Adversarially-Trained Nonnegative Matrix Factorization

TL;DR

This paper introduces an adversarially-trained nonnegative matrix factorization method that enhances generalization and predictive performance in matrix completion tasks by defending against bounded-norm data perturbations.

Contribution

It proposes a novel adversarial training framework for NMF that improves robustness and generalization, outperforming existing methods on synthetic and benchmark datasets.

Findings

Superior predictive performance on matrix completion tasks

Enhanced robustness against adversarial perturbations

Outperforms state-of-the-art competitors

Abstract

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.