Contrastive clustering based on generalized bias-variance decomposition

Abstract

Contrastive learning demonstrates remarkable generalization performance but lacks theoretical understanding, while contrastive clustering achieves promising performance but exhibits some shortcomings. We first introduce a generalized bias-variance decomposition to study contrastive learning, then present the concept of the conformal field, which unifies instance-level contrastive loss and cluster-level de-redundancy loss (Barlow Twins). Finally, we integrate the conformal field and self-labeling to propose the outstanding contrastive clustering model D3CF. D3CF consists of two novel stages: the pre-training stage simultaneously performs instance-level contrastive learning and multi-view cluster-level redundancy reduction, bringing positive samples together and separating negative samples in the row and column space of the augmented feature matrix; to alleviate the adverse effects caused by false-negative pairs and misclustered assignments in the pre-training stage, the boosting stage enhances contrastive learning from single-positive pairs to multiple-positive pairs by leveraging cross-sample similarities, while utilizing pseudo-labels with high confidence criteria for self-labeling to correct clustering assignments. Extensive experiments on six image benchmark datasets and two text benchmarks demonstrate D3CF’s superior performance and validate the effectiveness of its components. Particularly on CIFAR-10, ImageNet-10, and STL-10, D3CF achieves average accuracies of 89.5%, 97%, and 91%, improving NMI by 5.2%, 4.8%, and 2.1%, and ARI by 7%, 7.3%, and 7.3% over the closest baseline.