Paper Info
Title
Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization
Abstract
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise) assumed on the data. In many applications, the noise model is unknown and difficult to estimate. In this paper, we define a multi-objective NMF (MO-NMF) problem, where several objectives are combined within the same NMF model. We propose to use Lagrange duality to judiciously optimize for a set of weights to be used within the framework of the weighted-sum approach, that is, we minimize a single objective function which is a weighted sum of the all objective functions. We design a simple algorithm based on multiplicative updates to minimize this weighted sum. We show how this can be used to find distributionally robust NMF (DR-NMF) solutions, that is, solutions that minimize the largest error among all objectives, using a dual approach solved via a heuristic inspired from the Frank-Wolfe algorithm. We illustrate the effectiveness of this approach on synthetic, document and audio data sets. The results show that DR-NMF is robust to our incognizance of the noise model of the NMF problem.
Year
DOI
Venue
2019
10.1109/TPAMI.2021.3058693
IEEE Transactions on Pattern Analysis and Machine Intelligence
Keywords
DocType
Volume
Nonnegative matrix factorization,multiple objectives,distributional robustness,multiplicative updates
Journal
44
Issue
ISSN
Citations 
8
0162-8828
0
PageRank 
References 
Authors
0.34
30
4
Name
Order
Citations
PageRank
Nicolas Gillis150339.77
Le Thi Khanh Hien232.12
Valentin Leplat300.68
Vincent Yan Fu Tan449076.15