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

Publications

Computing the nearest stable matrix pairs


Published in: ISSN 1070-5325
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
DOI: 10.1137/18m1233339

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

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

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
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
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
DOI: 10.1109/icassp.2019.8682280

Introduction to Nonnegative Matrix Factorization

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