Adversarial Nonnegative Matrix Factorization

Lei Luo, Yanfu Zhang, Heng Huang
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:6479-6488, 2020.

Abstract

Nonnegative Matrix Factorization (NMF) has become an increasingly important research topic in machine learning. Despite all the practical success, most of existing NMF models are still vulnerable to adversarial attacks. To overcome this limitation, we propose a novel Adversarial NMF (ANMF) approach in which an adversary can exercise some control over the perturbed data generation process. Different from the traditional NMF models which focus on either the regular input or certain types of noise, our model considers potential test adversaries that are beyond the pre-defined constraints, which can cope with various noises (or perturbations). We formulate the proposed model as a bilevel optimization problem and use Alternating Direction Method of Multipliers (ADMM) to solve it with convergence analysis. Theoretically, the robustness analysis of ANMF is established under mild conditions dedicating asymptotically unbiased prediction. Extensive experiments verify that ANMF is robust to a broad categories of perturbations, and achieves state-of-the-art performances on distinct real-world benchmark datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-luo20c, title = {Adversarial Nonnegative Matrix Factorization}, author = {Luo, Lei and Zhang, Yanfu and Huang, Heng}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {6479--6488}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/luo20c/luo20c.pdf}, url = {https://proceedings.mlr.press/v119/luo20c.html}, abstract = {Nonnegative Matrix Factorization (NMF) has become an increasingly important research topic in machine learning. Despite all the practical success, most of existing NMF models are still vulnerable to adversarial attacks. To overcome this limitation, we propose a novel Adversarial NMF (ANMF) approach in which an adversary can exercise some control over the perturbed data generation process. Different from the traditional NMF models which focus on either the regular input or certain types of noise, our model considers potential test adversaries that are beyond the pre-defined constraints, which can cope with various noises (or perturbations). We formulate the proposed model as a bilevel optimization problem and use Alternating Direction Method of Multipliers (ADMM) to solve it with convergence analysis. Theoretically, the robustness analysis of ANMF is established under mild conditions dedicating asymptotically unbiased prediction. Extensive experiments verify that ANMF is robust to a broad categories of perturbations, and achieves state-of-the-art performances on distinct real-world benchmark datasets.} }
Endnote
%0 Conference Paper %T Adversarial Nonnegative Matrix Factorization %A Lei Luo %A Yanfu Zhang %A Heng Huang %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-luo20c %I PMLR %P 6479--6488 %U https://proceedings.mlr.press/v119/luo20c.html %V 119 %X Nonnegative Matrix Factorization (NMF) has become an increasingly important research topic in machine learning. Despite all the practical success, most of existing NMF models are still vulnerable to adversarial attacks. To overcome this limitation, we propose a novel Adversarial NMF (ANMF) approach in which an adversary can exercise some control over the perturbed data generation process. Different from the traditional NMF models which focus on either the regular input or certain types of noise, our model considers potential test adversaries that are beyond the pre-defined constraints, which can cope with various noises (or perturbations). We formulate the proposed model as a bilevel optimization problem and use Alternating Direction Method of Multipliers (ADMM) to solve it with convergence analysis. Theoretically, the robustness analysis of ANMF is established under mild conditions dedicating asymptotically unbiased prediction. Extensive experiments verify that ANMF is robust to a broad categories of perturbations, and achieves state-of-the-art performances on distinct real-world benchmark datasets.
APA
Luo, L., Zhang, Y. & Huang, H.. (2020). Adversarial Nonnegative Matrix Factorization. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:6479-6488 Available from https://proceedings.mlr.press/v119/luo20c.html.

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