Low-Rank and Relaxed-Nonnegative Attack on Nonnegative Matrix Factorization

Unsupervised learning provides efficient analytical tools for data-centric Internet of Things (IoT) applications. Nonnegative matrix factorization (NMF) is a fundamental tool in unsupervised machine learning, offering interpretable and part-based feature representations. While NMF is provably robust to bounded additive perturbations, the emergence of adversarial attacks highlights the need to reassess the certified robustness under strategically crafted perturbations. In this work, we propose a novel attack method that more effectively disrupts NMF factorization than existing adversarial methods by incorporating two key strategies: i) imposing low-rank constraints to guide perturbations toward principal subspaces; and ii) relaxing nonnegativity constraints on perturbations to inject negative components that effectively alter original feature additivity. We present analyses including ablation studies, convergence performance, and computational complexity. Extensive experiments on benchmark datasets show that the proposed method effectively attacks both vanilla NMF and existing adversarial NMF variants by disrupting the factorization and degrading performance in downstream tasks such as feature extraction and clustering.