  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}.
