The DOI matches its Crossref record; 42 of the 42 references it cites were found in a registry or an index.
Algorithms for Nonnegative Matrix Factorization with the β-Divergence
Abstract
This letter describes algorithms for nonnegative matrix factorization (NMF) with the β-divergence (β-NMF). The β-divergence is a family of cost functions parameterized by a single shape parameter β that takes the Euclidean distance, the Kullback-Leibler divergence, and the Itakura-Saito divergence as special cases (β = 2, 1, 0 respectively). The proposed algorithms are based on a surrogate auxiliary function (a local majorization of the criterion function). We first describe a majorization-minimization algorithm that leads to multiplicative updates, which differ from standard heuristic multiplicative updates by a β-dependent power exponent. The monotonicity of the heuristic algorithm can, however, be proven for β ∈ (0, 1) using the proposed auxiliary function. Then we introduce the concept of the majorization-equalization (ME) algorithm, which produces updates that move along constant level sets of the auxiliary function and lead to larger steps than MM. Simulations on synthetic and real data illustrate the faster convergence of the ME approach. The letter also describes how the proposed algorithms can be adapted to two common variants of NMF: penalized NMF (when a penalty function of the factors is added to the criterion function) and convex NMF (when the dictionary is assumed to belong to a known subspace).
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Citations
Cites
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
ALGORITHMS FOR NON-NEGATIVE MATRIX FACTORIZATION
Seung, D., & Lee, L.-W. (2001) · Cited by 4,753
Bayesian-Based Iterative Method of Image Restoration*
Richardson, W. H. (1972) · Journal of the Optical Society of America · doi:10.1364/josa.62.000055 · Cited by 4,160
An iterative technique for the rectification of observed distributions
Lucy, L. B. (1974) · The Astronomical Journal · doi:10.1086/111605 · Cited by 3,866 · cited 2×
“These algorithms are the iterative space reconstructing algorithm (ISRA) of Daube-Witherspoon and Muehllehner ( 1986 ) and the Richardson-Lucy (RL) algorithm of Richardson ( 1972 ) and Lucy ( 1974 ), which perform nonnegative linear regression with the Euclidean distance and KL divergence, respectively.”
MethodOnline Learning for Matrix Factorization and Sparse Coding
Mairal, J., Bach, F., Ponce, J., & Sapiro, G. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0908.0050 · Cited by 2,258
Metagenes and molecular pattern discovery using matrix factorization
Brunet, J.-P., Tamayo, P., Golub, T. R., & Mesirov, J. P. (2004) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0308531101 · Cited by 2,183
ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 16
Storkey, A. (2004) · neural information processing systems · Cited by 2,085
Advances in Neural Information Processing Systems 18
Murray, I., Mackay, D., Zoubin Ghahramani, A., & Skilling, J. (2006) · Cited by 1,927
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
Cited by
Majorization-Minimization Algorithms in Signal Processing, Communications, and Machine Learning
Sun, Y., Babu, P., & Palomar, D. P. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2016.2601299 · Cited by 1,820
Févotte, C., Bertin, N., & Durrieu, J.-L. (2009) · Neural Computation · doi:10.1162/neco.2008.04-08-771 · Cited by 1,119
Self-citationHong, M., Razaviyayn, M., Luo, Z.-Q., & Pang, J.-S. (2016) · IEEE Signal Processing Magazine · doi:10.1109/msp.2015.2481563 · Cited by 447
MOLI: multi-omics late integration with deep neural networks for drug response prediction
Sharifi-Noghabi, H., Zolotareva, O., Collins, C. C., & Ester, M. (2019) · Bioinformatics · doi:10.1093/bioinformatics/btz318 · Cited by 421
On Tensors, Sparsity, and Nonnegative Factorizations
Chi, E. C., & Kolda, T. G. (2012) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/110859063 · Cited by 274
Metadata
- Authors
- Févotte, C., & Idier, J.
- Venue
- Neural Computation
- Publisher
- MIT Press - Journals
- Published
- 2011-09
- Volume
- 23
- Issue
- 9
- Pages
- 2421-2456
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W2114508388
- Cited by
- 663
- References
- 42
- FWCI
- 26.22
- Type
- journal article
- Language
- en
- Open access
- closed
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