We consider an adversarially-trained version of the nonnegative matrix factorization, a popular latent dimensionality reduction technique. In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix. We design efficient algorithms inspired by adversarial training to optimize for dictionary and coefficient matrices with enhanced generalization abilities. Extensive simulations on synthetic and benchmark datasets demonstrate the superior predictive performance on matrix completion tasks of our proposed method compared to state-of-the-art competitors, including other variants of adversarial nonnegative matrix factorization.

翻译：我们认为,非负矩阵因子化是一种经过对抗性训练的无负矩阵因子化,是一种受欢迎的潜在维度减低技术。在我们的配方中,攻击者在给定的数据矩阵中添加了一条任意的封闭规范矩阵。我们设计了高效的算法,在对抗性培训的启发下,以优化字典和系数矩阵,提高通用能力。关于合成数据和基准数据集的广泛模拟表明,与最先进的竞争者相比,我们拟议方法在矩阵完成任务方面的预测性表现优异,包括其他对抗性非负矩阵因子化。