最先进性能，验证了单阶段深度聚类的有效性。代码见\url{https://github.com/idstcv/SeCu}。