Academy & Industry Research Collaboration Center (AIRCC)

Volume 9, Number 16, December 2019

Nonnegative Matrix Factorization Under Adversarial Noise


Peter Ballen, University of Pennsylvania, USA


Nonnegative Matrix Factorization (NMF) is a popular tool to estimate the missing entries of a dataset under the assumption that the true data has a low-dimensional factorization. One example of such a matrix is found in movie recommendation settings, where NMF corresponds to predicting how a user would rate a movie. Traditional NMF algorithms assume the input data is generated from the underlying representation plus mean-zero independent Gaussian noise. However, this simplistic assumption does not hold in real-world settings that contain more complex or adversarial noise. We provide a new NMF algorithm that is more robust towards these nonstandard noise patterns. Our algorithm outperforms existing algorithms on movie rating datasets, where adversarial noise corresponds to a group of adversarial users attempting to review-bomb a movie.


Nonnegative Matrix Factorization, Matrix Completion, Recommendation, Adversarial Noise, Outlier Detection, Linear Model