  Deep clustering, which learns representation and semantic clustering without
labels information, poses a great challenge for deep learning-based approaches.
Despite significant progress in recent years, most existing methods focus on
uniformly distributed datasets, significantly limiting the practical
applicability of their methods. In this paper, we propose a more practical
problem setting named deep imbalanced clustering, where the underlying classes
exhibit an imbalance distribution. To address this challenge, we introduce a
novel optimal transport-based pseudo-label learning framework. Our framework
formulates pseudo-label generation as a Semantic-regularized Progressive
Partial Optimal Transport (SP$^2$OT) problem, which progressively transports
each sample to imbalanced clusters under several prior distribution and
semantic relation constraints, thus generating high-quality and imbalance-aware
pseudo-labels. To solve SP$^2$OT, we develop a Majorization-Minimization-based
optimization algorithm. To be more precise, we employ the strategy of
majorization to reformulate the SP$^2$OT problem into a Progressive Partial
Optimal Transport problem, which can be transformed into an unbalanced optimal
transport problem with augmented constraints and can be solved efficiently by a
fast matrix scaling algorithm. Experiments on various datasets, including a
human-curated long-tailed CIFAR100, challenging ImageNet-R, and large-scale
subsets of fine-grained iNaturalist2018 datasets, demonstrate the superiority
of our method.
