The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Lower Rank Approximation of Matrices by Least Squares With Any Choice of Weights
Abstract
Reduced rank approximation of matrices has hitherto been possible only by unweighted least squares. This paper presents iterative techniques for obtaining such approximations when weights are introduced. The techniques involve criss-cross regressions with careful initialization. Possible applications of the approximation are in modelling, biplotting, contingency table analysis, fitting of missing values, checking outliers, etc.
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Cites
The biplot graphic display of matrices with application to principal component analysis
GABRIEL, K. R. (1971) · Biometrika · doi:10.1093/biomet/58.3.453 · Cited by 3,037
Self-citationSingular value decomposition and least squares solutions
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The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate
Golub, G. H., & Pereyra, V. (1973) · SIAM Journal on Numerical Analysis · doi:10.1137/0710036 · Cited by 1,430
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A New Analysis of Variance Model for Non-additive Data
Mandel, J. (1971) · Technometrics · doi:10.1080/00401706.1971.10488751 · Cited by 381
Algorithms for Separable Nonlinear Least Squares Problems
Ruhe, A., & Wedin, P. Å. (1980) · SIAM Review · doi:10.1137/1022057 · Cited by 284
Least Squares Approximation of Matrices by Additive and Multiplicative Models
Gabriel, K. R. (1978) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1978.tb01663.x · Cited by 224
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Pan, R., Zhou, Y., Cao, B., Liu, N. N., Lukose, R., Scholz, M., & Yang, Q. (2008) · 2008 Eighth IEEE International Conference on Data Mining · doi:10.1109/icdm.2008.16 · Cited by 1,015
Mapping the Ideological Marketplace
Bonica, A. (2014) · American Journal of Political Science · doi:10.1111/ajps.12062 · Cited by 680
Correcting systematic effects in a large set of photometric light curves
Tamuz, O., Mazeh, T., & Zucker, S. (2005) · Monthly Notices of the Royal Astronomical Society · doi:10.1111/j.1365-2966.2004.08585.x · Cited by 534
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Metadata
- Authors
- Gabriel, K. R., & Zamir, S.
- Venue
- Technometrics
- Publisher
- Informa UK Limited
- Published
- 1979-11
- Volume
- 21
- Issue
- 4
- Pages
- 489-498
- ISSN
- 0040-1706 (ISSN-L)
- 1537-2723
- OpenAlex
- W2071419850
- Cited by
- 295
- References
- 15
- FWCI
- 1.22
- Type
- journal article
- Language
- en
- Open access
- closed
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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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