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## Gillis, Nicolas

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 Author ID: gillis.nicolas Published as: Gillis, Nicolas External Links: ORCID
 Documents Indexed: 39 Publications since 2010, including 1 Book
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#### Co-Authors

 5 single-authored 8 Glineur, François 8 Sharma, Punit 4 Vandaele, Arnaud 2 Karow, Michael 2 Luce, Robert 2 Vavasis, Stephen A. 1 Abdolali, Maryam 1 Absil, Pierre-Antoine 1 Belachew, Melisew Tefera 1 Choudhary, Neelam 1 Cohen, Jeremy Emile 1 Del Buono, Nicoletta 1 Dhillon, Inderjit S. 1 Esposito, Flavia Lucia 1 Ghazli, Kahina 1 Hien, Le Thi Khanh 1 Idier, Jérôme 1 Kumar, Abhishek 1 Lei, Qi 1 Leplat, Valentin 1 Ma, Wing-Kin 1 Marrinan, Tim 1 Mehrmann, Volker 1 Moulaï, Mustapha 1 Mousseau, Vincent A. 1 Pirlot, Marc 1 Plemmons, Robert James 1 Shitov, Yaroslav Nikolaevich 1 Sobrie, Olivier 1 Tuyttens, Daniel 1 Zhong, Kai
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#### Serials

 8 Linear Algebra and its Applications 4 SIAM Journal on Matrix Analysis and Applications 2 IEEE Transactions on Signal Processing 2 Journal of Global Optimization 2 Numerical Linear Algebra with Applications 2 Journal of Machine Learning Research (JMLR) 2 SIAM Journal on Imaging Sciences 1 Information Processing Letters 1 Journal of Mathematical Biology 1 Automatica 1 Journal of Computational and Applied Mathematics 1 Journal of Optimization Theory and Applications 1 Mathematics of Operations Research 1 SIAM Journal on Numerical Analysis 1 Applied Numerical Mathematics 1 Journal of Scientific Computing 1 Annals of Operations Research 1 European Journal of Operational Research 1 Pattern Recognition 1 SIAM Journal on Optimization 1 Computational Optimization and Applications 1 IEEE Transactions on Image Processing 1 SIAM Journal on Mathematics of Data Science 1 Data Sci. Book Ser.
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#### Fields

 22 Numerical analysis (65-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 20 Operations research, mathematical programming (90-XX) 6 Computer science (68-XX) 5 Systems theory; control (93-XX) 5 Information and communication theory, circuits (94-XX) 3 Statistics (62-XX) 2 Convex and discrete geometry (52-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

25 Publications have been cited 167 times in 124 Documents Cited by Year
On the geometric interpretation of the nonnegative rank. Zbl 1258.65039
Gillis, Nicolas; Glineur, François
2012
Using underapproximations for sparse nonnegative matrix factorization. Zbl 1191.68783
Gillis, Nicolas; Glineur, François
2010
On computing the distance to stability for matrices using linear dissipative Hamiltonian systems. Zbl 1375.93110
Gillis, Nicolas; Sharma, Punit
2017
Low-rank matrix approximation with weights or missing data is NP-hard. Zbl 1242.65077
Gillis, Nicolas; Glineur, François
2011
Sparse and unique nonnegative matrix factorization through data preprocessing. Zbl 1436.15013
Gillis, Nicolas
2012
Semidefinite programming based preconditioning for more robust near-separable nonnegative matrix factorization. Zbl 1316.15015
Gillis, Nicolas; Vavasis, Stephen A.
2015
Heuristics for exact nonnegative matrix factorization. Zbl 1341.65057
Vandaele, Arnaud; Gillis, Nicolas; Glineur, François; Tuyttens, Daniel
2016
Finding the nearest positive-real system. Zbl 1390.93296
Gillis, Nicolas; Sharma, Punit
2018
A continuous characterization of the maximum-edge biclique problem. Zbl 1305.90349
Gillis, Nicolas; Glineur, François
2014
Robust near-separable nonnegative matrix factorization using linear optimization. Zbl 1319.90044
Gillis, Nicolas; Luce, Robert
2014
Robustness analysis of Hottopixx, a linear programming model for factoring nonnegative matrices. Zbl 1286.15016
Gillis, Nicolas
2013
Sparse nonnegative matrix underapproximation and its application to hyperspectral image analysis. Zbl 1281.65032
Gillis, Nicolas; Plemmons, Robert J.
2013
A multilevel approach for nonnegative matrix factorization. Zbl 1241.65039
Gillis, Nicolas; Glineur, François
2012
On the linear extension complexity of regular $$n$$-gons. Zbl 1360.52025
Vandaele, Arnaud; Gillis, Nicolas; Glineur, François
2017
Successive nonnegative projection algorithm for robust nonnegative blind source separation. Zbl 1296.65065
Gillis, Nicolas
2014
Enhancing pure-pixel identification performance via preconditioning. Zbl 1325.65083
Gillis, Nicolas; Ma, Wing-Kin
2015
Exact and heuristic algorithms for semi-nonnegative matrix factorization. Zbl 1327.15027
Gillis, Nicolas; Kumar, Abhishek
2015
Efficient and non-convex coordinate descent for symmetric nonnegative matrix factorization. Zbl 1414.94636
Vandaele, Arnaud; Gillis, Nicolas; Lei, Qi; Zhong, Kai; Dhillon, Inderjit
2016
Approximating the nearest stable discrete-time system. Zbl 1415.65086
Gillis, Nicolas; Karow, Michael; Sharma, Punit
2019
Low-rank matrix approximation in the infinity norm. Zbl 1423.15015
Gillis, Nicolas; Shitov, Yaroslav
2019
UTA-poly and UTA-splines: additive value functions with polynomial marginals. Zbl 1376.91075
Sobrie, Olivier; Gillis, Nicolas; Mousseau, Vincent; Pirlot, Marc
2018
A semi-analytical approach for the positive semidefinite Procrustes problem. Zbl 1380.65103
Gillis, Nicolas; Sharma, Punit
2018
On the complexity of robust PCA and $$\ell_1$$-norm low-rank matrix approximation. Zbl 1434.65054
Gillis, Nicolas; Vavasis, Stephen A.
2018
Solving the maximum clique problem with symmetric rank-one non-negative matrix approximation. Zbl 1380.65100
Belachew, Melisew Tefera; Gillis, Nicolas
2017
Algorithms for positive semidefinite factorization. Zbl 1427.90270
Vandaele, Arnaud; Glineur, François; Gillis, Nicolas
2018
Approximating the nearest stable discrete-time system. Zbl 1415.65086
Gillis, Nicolas; Karow, Michael; Sharma, Punit
2019
Low-rank matrix approximation in the infinity norm. Zbl 1423.15015
Gillis, Nicolas; Shitov, Yaroslav
2019
Finding the nearest positive-real system. Zbl 1390.93296
Gillis, Nicolas; Sharma, Punit
2018
UTA-poly and UTA-splines: additive value functions with polynomial marginals. Zbl 1376.91075
Sobrie, Olivier; Gillis, Nicolas; Mousseau, Vincent; Pirlot, Marc
2018
A semi-analytical approach for the positive semidefinite Procrustes problem. Zbl 1380.65103
Gillis, Nicolas; Sharma, Punit
2018
On the complexity of robust PCA and $$\ell_1$$-norm low-rank matrix approximation. Zbl 1434.65054
Gillis, Nicolas; Vavasis, Stephen A.
2018
Algorithms for positive semidefinite factorization. Zbl 1427.90270
Vandaele, Arnaud; Glineur, François; Gillis, Nicolas
2018
On computing the distance to stability for matrices using linear dissipative Hamiltonian systems. Zbl 1375.93110
Gillis, Nicolas; Sharma, Punit
2017
On the linear extension complexity of regular $$n$$-gons. Zbl 1360.52025
Vandaele, Arnaud; Gillis, Nicolas; Glineur, François
2017
Solving the maximum clique problem with symmetric rank-one non-negative matrix approximation. Zbl 1380.65100
Belachew, Melisew Tefera; Gillis, Nicolas
2017
Heuristics for exact nonnegative matrix factorization. Zbl 1341.65057
Vandaele, Arnaud; Gillis, Nicolas; Glineur, François; Tuyttens, Daniel
2016
Efficient and non-convex coordinate descent for symmetric nonnegative matrix factorization. Zbl 1414.94636
Vandaele, Arnaud; Gillis, Nicolas; Lei, Qi; Zhong, Kai; Dhillon, Inderjit
2016
Semidefinite programming based preconditioning for more robust near-separable nonnegative matrix factorization. Zbl 1316.15015
Gillis, Nicolas; Vavasis, Stephen A.
2015
Enhancing pure-pixel identification performance via preconditioning. Zbl 1325.65083
Gillis, Nicolas; Ma, Wing-Kin
2015
Exact and heuristic algorithms for semi-nonnegative matrix factorization. Zbl 1327.15027
Gillis, Nicolas; Kumar, Abhishek
2015
A continuous characterization of the maximum-edge biclique problem. Zbl 1305.90349
Gillis, Nicolas; Glineur, François
2014
Robust near-separable nonnegative matrix factorization using linear optimization. Zbl 1319.90044
Gillis, Nicolas; Luce, Robert
2014
Successive nonnegative projection algorithm for robust nonnegative blind source separation. Zbl 1296.65065
Gillis, Nicolas
2014
Robustness analysis of Hottopixx, a linear programming model for factoring nonnegative matrices. Zbl 1286.15016
Gillis, Nicolas
2013
Sparse nonnegative matrix underapproximation and its application to hyperspectral image analysis. Zbl 1281.65032
Gillis, Nicolas; Plemmons, Robert J.
2013
On the geometric interpretation of the nonnegative rank. Zbl 1258.65039
Gillis, Nicolas; Glineur, François
2012
Sparse and unique nonnegative matrix factorization through data preprocessing. Zbl 1436.15013
Gillis, Nicolas
2012
A multilevel approach for nonnegative matrix factorization. Zbl 1241.65039
Gillis, Nicolas; Glineur, François
2012
Low-rank matrix approximation with weights or missing data is NP-hard. Zbl 1242.65077
Gillis, Nicolas; Glineur, François
2011
Using underapproximations for sparse nonnegative matrix factorization. Zbl 1191.68783
Gillis, Nicolas; Glineur, François
2010
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#### Cited by 239 Authors

 19 Gillis, Nicolas 7 Shitov, Yaroslav Nikolaevich 6 Sharma, Punit 5 Gouveia, Joao 5 Mehrmann, Volker 4 Glineur, François 4 Guglielmi, Nicola 4 Parrilo, Pablo A. 4 Punnen, Abraham P. 4 Robinson, Richard Z. 4 Thomas, Rekha R. 3 Fawzi, Hamza 3 Karapetyan, Daniel 3 Protasov, Vladimir Yu. 3 Van Dooren, Paul M. 3 Vandaele, Arnaud 2 Braun, Gábor 2 Cvetković, Aleksandar S. 2 Devarajan, Karthik 2 Dong, Bo 2 Fiorini, Samuel 2 Glover, Fred W. 2 Kadziński, Miłosz 2 Karow, Michael 2 Kubjas, Kaie 2 Lin, Matthew M. 2 Ma, Wing-Kin 2 Mehl, Christian 2 Mirzal, Andri 2 Mizutani, Tomohiko 2 Park, Haesun 2 Plemmons, Robert James 2 Pokutta, Sebastian 2 Scalone, Carmela 2 Sripratak, Piyashat 2 Vavasis, Stephen A. 1 Abdolali, Maryam 1 Absil, Pierre-Antoine 1 Alemany, Sandra 1 Avis, David M. 1 Banks, David L. 1 Beattie, Christopher A. 1 Belachew, Melisew Tefera 1 Bensmail, Halima 1 Berisha, Sebastian 1 Bobin, Jérôme 1 Bohn, Adam 1 Bolte, Jérôme 1 Boukhetala, Kamel 1 Boumal, Nicolas 1 Bremner, David 1 Burger, Thomas 1 Che, Hangjun 1 Chen, Lixia 1 Chen, Wensheng 1 Cheng, Huan-Chang 1 Chenot, Cécile 1 Cheung, Vincent C. K. 1 Chewle, Surahit 1 Chi, Chong-Yung 1 Chistikov, Dmitry V. 1 Choi, Kup-Sze 1 Chouh, Meriem 1 Chu, Moody T. 1 Cinelli, Marco 1 Colubi, Ana 1 Corrente, Salvatore 1 Courty, Nicolas 1 Dai, Xiangguang 1 d’Aspremont, Alexandre 1 de Laat, David 1 Del Buono, Nicoletta 1 Derbanosov, R. Yu. 1 Deville, Yannick 1 Dragomir, Radu-Alexandru 1 Duarte, Abraham 1 Duginov, O. I. 1 Ebrahimi, Nader D. 1 Elser, Veit 1 Epifanio, Irene 1 Esposito, Flavia Lucia 1 Fackeldey, Konstantin 1 Faenza, Yuri 1 Fisikopoulos, Vissarion 1 Gallopoulos, Efstratios 1 Gao, Xin 1 García-Bárzana, Marta 1 García Mollá, Victor Manuel 1 Gillard, Jonathan W. 1 Glynn, Chris 1 Gong, Pinghua 1 Gong, Xing 1 Goucha, António Pedro 1 Greco, Salvatore 1 Gribling, Sander 1 Guillemard, Mijail 1 Hanafi, Mohamed 1 Hao, Jin-Kao 1 He, Yunlong 1 Hosseini, Shahram ...and 139 more Authors
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#### Cited in 63 Serials

 14 Linear Algebra and its Applications 8 SIAM Journal on Matrix Analysis and Applications 7 Mathematical Programming. Series A. Series B 5 Pattern Recognition 3 Journal of Computational and Applied Mathematics 3 Machine Learning 3 Journal of Global Optimization 3 European Journal of Operational Research 3 Computational Optimization and Applications 3 SIAM Journal on Imaging Sciences 2 Discrete Applied Mathematics 2 Automatica 2 Journal of Optimization Theory and Applications 2 Mathematics of Operations Research 2 SIAM Journal on Numerical Analysis 2 Discrete & Computational Geometry 2 Computers & Operations Research 2 SIAM Journal on Discrete Mathematics 2 Journal of Scientific Computing 2 Neural Networks 2 Neural Computation 2 Computational Mathematics and Mathematical Physics 2 Numerical Linear Algebra with Applications 2 ELA. The Electronic Journal of Linear Algebra 2 SIAM Journal on Mathematics of Data Science 1 Communications in Algebra 1 Journal of Computational Physics 1 Journal of Mathematical Biology 1 Linear and Multilinear Algebra 1 Calcolo 1 Information Sciences 1 Journal of the American Statistical Association 1 Journal of Combinatorial Theory. Series A 1 SIAM Journal on Control and Optimization 1 Theoretical Computer Science 1 Applied Numerical Mathematics 1 Algorithmica 1 International Journal of Approximate Reasoning 1 Multidimensional Systems and Signal Processing 1 Numerical Algorithms 1 Computational Statistics 1 Computational Statistics and Data Analysis 1 SIAM Journal on Optimization 1 Vestnik St. Petersburg University. Mathematics 1 SIAM Journal on Scientific Computing 1 Statistical Papers 1 International Journal of Computer Vision 1 Advances in Computational Mathematics 1 INFORMS Journal on Computing 1 Journal of Mathematical Chemistry 1 Doklady Mathematics 1 Data Mining and Knowledge Discovery 1 Trudy Instituta Matematiki 1 Foundations of Computational Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Systems Science and Complexity 1 Sampling Theory in Signal and Image Processing 1 Advances in Data Analysis and Classification. ADAC 1 Mathematical Programming Computation 1 Numerical Algebra, Control and Optimization 1 Axioms 1 Bayesian Analysis 1 SIAM Journal on Applied Algebra and Geometry
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#### Cited in 23 Fields

 61 Linear and multilinear algebra; matrix theory (15-XX) 49 Operations research, mathematical programming (90-XX) 43 Numerical analysis (65-XX) 28 Computer science (68-XX) 15 Convex and discrete geometry (52-XX) 14 Statistics (62-XX) 10 Systems theory; control (93-XX) 8 Information and communication theory, circuits (94-XX) 7 Combinatorics (05-XX) 3 Ordinary differential equations (34-XX) 3 Biology and other natural sciences (92-XX) 2 Algebraic geometry (14-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)