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

Project Information

COLORAMAP

Grant agreement ID: 679515

DOI

10.3030/679515

Project closed

EC signature date 11 April 2016

Start date 1 September 2016

End date 31 August 2021

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 291 750,00

EU contribution

€ 1 291 750,00

Coordinated by

UNIVERSITE DE MONS
Belgium

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Conference proceedings (11)

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), Issue 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), Issue 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

Peer reviewed articles (34)

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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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, Issue 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

Non-peer reviewed articles (7)

Near-Convex Archetypal Analysis

Author(s): Pierre De Handschutter, Nicolas Gillis, Arnaud Vandaele, Xavier Siebert
Published in: IEEE Signal Processing Letters, Issue 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, Issue 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, Issue 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, Issue 37/5, 2020, Page(s) 78-94, ISSN 1053-5888
Publisher: Institute of Electrical and Electronics Engineers
DOI: 10.1109/msp.2020.3003544

Monographic books (1)

Nonnegative Matrix Factorization

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

Other (1)

Introduction to Nonnegative Matrix Factorization

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

Book chapters (1)

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, Issue 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