ANC Seminar - Nicolas Gillis

Tuesday, 11th April 2023

Nonnegative Matrix Factorization: Algorithms and Applications 

Abstract: Given a nonnegative matrix X and a factorization rank r, nonnegative matrix factorization (NMF) approximates the matrix X as the product of a nonnegative matrix W with r columns and a nonnegative matrix H with r rows. NMF has become a standard linear dimensionality reduction technique in data mining and machine learning. In this talk, we first introduce NMF and show how it can be used as an interpretable unsupervised data analysis tool in various applications, including hyperspectral image unmixing, image feature extraction, and document classification. Then, we discuss the issue of non-uniqueness of NMF decompositions, also known as the identifiability issue, and how it can be tackle with three widely-used NMF models, namely separable, minimum-volume and sparse NMF. We also discuss how the factors (W,H) in such models can be computed. We illustrate these results on the aforementioned applications.

Bio: Nicolas Gillis is Professor with the Department of Mathematics and Operational Research, University of Mons, Belgium. He is recipient of the Householder award (2014), an ERC starting grant (2015), and an ERC consolidator grant (2022). He is editor for the IEEEE Transactions on Signal Processing, and the SIAM Journals on Matrix Analysis and Applications and on Mathematics of Data Science. His research interests lie in optimization, numerical linear algebra, signal processing, machine learning and data mining. 

Event type: Seminar

Date: Tuesday, 11th April 2023

Time: 13:00 (note change in time)

Location: G.03

Speaker(s): Nicolas Gillis (

Chair/Host: Antonio Vergari