P$^2$OT: Progressive Partial Optimal Transport for Deep Imbalanced
  Clustering
Chuyu Zhang Hui Ren Xuming He
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 first introduce a more
practical problem setting named deep imbalanced clustering, where the
underlying classes exhibit an imbalance distribution. To tackle this problem,
we propose a novel pseudo-labeling-based learning framework. Our framework
formulates pseudo-label generation as a progressive partial optimal transport
problem, which progressively transports each sample to imbalanced clusters
under prior distribution constraints, thus generating imbalance-aware
pseudo-labels and learning from high-confident samples. In addition, we
transform the initial formulation into an unbalanced optimal transport problem
with augmented constraints, which 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.