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.

中文翻译：

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对抗训练的非负矩阵分解


我们考虑非负矩阵分解的对抗训练版本，这是一种流行的潜在降维技术。在我们的公式中，攻击者将任意有界范数矩阵添加到给定的数据矩阵中。我们受对抗性训练的启发，设计了高效的算法，以增强泛化能力来优化字典和系数矩阵。对合成数据集和基准数据集的广泛模拟表明，与最先进的竞争对手（包括对抗性非负矩阵分解的其他变体）相比，我们提出的方法在矩阵完成任务上具有卓越的预测性能。