Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric
  Regularization Approach
Tri Nguyen Shahana Ibrahim Xiao Fu
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.