The recent integration of deep learning and pairwise similarity
annotation-based constrained clustering -- i.e., $\textit{deep constrained
clustering}$ (DCC) -- has proven effective for incorporating weak supervision
into massive data clustering: Less than 1% of pair similarity annotations can
often substantially enhance the clustering accuracy. However, beyond empirical
successes, there is a lack of understanding of DCC. In addition, many DCC
paradigms are sensitive to annotation noise, but performance-guaranteed noisy
DCC methods have been largely elusive. This work first takes a deep look into a
recently emerged logistic loss function of DCC, and characterizes its
theoretical properties. Our result shows that the logistic DCC loss ensures the
identifiability of data membership under reasonable conditions, which may shed
light on its effectiveness in practice. Building upon this understanding, a new
loss function based on geometric factor analysis is proposed to fend against
noisy annotations. It is shown that even under $\textit{unknown}$ annotation
confusions, the data membership can still be $\textit{provably}$ identified
under our proposed learning criterion. The proposed approach is tested over
multiple datasets to validate our claims.

本论文通过研究深度约束聚类（DCC）的一种新的逻辑损失函数，探讨其理论性质，并提出了一种基于几何因子分析的新的损失函数来对抗噪声注释。该方法经过多个数据集的测试验证，表明即使在未知注释混淆的情况下，我们提出的学习标准下数据成员仍可被证明地识别。