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

Total Cost €


EC-Contrib. €






Project "COLORAMAP" data sheet

The following table provides information about the project.


Organization address
address: PLACE DU PARC 20
city: MONS
postcode: 7000

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Belgium [BE]
 Project website
 Total cost 1˙291˙750 €
 EC max contribution 1˙291˙750 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-09-01   to  2021-08-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITE DE MONS BE (MONS) coordinator 1˙291˙750.00


 Project objective

Low-rank matrix approximation (LRA) techniques such as principal component analysis (PCA) are powerful tools for the representation and analysis of high dimensional data, and are used in a wide variety of areas such as machine learning, signal and image processing, data mining, and optimization. Without any constraints and using the least squares error, LRA can be solved via the singular value decomposition. However, in practice, this model is often not suitable mainly because (i) the data might be contaminated with outliers, missing data and non-Gaussian noise, and (ii) the low-rank factors of the decomposition might have to satisfy some specific constraints. Hence, in recent years, many variants of LRA have been introduced, using different constraints on the factors and using different objective functions to assess the quality of the approximation; e.g., sparse PCA, PCA with missing data, independent component analysis and nonnegative matrix factorization. Although these new constrained LRA models have become very popular and standard in some fields, there is still a significant gap between theory and practice. In this project, our goal is to reduce this gap by attacking the problem in an integrated way making connections between LRA variants, and by using four very different but complementary perspectives: (1) computational complexity issues, (2) provably correct algorithms, (3) heuristics for difficult instances, and (4) application-oriented aspects. This unified and multi-disciplinary approach will enable us to understand these problems better, to develop and analyze new and existing algorithms and to then use them for applications. Our ultimate goal is to provide practitioners with new tools and to allow them to decide which method to use in which situation and to know what to expect from it.


year authors and title journal last update
List of publications.
2019 Jeremy E. Cohen, Nicolas Gillis
Identifiability of Complete Dictionary Learning
published pages: 518-536, ISSN: 2577-0187, DOI: 10.1137/18m1233339
SIAM Journal on Mathematics of Data Science 1/3 2019-09-26
2019 Nicolas Gillis, Michael Karow, Punit Sharma
A note on approximating the nearest stable discrete-time descriptor systems with fixed rank
published pages: , ISSN: 0168-9274, DOI: 10.1016/j.apnum.2019.09.004
Applied Numerical Mathematics 2019-09-26
2019 Andersen Man Shun Ang, Nicolas Gillis
Accelerating Nonnegative Matrix Factorization Algorithms Using Extrapolation
published pages: 417-439, ISSN: 0899-7667, DOI: 10.1162/neco_a_01157
Neural Computation 31/2 2019-06-19
2017 Cohen, Jérémy E.,; Comon, Pierre; Gillis, Nicolas
Some theory on Non-negative Tucker Decomposition
published pages: , ISSN: , DOI:
13th International Conference on Latent Variable Analysis and Signal Separation (LVA/ICA 2017) 1 2019-06-19
2018 Nicolas Gillis, Robert Luce
A Fast Gradient Method for Nonnegative Sparse Regression With Self-Dictionary
published pages: 24-37, ISSN: 1057-7149, DOI: 10.1109/TIP.2017.2753400
IEEE Transactions on Image Processing 27/1 2019-06-19
2017 Gabriella Casalino, Nicolas Gillis
Sequential dimensionality reduction for extracting localized features
published pages: 15-29, ISSN: 0031-3203, DOI: 10.1016/j.patcog.2016.09.006
Pattern Recognition 63 2019-06-19
2018 Nicolas Gillis, Punit Sharma
A semi-analytical approach for the positive semidefinite Procrustes problem
published pages: 112-137, ISSN: 0024-3795, DOI: 10.1016/j.laa.2017.11.023
Linear Algebra and its Applications 540 2019-06-19
2018 Nicolas Gillis
Multiplicative updates for polynomial root finding
published pages: 14-18, ISSN: 0020-0190, DOI: 10.1016/j.ipl.2017.11.008
Information Processing Letters 132 2019-06-19
2018 Nicolas Gillis, Volker Mehrmann, Punit Sharma
Computing the nearest stable matrix pairs
published pages: e2153, ISSN: 1070-5325, DOI: 10.1002/nla.2153
Numerical Linear Algebra with Applications 2019-06-19
2018 Nicolas Gillis, Punit Sharma
Finding the Nearest Positive-Real System
published pages: 1022-1047, ISSN: 0036-1429, DOI: 10.1137/17m1137176
SIAM Journal on Numerical Analysis 56/2 2019-06-19
2017 Melisew Tefera Belachew, Nicolas Gillis
Solving the Maximum Clique Problem with Symmetric Rank-One Non-negative Matrix Approximation
published pages: 279-296, ISSN: 0022-3239, DOI: 10.1007/s10957-016-1043-6
Journal of Optimization Theory and Applications 173/1 2019-06-19
2017 Nicolas Gillis, Punit Sharma
On computing the distance to stability for matrices using linear dissipative Hamiltonian systems
published pages: 113-121, ISSN: 0005-1098, DOI: 10.1016/j.automatica.2017.07.047
Automatica 85 2019-06-19
2017 Cohen, Jérémy E.,; Gillis, Nicolas
A New Approach to Dictionary-Based Nonnegative Matrix Factorization
published pages: 523-527, ISSN: , DOI:
25th European Signal Processing Conference (EUSIPCO) 1 2019-06-19
2018 Jeremy E. Cohen, Nicolas Gillis
Spectral Unmixing With Multiple Dictionaries
published pages: 187-191, ISSN: 1545-598X, DOI: 10.1109/LGRS.2017.2779477
IEEE Geoscience and Remote Sensing Letters 15/2 2019-06-19
2017 Arnaud Vandaele, Nicolas Gillis, François Glineur
On the linear extension complexity of regular n-gons
published pages: 217-239, ISSN: 0024-3795, DOI: 10.1016/j.laa.2016.12.023
Linear Algebra and its Applications 521 2019-06-19
2019 Syed Muhammad Atif, Sameer Qazi, Nicolas Gillis
Improved SVD-based initialization for nonnegative matrix factorization using low-rank correction
published pages: 53-59, ISSN: 0167-8655, DOI: 10.1016/j.patrec.2019.02.018
Pattern Recognition Letters 122 2019-06-19
2019 Maryam Abdolali, Nicolas Gillis, Mohammad Rahmati
Scalable and Robust Sparse Subspace Clustering Using Randomized Clustering and Multilayer Graphs
published pages: 166-180, ISSN: 0165-1684, DOI: 10.1016/j.sigpro.2019.05.017
Signal Processing 2019-08-05
2019 Nicolas Gillis, Michael Karow, Punit Sharma
Approximating the nearest stable discrete-time system
published pages: 37-53, ISSN: 0024-3795, DOI: 10.1016/j.laa.2019.03.014
Linear Algebra and its Applications 573 2019-05-27
2019 Flavia Esposito, Nicolas Gillis, Nicoletta Del Buono
Orthogonal joint sparse NMF for microarray data analysis
published pages: , ISSN: 0303-6812, DOI: 10.1007/s00285-019-01355-2
Journal of Mathematical Biology 2019-05-27
2018 Jeremy Emile Cohen, Nicolas Gillis
Dictionary-Based Tensor Canonical Polyadic Decomposition
published pages: 1876-1889, ISSN: 1053-587X, DOI: 10.1109/tsp.2017.2777393
IEEE Transactions on Signal Processing 66/7 2019-04-18
2018 Arnaud Vandaele, François Glineur, Nicolas Gillis
Algorithms for positive semidefinite factorization
published pages: 193-219, ISSN: 0926-6003, DOI: 10.1007/s10589-018-9998-x
Computational Optimization and Applications 71/1 2019-04-18
2017 Nicolas Gillis
Introduction to Nonnegative Matrix Factorization
published pages: 7-16, ISSN: , DOI:
SIAG/OPT Views and News 25 2019-04-18
2018 Nicolas Gillis, Stephen A. Vavasis
On the Complexity of Robust PCA and â„“ 1 -Norm Low-Rank Matrix Approximation
published pages: 1072-1084, ISSN: 0364-765X, DOI: 10.1287/moor.2017.0895
Mathematics of Operations Research 43/4 2019-04-18
2019 Nicolas Gillis, Yaroslav Shitov
Low-rank matrix approximation in the infinity norm
published pages: 367-382, ISSN: 0024-3795, DOI: 10.1016/j.laa.2019.07.017
Linear Algebra and its Applications 581 2019-08-29
2019 Andersen Man Shun Ang, Nicolas Gillis
Algorithms and Comparisons of Nonnegative Matrix Factorizations With Volume Regularization for Hyperspectral Unmixing
published pages: 1-11, ISSN: 1939-1404, DOI: 10.1109/jstars.2019.2925098
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 2019-08-29

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