SP$^2$OT: Semantic-Regularized Progressive Partial Optimal Transport for Imbalanced Clustering

Abstract

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 prior and semantic relation constraints, thus generating high-quality and imbalance-aware pseudo-labels. To solve the SP$^2$OT problem, we propose a projected mirror descent algorithm, which alternates between: (1) computing the gradient of the SP$^2$OT objective, and (2) performing gradient descent with projection via an entropy-regularized progressive partial optimal transport formulation. Furthermore, we formulate the second step as an unbalanced optimal transport problem with augmented constraints and develop an efficient solution based on fast matrix scaling algorithms. 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. Code is available: https://github.com/rhfeiyang/SPPOT