De handschutter, Pierre ; Université de Mons - UMONS > Recherche > Service ERC Unit - Matrix Theory and Optimization
Gillis, Nicolas ; Université de Mons - UMONS > Faculté Polytechnique > Service de Mathématique et Recherche opérationnelle
Language :
English
Title :
A consistent and flexible framework for deep matrix factorizations
Publication date :
01 January 2023
Journal title :
Pattern Recognition
ISSN :
0031-3203
Publisher :
Elsevier, United Kingdom
Special issue title :
134
Pages :
109102
Peer reviewed :
Peer Reviewed verified by ORBi
Research unit :
F151 - Mathématique et Recherche opérationnelle
Research institute :
R450 - Institut NUMEDIART pour les Technologies des Arts Numériques R300 - Institut de Recherche en Technologies de l'Information et Sciences de l'Informatique
Lee, D.D., Seung, H.S., Learning the parts of objects by non-negative matrix factorization. Nature 401 (1999), 788–791.
d'Aspremont, A., Ghaoui, L., Jordan, M., Lanckriet, G., A direct formulation for sparse PCA using semidefinite programming. Adv Neural Inf Process Syst, 17, 2004.
Zou, H., Hastie, T., Tibshirani, R., Sparse principal component analysis. J. Comput. Graph. Stat. 15:2 (2006), 265–286.
Gribonval, R., Schnass, K., Dictionary identificationsparse matrix-factorization via ℓ1-minimization. IEEE Trans. Inf. Theory 56:7 (2010), 3523–3539.
Fu, X., Huang, K., Sidiropoulos, N.D., Ma, W.-K., Nonnegative matrix factorization for signal and data analytics: identifiability, algorithms, and applications. IEEE Signal Process. Mag. 36:2 (2019), 59–80.
Wan, L., Xia, F., Kong, X., Hsu, C.-H., Huang, R., Ma, J., Deep matrix factorization for trust-aware recommendation in social networks. IEEE Trans. Network Sci. Eng. 8:1 (2020), 511–528.
Zhao, H., Ding, Z., Fu, Y., Multi-view clustering via deep matrix factorization. AAAI Conference on Artificial Intelligence, 2017.
Huang, S., Kang, Z., Xu, Z., Auto-weighted multi-view clustering via deep matrix decomposition. Pattern Recognit, 97, 2020, 107015.
Luong, K., Nayak, R., Balasubramaniam, T., Bashar, M.A., Multi-layer manifold learning for deep non-negative matrix factorization-based multi-view clustering. Pattern Recognit, 2022, 108815.
De Handschutter, P., Gillis, N., Siebert, X., A survey on deep matrix factorizations. Computer Science Review, 42, 2021, 100423.
Chen, W.-S., Zeng, Q., Pan, B., A survey of deep nonnegative matrix factorization. Neurocomputing, 2022.
Zhang, Y., Zhang, Z., Zhang, Z., Zhao, M., Zhang, L., Zha, Z., Wang, M., Deep self-representative concept factorization network for representation learning. SIAM International Conference on Data Mining, 2020, 361–369.
Cichocki, A., Zdunek, R., Multilayer nonnegative matrix factorisation. Electron Lett 42:16 (2006), 947–948.
Trigeorgis, G., Bousmalis, K., Zafeiriou, S., Schuller, B., A deep matrix factorization method for learning attribute representations. IEEE Trans. Pattern Anal. Mach. 39:3 (2016), 417–429.
Arora, S., Cohen, N., Hu, W., Luo, Y., Implicit regularization in deep matrix factorization. Advances in Neural Information Processing Systems, 2019, 7411–7422.
Bolte, J., Sabach, S., Teboulle, M., Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math Program 146:1 (2014), 459–494.
Razaviyayn, M., Hong, M., Luo, Z.-Q., A unified convergence analysis of block successive minimization methods for nonsmooth optimization. SIAM J. Optim. 23:2 (2013), 1126–1153.
Nesterov, Y.E., A method of solving a convex programming problem with convergence rate O(1/k2. Dokl. akad. nauk Sssr 269 (1983), 543–547.
O'donoghue, B., Candès, E., Adaptive restart for accelerated gradient schemes. Found. Comput. Math. 15:3 (2015), 715–732.
Xu, Y., Yin, W., A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion. SIAM J. Imaging 6:3 (2013), 1758–1789.
Xu, Y., Yin, W., A globally convergent algorithm for nonconvex optimization based on block coordinate update. J Sci Comput 72:2 (2017), 700–734.
Abdolali, M., Gillis, N., Simplex-structured matrix factorization: sparsity-based identifiability and provably correct algorithms. SIAM Journal on Mathematics of Data Science 3:2 (2021), 593–623.
Hoyer, P.O., Non-negative matrix factorization with sparseness constraints. Journal of machine learning research, 5(9), 2004.
Kim, H., Park, H., Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis. Bioinformatics 23:12 (2007), 1495–1502.
Gribonval, R., Jenatton, R., Bach, F., Sparse and spurious: dictionary learning with noise and outliers. IEEE Trans. Inf. Theory 61:11 (2015), 6298–6319.
Georgiev, P., Theis, F., Cichocki, A., Sparse component analysis and blind source separation of underdetermined mixtures. IEEE Trans. Neural Netw. 16:4 (2005), 992–996.
Ohib, R., Gillis, N., Dalmasso, N., Shah, S., Potluru, V.K., Plis, S., Explicit group sparse projection with applications to deep learning and NMF. arXiv:1912.03896, 2019.
Miao, L., Qi, H., Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization. IEEE Trans. Geosci. Remote Sens. 45:3 (2007), 765–777.
Chan, T.-H., Chi, C.-Y., Huang, Y.-M., Ma, W.-K., A convex analysis-based minimum-volume enclosing simplex algorithm for hyperspectral unmixing. IEEE Trans. Signal Process. 57:11 (2009), 4418–4432.
Fu, X., Huang, K., Yang, B., Ma, W.-K., Sidiropoulos, N.D., Robust volume minimization-based matrix factorization for remote sensing and document clustering. IEEE Trans. Signal Process. 64:23 (2016), 6254–6268.
Leplat, V., Ang, A.M.S., Gillis, N., Minimum-volume rank-deficient nonnegative matrix factorizations. International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2019, IEEE, 3402–3406.
Gillis, N., Successive nonnegative projection algorithm for robust nonnegative blind source separation. SIAM J. Imaging 7:2 (2014), 1420–1450.
Bioucas-Dias, J.M., Plaza, A., Dobigeon, N., Parente, M., Du, Q., Gader, P., Chanussot, J., Hyperspectral unmixing overview: geometrical, statistical, and sparse regression-based approaches. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 5:2 (2012), 354–379.
Tong, L., Yu, J., Xiao, C., Qian, B., Hyperspectral unmixing via deep matrix factorization. Int J Wavelets Multiresolut Inf Process, 15(06), 2017, 1750058.
De Handschutter, P., Gillis, N., Deep orthogonal matrix factorization as a hierarchical clustering technique. European Signal Processing Conference (EUSIPCO), 2021, IEEE, 1466–1470.
Zhu, F., Spectral unmixing datasets with ground truths. arXiv:1708.05125, 2017.
Gillis, N., Kuang, D., Park, H., Hierarchical clustering of hyperspectral images using rank-two nonnegative matrix factorization. IEEE Trans. Geosci. Remote Sens. 53:4 (2015), 2066–2078.
Hien, L.T.K., Phan, D.N., Gillis, N., An inertial block majorization minimization framework for nonsmooth nonconvex optimization. arXiv:2010.12133, 2020.
Malgouyres, F., Landsberg, J., On the identifiability and stable recovery of deep/multi-layer structured matrix factorization. 2016 IEEE Information Theory Workshop (ITW), 2016, IEEE, 315–319.
Zheng, L., Riccietti, E., Gribonval, R., Hierarchical identifiability in multi-layer sparse matrix factorization. arXiv:2110.01230, 2021.
