The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Selection of the Number of Principal Components: The Variance of the Reconstruction Error Criterion with a Comparison to Other Methods
Abstract
One of the main difficulties in using principal component analysis (PCA) is the selection of the number of principal components (PCs). There exist a plethora of methods to calculate the number of PCs, but most of them use monotonically increasing or decreasing indices. Therefore, the decision to choose the number of principal components is very subjective. In this paper, we present a method based on the variance of the reconstruction error to select the number of PCs. This method demonstrates a minimum over the number of PCs. Conditions are given under which this minimum corresponds to the true number of PCs. Ten other methods available in the signal processing and chemometrics literature are overviewed and compared with the proposed method. Three data sets are used to test the different methods for selecting the number of PCs: two of them are real process data and the other one is a batch reactor simulation.
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Cites
Information Theory and an Extension of the Maximum Likelihood Principle
Akaike, H. (1998) · Springer Series in Statistics · doi:10.1007/978-1-4612-1694-0_15 · Cited by 17,781
The Scree Test For The Number Of Factors
Cattell, R. B. (1966) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr0102_10 · Cited by 13,554
The application of electronic computers to factor analysis
Kaiser, H. F. (1960) · Educational and Psychological Measurement · doi:10.1177/001316446002000116 · Cited by 12,459
LIII. On lines and planes of closest fit to systems of points in space
Pearson, K. (1901) · The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786440109462720 · Cited by 11,934
Wold, S., Esbensen, K., & Geladi, P. (1987) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/0169-7439(87)80084-9 · Cited by 11,606
Analysis of a complex of statistical variables into principal components.
Hotelling, H. (1933) · Journal of Educational Psychology · doi:10.1037/h0071325 · Cited by 9,633
A Rationale and Test for the Number of Factors in Factor Analysis
Horn, J. L. (1965) · Psychometrika · doi:10.1007/bf02289447 · Cited by 8,714
Modeling by shortest data description
Rissanen, J. (1978) · Automatica · doi:10.1016/0005-1098(78)90005-5 · Cited by 6,011
Comparison of five rules for determining the number of components to retain.
Zwick, W. R., & Velicer, W. F. (1986) · Psychological Bulletin · doi:10.1037//0033-2909.99.3.432 · Cited by 3,129
Nonlinear principal component analysis using autoassociative neural networks
Kramer, M. A. (1991) · AIChE Journal · doi:10.1002/aic.690370209 · Cited by 3,037
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Metadata
- Authors
- Valle, S., Li, W., & Qin, S. J.
- Venue
- Industrial & Engineering Chemistry Research
- Publisher
- American Chemical Society (ACS)
- Published
- 1999-09-30
- Volume
- 38
- Issue
- 11
- Pages
- 4389-4401
- ISSN
- 0888-5885 (ISSN-L)
- 1520-5045
- OpenAlex
- W2074058676
- Cited by
- 549
- References
- 25
- FWCI
- 6.42
- Type
- journal article
- Language
- en
- Open access
- closed
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- Valle, S., Li, W., & Qin, S. J. (1999). Selection of the Number of Principal Components: The Variance of the Reconstruction Error Criterion with a Comparison to Other Methods. Industrial & Engineering Chemistry Research. https://doi.org/10.1021/ie990110i
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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