Factor analysis, often regarded as a Bayesian variant of matrix factorization, offers superior capabilities in capturing uncertainty, modeling complex dependencies, and ensuring robustness. As the deep learning era arrives, factor analysis is receiving less and less attention due to their limited expressive ability. On the contrary, contrastive learning has emerged as a potent technique with demonstrated efficacy in unsupervised representational learning. While the two methods are different paradigms, recent theoretical analysis has revealed the mathematical equivalence between contrastive learning and matrix factorization, providing a potential possibility for factor analysis combined with contrastive learning. Motivated by the interconnectedness of contrastive learning, matrix factorization, and factor analysis, this paper introduces a novel Contrastive Factor Analysis framework, aiming to leverage factor analysis's advantageous properties within the realm of contrastive learning. To further leverage the interpretability properties of non-negative factor analysis, which can learn disentangled representations, contrastive factor analysis is extended to a non-negative version. Finally, extensive experimental validation showcases the efficacy of the proposed contrastive (non-negative) factor analysis methodology across multiple key properties, including expressiveness, robustness, interpretability, and accurate uncertainty estimation.

翻译：因子分析常被视为矩阵分解的贝叶斯变体，其在捕捉不确定性、建模复杂依赖关系和确保鲁棒性方面具有优越能力。随着深度学习时代的到来，因子分析因其有限的表达能力而受到越来越少的关注。相反，对比学习已成为一种强大的技术，在无监督表征学习中展现出显著效能。虽然这两种方法属于不同范式，但近期的理论分析揭示了对比学习与矩阵分解之间的数学等价性，这为因子分析与对比学习的结合提供了潜在可能。受对比学习、矩阵分解和因子分析之间相互关联性的启发，本文提出了一种新颖的对比因子分析框架，旨在将因子分析的有利特性引入对比学习领域。为了进一步利用非负因子分析的可解释性特性（其能够学习解耦表征），对比因子分析被扩展为非负版本。最后，广泛的实验验证展示了所提出的对比（非负）因子分析方法在多个关键特性上的有效性，包括表达能力、鲁棒性、可解释性以及准确的不确定性估计。