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Constrained Low-Rank Matrix Approximations: Theoretical and Algorithmic Developments for Practitioners

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Publications

Inertial Block Proximal Methods for Non-Convex Non-Smooth Optimization

Author(s): Le Thi Khanh Hien, Nicolas Gillis, Panagiotis Patrinos
Published in: Proceedings of the 37th International Conference on Machine Learning, 2020, Page(s) 5671-5681
Publisher: Proceedings of Machine Learning Research

Successive Projection Algorithm Robust to Outliers

Author(s): Nicolas Gillis
Published in: 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2019, Page(s) 331-335, ISBN 978-1-7281-5549-4
Publisher: IEEE
DOI: 10.1109/camsap45676.2019.9022488

Extrapolated Alternating Algorithms for Approximate Canonical Polyadic Decomposition

Author(s): Andersen Man Shun Ang, Jeremy E. Cohen, Le Thi Khanh Hien, Nicolas Gillis
Published in: ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020, Page(s) 3147-3151, ISBN 978-1-5090-6631-5
Publisher: IEEE
DOI: 10.1109/icassp40776.2020.9053849

Exact Sparse Nonnegative Least Squares

Author(s): Nicolas Nadisic, Arnaud Vandaele, Nicolas Gillis, Jeremy E. Cohen
Published in: ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020, Page(s) 5395-5399, ISBN 978-1-5090-6631-5
Publisher: IEEE
DOI: 10.1109/ICASSP40776.2020.9053295

Hyperspectral Unmixing with Rare Endmembers via Minimax Nonnegative Matrix Factorization

Author(s): Timothy Marrinan, Nicolas Gillis
Published in: 2020 28th European Signal Processing Conference (EUSIPCO), 2021, Page(s) 1015-1019, ISBN 978-9-0827-9705-3
Publisher: IEEE
DOI: 10.23919/eusipco47968.2020.9287456

A New Approach to Dictionary-Based Nonnegative Matrix Factorization

Author(s): Cohen, Jérémy E.,; Gillis, Nicolas
Published in: 25th European Signal Processing Conference (EUSIPCO), 1, 2017, Page(s) 523-527
Publisher: EUSIPCO

Some theory on Non-negative Tucker Decomposition

Author(s): Cohen, Jérémy E.,; Comon, Pierre; Gillis, Nicolas
Published in: 13th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA 2017), 1, 2017
Publisher: EURASIP

Separable Simplex-structured Matrix Factorization: Robustness of Combinatorial Approaches

Author(s): Nicolas Gillis
Published in: ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, Page(s) 5521-5525, ISBN 978-1-4799-8131-1
Publisher: IEEE
DOI: 10.1109/icassp.2019.8682644

Nonnegative Low-rank Sparse Component Analysis

Author(s): Jeremy E. Cohen, Nicolas Gillis
Published in: ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, Page(s) 8226-8230, ISBN 978-1-4799-8131-1
Publisher: IEEE
DOI: 10.1109/icassp.2019.8682188

Minimum-volume Rank-deficient Nonnegative Matrix Factorizations

Author(s): Valentin Leplat, Andersen M.S. Ang, Nicolas Gillis
Published in: ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, Page(s) 3402-3406, ISBN 978-1-4799-8131-1
Publisher: IEEE
DOI: 10.1109/icassp.2019.8682280

Successive Nonnegative Projection Algorithm for Linear Quadratic Mixtures

Author(s): Christophe Kervazo, Nicolas Gillis, Nicolas Dobigeon
Published in: 2020 28th European Signal Processing Conference (EUSIPCO), 2021, Page(s) 1951-1955, ISBN 978-9-0827-9705-3
Publisher: IEEE
DOI: 10.23919/eusipco47968.2020.9287788

Off-diagonal symmetric nonnegative matrix factorization

Author(s): François Moutier, Arnaud Vandaele, Nicolas Gillis
Published in: Numerical Algorithms, 2021, ISSN 1017-1398
Publisher: Baltzer Science Publishers B.V.
DOI: 10.1007/s11075-020-01063-9

Simplex-Structured Matrix Factorization: Sparsity-Based Identifiability and Provably Correct Algorithms

Author(s): Maryam Abdolali, Nicolas Gillis
Published in: SIAM Journal on Mathematics of Data Science, 3/2, 2021, Page(s) 593-623, ISSN 2577-0187
Publisher: SIAM
DOI: 10.1137/20m1354982

Accelerating block coordinate descent for nonnegative tensor factorization

Author(s): Andersen Man Shun Ang, Jeremy E. Cohen, Nicolas Gillis, Le Thi Khanh Hien
Published in: Numerical Linear Algebra with Applications, 2020, ISSN 1070-5325
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/nla.2373

Generalized Separable Nonnegative Matrix Factorization

Author(s): Junjun Pan, Nicolas Gillis
Published in: IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019, Page(s) 1-1, ISSN 0162-8828
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tpami.2019.2956046

Characterization of the dissipative mappings and their application to perturbations of dissipative‐Hamiltonian systems

Author(s): Mohit Kumar Baghel, Nicolas Gillis, Punit Sharma
Published in: Numerical Linear Algebra with Applications, 2021, ISSN 1070-5325
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/nla.2402

Deep matrix factorizations

Author(s): Pierre De Handschutter, Nicolas Gillis, Xavier Siebert
Published in: Computer Science Review, 42, 2021, Page(s) 100423, ISSN 1574-0137
Publisher: Elsevier BV
DOI: 10.1016/j.cosrev.2021.100423

On a minimum enclosing ball of a collection of linear subspaces

Author(s): Tim Marrinan, P.-A. Absil, Nicolas Gillis
Published in: Linear Algebra and its Applications, 625, 2021, Page(s) 248-278, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2021.05.006

Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization

Author(s): Masoud Ahookhosh, Le Thi Khanh Hien, Nicolas Gillis, Panagiotis Patrinos
Published in: Computational Optimization and Applications, 79/3, 2021, Page(s) 681-715, ISSN 0926-6003
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10589-021-00286-3

Computing the nearest stable matrix pairs

Author(s): Nicolas Gillis, Volker Mehrmann, Punit Sharma
Published in: Numerical Linear Algebra with Applications, 2018, Page(s) e2153, ISSN 1070-5325
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/nla.2153

Solving the Maximum Clique Problem with Symmetric Rank-One Non-negative Matrix Approximation

Author(s): Melisew Tefera Belachew, Nicolas Gillis
Published in: Journal of Optimization Theory and Applications, 173/1, 2017, Page(s) 279-296, ISSN 0022-3239
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10957-016-1043-6

On the linear extension complexity of regular n-gons

Author(s): Arnaud Vandaele, Nicolas Gillis, François Glineur
Published in: Linear Algebra and its Applications, 521, 2017, Page(s) 217-239, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2016.12.023

On computing the distance to stability for matrices using linear dissipative Hamiltonian systems

Author(s): Nicolas Gillis, Punit Sharma
Published in: Automatica, 85, 2017, Page(s) 113-121, ISSN 0005-1098
Publisher: Pergamon Press Ltd.
DOI: 10.1016/j.automatica.2017.07.047

Multiplicative updates for polynomial root finding

Author(s): Nicolas Gillis
Published in: Information Processing Letters, 132, 2018, Page(s) 14-18, ISSN 0020-0190
Publisher: Elsevier BV
DOI: 10.1016/j.ipl.2017.11.008

A semi-analytical approach for the positive semidefinite Procrustes problem

Author(s): Nicolas Gillis, Punit Sharma
Published in: Linear Algebra and its Applications, 540, 2018, Page(s) 112-137, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2017.11.023

A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary

Author(s): Nicolas Gillis, Robert Luce
Published in: IEEE Transactions on Image Processing, 27/1, 2018, Page(s) 24-37, ISSN 1057-7149
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/TIP.2017.2753400

Sequential dimensionality reduction for extracting localized features

Author(s): Gabriella Casalino, Nicolas Gillis
Published in: Pattern Recognition, 63, 2017, Page(s) 15-29, ISSN 0031-3203
Publisher: Pergamon Press
DOI: 10.1016/j.patcog.2016.09.006

Spectral Unmixing With Multiple Dictionaries

Author(s): Jeremy E. Cohen, Nicolas Gillis
Published in: IEEE Geoscience and Remote Sensing Letters, 15/2, 2018, Page(s) 187-191, ISSN 1545-598X
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/LGRS.2017.2779477

Finding the Nearest Positive-Real System

Author(s): Nicolas Gillis, Punit Sharma
Published in: SIAM Journal on Numerical Analysis, 56/2, 2018, Page(s) 1022-1047, ISSN 0036-1429
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/17m1137176

Accelerating Nonnegative Matrix Factorization Algorithms Using Extrapolation

Author(s): Andersen Man Shun Ang, Nicolas Gillis
Published in: Neural Computation, 31/2, 2019, Page(s) 417-439, ISSN 0899-7667
Publisher: MIT Press
DOI: 10.1162/neco_a_01157

Improved SVD-based initialization for nonnegative matrix factorization using low-rank correction

Author(s): Syed Muhammad Atif, Sameer Qazi, Nicolas Gillis
Published in: Pattern Recognition Letters, 122, 2019, Page(s) 53-59, ISSN 0167-8655
Publisher: Elsevier BV
DOI: 10.1016/j.patrec.2019.02.018

Dictionary-Based Tensor Canonical Polyadic Decomposition

Author(s): Jeremy Emile Cohen, Nicolas Gillis
Published in: IEEE Transactions on Signal Processing, 66/7, 2018, Page(s) 1876-1889, ISSN 1053-587X
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tsp.2017.2777393

On the Complexity of Robust PCA and ℓ 1 -Norm Low-Rank Matrix Approximation

Author(s): Nicolas Gillis, Stephen A. Vavasis
Published in: Mathematics of Operations Research, 43/4, 2018, Page(s) 1072-1084, ISSN 0364-765X
Publisher: Institute for Operations Research and the Management Sciences
DOI: 10.1287/moor.2017.0895

Algorithms for positive semidefinite factorization

Author(s): Arnaud Vandaele, François Glineur, Nicolas Gillis
Published in: Computational Optimization and Applications, 71/1, 2018, Page(s) 193-219, ISSN 0926-6003
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s10589-018-9998-x

Approximating the nearest stable discrete-time system

Author(s): Nicolas Gillis, Michael Karow, Punit Sharma
Published in: Linear Algebra and its Applications, 573, 2019, Page(s) 37-53, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2019.03.014

Orthogonal joint sparse NMF for microarray data analysis

Author(s): Flavia Esposito, Nicolas Gillis, Nicoletta Del Buono
Published in: Journal of Mathematical Biology, 2019, ISSN 0303-6812
Publisher: Springer Verlag
DOI: 10.1007/s00285-019-01355-2

Scalable and Robust Sparse Subspace Clustering Using Randomized Clustering and Multilayer Graphs

Author(s): Maryam Abdolali, Nicolas Gillis, Mohammad Rahmati
Published in: Signal Processing, 2019, Page(s) 166-180, ISSN 0165-1684
Publisher: Elsevier BV
DOI: 10.1016/j.sigpro.2019.05.017

Low-rank matrix approximation in the infinity norm

Author(s): Nicolas Gillis, Yaroslav Shitov
Published in: Linear Algebra and its Applications, 581, 2019, Page(s) 367-382, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2019.07.017

Algorithms and Comparisons of Nonnegative Matrix Factorizations With Volume Regularization for Hyperspectral Unmixing

Author(s): Andersen Man Shun Ang, Nicolas Gillis
Published in: IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2019, Page(s) 1-11, ISSN 1939-1404
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/jstars.2019.2925098

A note on approximating the nearest stable discrete-time descriptor systems with fixed rank

Author(s): Nicolas Gillis, Michael Karow, Punit Sharma
Published in: Applied Numerical Mathematics, 2019, ISSN 0168-9274
Publisher: Elsevier BV
DOI: 10.1016/j.apnum.2019.09.004

Identifiability of Complete Dictionary Learning

Author(s): Jeremy E. Cohen, Nicolas Gillis
Published in: SIAM Journal on Mathematics of Data Science, 1/3, 2019, Page(s) 518-536, ISSN 2577-0187
Publisher: SIAM
DOI: 10.1137/18m1233339

Multiplicative Updates for NMF with $\beta$-Divergences under Disjoint Equality Constraints

Author(s): Valentin Leplat, Nicolas Gillis, Jérôme Idier
Published in: SIAM Journal on Matrix Analysis and Applications, 42/2, 2021, Page(s) 730-752, ISSN 0895-4798
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1377278

Algorithms for Nonnegative Matrix Factorization with the Kullback–Leibler Divergence

Author(s): Le Thi Khanh Hien, Nicolas Gillis
Published in: Journal of Scientific Computing, 87/3, 2021, ISSN 0885-7474
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-021-01504-0

A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization

Author(s): Masoud Ahookhosh, Le Thi Khanh Hien, Nicolas Gillis, Panagiotis Patrinos
Published in: Journal of Optimization Theory and Applications, 190/1, 2021, Page(s) 234-258, ISSN 0022-3239
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10957-021-01880-5

Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization

Author(s): Nicolas Gillis, Le Thi Khanh Hien, Valentin Leplat, Vincent Tan
Published in: IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019, Page(s) 1-1, ISSN 0162-8828
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tpami.2021.3058693

Near-Convex Archetypal Analysis

Author(s): Pierre De Handschutter, Nicolas Gillis, Arnaud Vandaele, Xavier Siebert
Published in: IEEE Signal Processing Letters, 27, 2020, Page(s) 81-85, ISSN 1070-9908
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/lsp.2019.2957604

Blind Audio Source Separation With Minimum-Volume Beta-Divergence NMF

Author(s): Valentin Leplat, Nicolas Gillis, Andersen M.S. Ang
Published in: IEEE Transactions on Signal Processing, 68, 2020, Page(s) 3400-3410, ISSN 1053-587X
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tsp.2020.2991801

On approximating the nearest Ω‐stable matrix

Author(s): Neelam Choudhary, Nicolas Gillis, Punit Sharma
Published in: Numerical Linear Algebra with Applications, 27/3, 2020, ISSN 1070-5325
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/nla.2282

A geometric lower bound on the extension complexity of polytopes based on the f -vector

Author(s): Julien Dewez, Nicolas Gillis, François Glineur
Published in: Discrete Applied Mathematics, 2020, ISSN 0166-218X
Publisher: Elsevier BV
DOI: 10.1016/j.dam.2020.09.028

A Provably Correct and Robust Algorithm for Convolutive Nonnegative Matrix Factorization

Author(s): Anthony Degleris, Nicolas Gillis
Published in: IEEE Transactions on Signal Processing, 2020, Page(s) 1-1, ISSN 1053-587X
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/tsp.2020.2984163

Minimal-norm static feedbacks using dissipative Hamiltonian matrices

Author(s): Nicolas Gillis, Punit Sharma
Published in: Linear Algebra and its Applications, 2020, ISSN 0024-3795
Publisher: Elsevier BV
DOI: 10.1016/j.laa.2020.02.008

Computing Large-Scale Matrix and Tensor Decomposition With Structured Factors: A Unified Nonconvex Optimization Perspective

Author(s): Xiao Fu, Nico Vervliet, Lieven De Lathauwer, Kejun Huang, Nicolas Gillis
Published in: IEEE Signal Processing Magazine, 37/5, 2020, Page(s) 78-94, ISSN 1053-5888
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/msp.2020.3003544

Nonnegative Matrix Factorization

Author(s): Nicolas Gillis
Published in: 2020, ISBN 978-1-61197-641-0
Publisher: SIAM
DOI: 10.1137/1.9781611976410

Introduction to Nonnegative Matrix Factorization

Author(s): Nicolas Gillis
Published in: SIAG/OPT Views and News, 25, 2017, Page(s) 7-16
Publisher: SIAM

Sparse Separable Nonnegative Matrix Factorization

Author(s): Nicolas Nadisic, Arnaud Vandaele, Jeremy E. Cohen, Nicolas Gillis
Published in: Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2020, Ghent, Belgium, September 14–18, 2020, Proceedings, Part I, 12457, 2021, Page(s) 335-350, ISBN 978-3-030-67657-5
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-67658-2_20