The DOI matches its Crossref record; 49 of the 49 references it cites were found in a registry or an index.
On Tensors, Sparsity, and Nonnegative Factorizations
Open accessAbstract
Tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive tensor factorization model of such data, along with appropriate algorithms and theory. To do so, we propose that the random variation is best described via a Poisson distribution, which better describes the zeros observed in the data as compared to the typical assumption of a Gaussian distribution. Under a Poisson assumption, we fit a model to observed data using the negative log-likelihood score. We present a new algorithm for Poisson tensor factorization called CANDECOMP--PARAFAC alternating Poisson regression (CP-APR) that is based on a majorization-minimization approach. It can be shown that CP-APR is a generalization of the Lee--Seung multiplicative updates. We show how to prevent the algorithm from converging to non-KKT points and prove convergence of CP-APR under mild conditions. We also explain how to implement CP-APR for large-scale sparse tensors and present results on several data sets, both real and simulated.
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(2005) · Statistics for Biology and Health · doi:10.1007/0-387-27255-0_9 · Cited by 20,133
McCullagh, P., & Nelder, J. A. (1989) · doi:10.1007/978-1-4899-3242-6 · Cited by 16,836
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
(2021) · A First Course in Statistical Programming with R · doi:10.1017/9781108993456.011 · Cited by 13,724
(1999) · Springer Series in Operations Research and Financial Engineering · doi:10.1007/b98874 · Cited by 9,482
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
Parallel and Distributed Computation: Numerical Methods
Bertsekas, D. P., & Tsitsiklis, J. N. (1989) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 5,293
ALGORITHMS FOR NON-NEGATIVE MATRIX FACTORIZATION
Seung, D., & Lee, L.-W. (2001) · Cited by 4,753
Carroll, J. D., & Chang, J.-J. (1970) · Psychometrika · doi:10.1007/bf02310791 · Cited by 4,678
Cited by
Si, Y., Du, J., Li, Z., Jiang, X., Miller, T., Wang, F., Jim Zheng, W., & Roberts, K. (2021) · Journal of Biomedical Informatics · doi:10.1016/j.jbi.2020.103671 · Cited by 235
Privacy-Preserving Tensor Factorization for Collaborative Health Data Analysis
Ma, J., Zhang, Q., Lou, J., Ho, J. C., Xiong, L., & Jiang, X. (2019) · Proceedings of the 28th ACM International Conference on Information and Knowledge Management · doi:10.1145/3357384.3357878 · Cited by 51
Yang, K., Li, X., Liu, H., Mei, J., Xie, G., Zhao, J., Xie, B., & Wang, F. (2017) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v31i1.10864 · Cited by 30
Yin, K., Qian, D., Cheung, W. K., Fung, B. C. M., & Poon, J. (2019) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v33i01.33011246 · Cited by 19
Metadata
- Authors
- Chi, E. C., & Kolda, T. G.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 2012-01
- Volume
- 33
- Issue
- 4
- Pages
- 1272-1299
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2024356620
- Cited by
- 274
- References
- 49
- FWCI
- 4.86
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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