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On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization
Abstract
Nonnegative matrix factorization (NMF) is useful to find basis information of nonnegative data. Currently, multiplicative updates are a simple and popular way to find the factorization. However, for the common NMF approach of minimizing the Euclidean distance between approximate and true values, no proof has shown that multiplicative updates converge to a stationary point of the NMF optimization problem. Stationarity is important as it is a necessary condition of a local minimum. This paper discusses the difficulty of proving the convergence. We propose slight modifications of existing updates and prove their convergence. Techniques invented in this paper may be applied to prove the convergence for other bound-constrained optimization problems.
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Citations
Cited by
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
Self-citationAlgorithms and applications for approximate nonnegative matrix factorization
Berry, M. W., Browne, M., Langville, A. N., Pauca, V. P., & Plemmons, R. J. (2007) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2006.11.006 · Cited by 1,512
Nonnegative Matrix Factorization: A Comprehensive Review
Wang, Y.-X., & Zhang, Y.-J. (2013) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2012.51 · Cited by 981
Kim, J., He, Y., & Park, H. (2014) · Journal of Global Optimization · doi:10.1007/s10898-013-0035-4 · Cited by 352
Uncovering novel mutational signatures by de novo extraction with SigProfilerExtractor
Islam, S. M. A., Díaz-Gay, M., Wu, Y., Barnes, M., Vangara, R., Bergstrom, E. N., He, Y., Vella, M., Wang, J., Teague, J. W., et al. (2022) · Cell Genomics · doi:10.1016/j.xgen.2022.100179 · Cited by 365
Metadata
- Authors
- Lin, C.-J.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 2007-11
- Volume
- 18
- Issue
- 6
- Pages
- 1589-1596
- ISSN
- 1045-9227 (ISSN-L)
- 1941-0093
- OpenAlex
- W2132538571
- Cited by
- 416
- References
- 0
- FWCI
- 22.69
- Type
- journal article
- Language
- en
- Open access
- closed
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