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Nonnegative Matrix Factorization: A Comprehensive Review
Abstract
Nonnegative Matrix Factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception. It incorporates the nonnegativity constraint and thus obtains the parts-based representation as well as enhancing the interpretability of the issue correspondingly. This survey paper mainly focuses on the theoretical research into NMF over the last 5 years, where the principles, basic models, properties, and algorithms of NMF along with its various modifications, extensions, and generalizations are summarized systematically. The existing NMF algorithms are divided into four categories: Basic NMF (BNMF), Constrained NMF (CNMF), Structured NMF (SNMF), and Generalized NMF (GNMF), upon which the design principles, characteristics, problems, relationships, and evolution of these algorithms are presented and analyzed comprehensively. Some related work not on NMF that NMF should learn from or has connections with is involved too. Moreover, some open issues remained to be solved are discussed. Several relevant application areas of NMF are also briefly described. This survey aims to construct an integrated, state-of-the-art framework for NMF concept, from which the follow-up research may benefit.
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Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Learning the parts of objects by non-negative matrix factorization
Lee, D. D., & Seung, H. S. (1999) · Nature · doi:10.1038/44565 · Cited by 13,868
ALGORITHMS FOR NON-NEGATIVE MATRIX FACTORIZATION
Lee, D. D., & Seung, H. S. (2000) · Cited by 7,952
Paatero, P., & Tapper, U. (1994) · Environmetrics · doi:10.1002/env.3170050203 · Cited by 6,023
ALGORITHMS FOR NON-NEGATIVE MATRIX FACTORIZATION
Seung, D., & Lee, L.-W. (2001) · Cited by 4,753
Non-negative matrix factorization with sparseness constraints
Hoyer, P. O. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.cs/0408058 · Cited by 2,591
Graph Regularized Nonnegative Matrix Factorization for Data Representation
Cai, D., He, X., Han, J., & Huang, T. S. (2011) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2010.231 · Cited by 2,451
Least squares formulation of robust non-negative factor analysis
Paatero, P. (1997) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(96)00044-5 · Cited by 1,978
Document clustering based on non-negative matrix factorization
Xu, W., Liu, X., & Gong, Y. (2003) · Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval · doi:10.1145/860435.860485 · Cited by 1,860
Projected Gradient Methods for Nonnegative Matrix Factorization
Lin, C.-J. (2007) · Neural Computation · doi:10.1162/neco.2007.19.10.2756 · Cited by 1,737
Research works printed but not linked: 43
- 10.1109/ICASSP.2005.1416297 · doi:10.1109/icassp.2005.1416297
- 10.1137/1.9781611972795.58 · doi:10.1137/1.9781611972795.58
- gupta, 2010, Additive Non-Negative Matrix Factorization for Missing Data, arXiv preprint arXiv 1007 0380
- 10.1137/1016064 · doi:10.1137/1016064
- chu, 2004, Optimality, Computation, and Interpretation of Nonnegative Matrix Factorizations, Technical Report
- tropp, 2003, Literature Survey: Nonnegative Matrix Factorization, Technical Report
- 10.1109/ISSPIT.2007.4458186 · doi:10.1109/isspit.2007.4458186
- 10.1109/TASL.2010.2040784 · doi:10.1109/tasl.2010.2040784
- 10.1155/2008/764206 · doi:10.1155/2008/764206
- 2012, Non-Negative Matrix Factorization, Wikipedia
- 10.1109/CISS.2008.4558681 · doi:10.1109/ciss.2008.4558681
- theis, 2005, First Results on Uniqueness of Sparse Non-Negative Matrix Factorization, Proc 13th European Signal Processing Conf (EUSIPCO '05)
- 10.1016/j.patcog.2011.05.015 · doi:10.1016/j.patcog.2011.05.015
- 10.1109/ICASSP.2011.5946900 · doi:10.1109/icassp.2011.5946900
- 10.1109/MSP.2008.4408452 · doi:10.1109/msp.2008.4408452
- li, 2009, Bilinear Form-Based Non-Negative Matrix Set Factorization, Chinese J Computers, 32, 1536
- li, 2009, Non-Negative Matrix-Set Factorization, Journal of Electronic & Information Technology China, 31, 255
- zhang, 2006, Non-Negative Matrix Factorization on Kernels, Proc Ninth Pacific Rim Int'l Conf Artificial Intelligence, 4099, 404
- chen, 2008, A Novel Constraint Non-Negative Matrix Factorization Criterion Based Incremental Learning in Face Recognition, Proc Int Conf Wavelet Analysis and Pattern Recognition, 1, 292
- 10.1145/1772690.1772760 · doi:10.1145/1772690.1772760
- 10.1016/j.patcog.2011.03.023 · doi:10.1016/j.patcog.2011.03.023
- 10.1016/j.sigpro.2010.01.019 · doi:10.1016/j.sigpro.2010.01.019
- 10.1142/S0129065707001275 · doi:10.1142/s0129065707001275
- 10.1109/ICPR.2008.4761256 · doi:10.1109/icpr.2008.4761256
- 10.1117/1.3184771 · doi:10.1117/1.3184771
- 10.1145/1008992.1009029 · doi:10.1145/1008992.1009029
- 10.3724/SP.J.1004.2010.00023 · doi:10.3724/sp.j.1004.2010.00023
- 10.1109/ICASSP.2007.366320 · doi:10.1109/icassp.2007.366320
- 10.1016/j.patrec.2011.01.012 · doi:10.1016/j.patrec.2011.01.012
- shen, 2010, Nonnegative Matrix Factorization Clustering on Multiple Manifolds, Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), 575, 10.1609/aaai.v24i1.7664 · doi:10.1609/aaai.v24i1.7664
- 10.5244/C.23.9 · doi:10.5244/c.23.9
- buciu, 2008, Non-Negative Matrix Factorization, a New Tool for Feature Extraction: Theory and Applications, Int J Comput Commun Control, 3, 67
- chu, 2005, Nonnegative Matrix Factorization and Applications, Bull of the Int'l Linear Algebra Soc, 34, 2
- sra, 2006, Nonnegative Matrix Approximation: Algorithms and Applications, Technical Report
- drakakis, 2008, Analysis of Financial Data Using Non-Negative Matrix Factorization, Int Math Forum, 3, 1853
- 10.1016/j.engappai.2006.03.001 · doi:10.1016/j.engappai.2006.03.001
- 10.1016/j.amc.2008.05.106 · doi:10.1016/j.amc.2008.05.106
- langville, 2006, Initializations for the Nonnegative Matrix Factorization, Proc 12th ACM SIGKDD Int'l Conf Knowledge Discovery and Data Mining
- janecek, 2011, Using Population Based Algorithms for Initializing Nonnegative Matrix Factorization, Advances in Swarm Intelligence, 6729, 307, 10.1007/978-3-642-21524-7_37 · doi:10.1007/978-3-642-21524-7_37
- 10.1109/SSIAI.2008.4512287 · doi:10.1109/ssiai.2008.4512287
- 10.1007/s10618-010-0196-4 · doi:10.1007/s10618-010-0196-4
- 10.1049/el:20060983 · doi:10.1049/el:20060983
- 10.1109/ISSPIT.2009.5407557 · doi:10.1109/isspit.2009.5407557
Cited by
Machine learning in wireless sensor networks: Algorithms, strategies, and applications
Alsheikh, M. A., Lin, S., Niyato, D., & Tan, H.-P. (2014) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2014.2320099 · Cited by 965
Fadlullah, Z. M., Tang, F., Mao, B., Kato, N., Akashi, O., Inoue, T., & Mizutani, K. (2017) · IEEE Communications Surveys & Tutorials · doi:10.1109/comst.2017.2707140 · Cited by 810
Deep Learning for Change Detection in Remote Sensing Images: Comprehensive Review and Meta-Analysis
Khelifi, L., & Mignotte, M. (2020) · IEEE Access · doi:10.1109/access.2020.3008036 · Cited by 441
Multimodal learning for facial expression recognition
Zhang, W., Zhang, Y., Ma, L., Guan, J., & Gong, S. (2015) · Pattern Recognition · doi:10.1016/j.patcog.2015.04.012 · Cited by 100
Self-citationContinuous AU intensity estimation using localized, sparse facial feature space
Jeni, L. A., Girard, J. M., Cohn, J. F., & De La Torre, F. (2013) · 2013 10th IEEE International Conference and Workshops on Automatic Face and Gesture Recognition (FG) · doi:10.1109/fg.2013.6553808 · Cited by 93
Metadata
- Authors
- Wang, Y.-X., & Zhang, Y.-J.
- Venue
- IEEE Transactions on Knowledge and Data Engineering
- Published
- 2013-06
- Volume
- 25
- Issue
- 6
- Pages
- 1336-1353
- ISSN
- 1041-4347 (ISSN-L)
- OpenAlex
- W2144359569
- Cited by
- 981
- References
- 95
- FWCI
- 28.52
- Type
- journal article
- Language
- en
- Open access
- closed
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