EUROPT 2025
Abstract Submission

216. Instance-wise Distributionally Robust Nonnegative Matrix Factorization

Invited abstract in session MC-2: Matrix factorization, stream Nonsmooth and nonconvex optimization.

Monday, 14:00-16:00
Room: B100/7011

Authors (first author is the speaker)

1. Amjad Seyedi
Mathematics and Operational Research, Université de Mons
2. Nicolas Gillis
Mathematics and Operational Research, Université de Mons

Abstract

Nonnegative matrix factorization (NMF) is a widely used data representation model across diverse domains, including machine learning. At its core, NMF aims to minimize the distance between the original input and its lower-rank approximation. However, when data are noisy or contain outliers, NMF often struggles to provide accurate results. Existing robust methods depend on known distributional assumptions, which can limit their effectiveness in real-world scenarios where the noise distribution is unknown. To address this limitation, we introduce the instance-wise distributionally robust NMF (iDRNMF), a model designed to accommodate a wide range of noise distributions. By employing a weighted-sum multi-objective method, iDRNMF handles multiple noise distributions and their combinations. Furthermore, while entry-wise models assume noise contamination at individual matrix entries, our proposed instance-wise model assumes contamination at the level of entire instances. This perspective is often more suitable for data representation tasks, as it addresses noise affecting whole feature vectors rather than isolated features. To train the model, we develop a unified multi-objective optimization framework based on an iterative reweighted algorithm, maintaining computational efficiency as it is comparable to single-objective NMFs. This framework offers flexible updating rules, making it well-suited for optimizing a wide range of robust and distributionally robust objectives.

Keywords

Status: accepted

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