Nonnegative Matrix Factorization: Identifiability and Computation

Nov 23, 2021 04:00 PM Singapore (Registration will open at 03:50 PM.)

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Meeting ID: 996 4913 3322
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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 U with r columns and a nonnegative matrix V 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 recall several applications of NMF, namely blind hyperspectral unmixing, topic modeling, and feature extraction in images. Then we discuss two key issues of NMF. First, we discuss the non-uniqueness of NMF decompositions, also known as the identifiability issue, which is crucial in many applications. We explain how identifiability can be checked in practice, and how adding constraints in the model leads to stronger identifiability results. Second, we discuss how to compute NMF, relying on a recently introduced inerTial block majorIzation minimization framework for non-smooth non-convex opTimizAtioN (TITAN). We illustrate these results on several numerical examples.

This talk is based on joint work with Olivier Vu Thanh, Le Hien, Timothy Marrinan and Fabian Lecron.

The paper can be found at: https://www.researchgate.net/publication/355043833_Bounded_Simplex-Structured_Matrix_Factorization 

About the Speaker

Nicolas Gillis is professor in the department of Mathematics and Operational Research at the University of Mons in Belgium. He is a recipient of the Householder Award and an ERC Starting Grant. His research interests include optimization, numerical linear algebra, machine learning, signal processing, and data mining. A member of SIAM and IEEE, he serves as an associate editor of SIAM Journal on Matrix Analysis and Applications and IEEE Transactions on Signal Processing.

For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg

Nicolas Gillis (Université de Mons) - Nonnegative Matrix Factorization: Identifiability and Computation