Principal component analysis
Open accessAbstract
Principal component analysis is one of the most important and powerful methods in chemometrics as well as in a wealth of other areas.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Attackers often use techniques such as spoofing real UDP and ICMP to induce flooding.
“The attacker often uses techniques such as spoofing real User Datagram Protocol (UDP) [54] and Internet Control Message Protocol (ICMP) [97] to induce flooding.”
From Comparative Analysis of Intrusion Detection Systems and Machine Learning Based Model Analysis through Decision Tree (2023) · cites this paper as [54]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
LIII. On lines and planes of closest fit to systems of points in space
Karl Pearson, F. R. S. (1901) · The London Edinburgh and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786440109462720 · Cited by 13,658 · see citing works
The Scree Test For The Number Of Factors
Cattell, R. B. (1966) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr0102_10 · Cited by 13,554 · see citing works
The application of electronic computers to factor analysis
Kaiser, H. F. (1960) · Educational and Psychological Measurement · doi:10.1177/001316446002000116 · Cited by 12,459 · see citing works
Analysis of a complex of statistical variables into principal components.
Hotelling, H. (1933) · Journal of Educational Psychology · doi:10.1037/h0071325 · Cited by 9,691 · see citing works
An Introduction to Multivariate Statistical Analysis
Muirhead, R. J., & Anderson, T. W. (1986) · Journal of Business and Economic Statistics · doi:10.2307/1391399 · Cited by 9,209 · see citing works
An Introduction to Multivariate Statistical Analysis.
Skinner, C. J., & Anderson, T. W. (1985) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2981950 · Cited by 3,282 · see citing works
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 3,028 · see citing works
Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models
Wold, S. (1978) · Technometrics · doi:10.1080/00401706.1978.10489693 · Cited by 2,506 · see citing works
van den Berg, R. A., Hoefsloot, H. C., Westerhuis, J. A., Smilde, A. K., & van der Werf, M. J. (2006) · BMC Genomics · doi:10.1186/1471-2164-7-142 · Cited by 2,450 · see citing works
Self-citationSome necessary conditions for common-factor analysis
Guttman, L. (1954) · Psychometrika · doi:10.1007/bf02289162 · Cited by 1,697 · see citing works
The Generalization of Student's Ratio
Hotelling, H. (1931) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177732979 · Cited by 1,512 · see citing works
An Introduction to the Theory of Statistics
Dempster, A. P., & Plackett, R. L. (1973) · International Statistical Review · doi:10.2307/1402858 · Cited by 1,468 · see citing works
Multivariate SPC Charts for Monitoring Batch Processes
Nomikos, P., & MacGregor, J. F. (1995) · Technometrics · doi:10.1080/00401706.1995.10485888 · Cited by 1,391 · see citing works
ON THE RELATIVE ABUNDANCE OF BIRD SPECIES
MacArthur, R. H. (1957) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.43.3.293 · Cited by 1,182 · see citing works
The Generalization of Student’s Ratio
Hotelling, H. (1992) · Springer series in statistics · doi:10.1007/978-1-4612-0919-5_4 · Cited by 1,082 · see citing works
ROBPCA: A New Approach to Robust Principal Component Analysis
Hubert, M., Rousseeuw, P. J., & Vanden Branden, K. (2005) · Technometrics · doi:10.1198/004017004000000563 · Cited by 1,052 · see citing works
Introduction to the Theory of Statistics, 3rd ed.
Kass, G. V., Mood, A. M., Graybill, F. A., & Boes, D. C. (1974) · Journal of the American Statistical Association · doi:10.2307/2286195 · Cited by 975 · see citing works
Chemometrics, mathematics and statistics in chemistry
Kowalski, B. R., Schilling, E. E., Kilian, N., Jones, K. E., & Dias, E. F. (1984) · D. Reidel , Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers eBooks · Cited by 537 · see citing works
Martens, H., & Stark, E. (1991) · Journal of Pharmaceutical and Biomedical Analysis · doi:10.1016/0731-7085(91)80188-f · Cited by 515 · see citing works
Generalized contribution plots in multivariate statistical process monitoring
Westerhuis, J. A., Gurden, S. P., & Smilde, A. K. (2000) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(00)00062-9 · Cited by 509 · see citing works
Self-citationThe eigenvalues-greater-than-one rule and the reliability of components.
Cliff, N. (1988) · Psychological Bulletin · doi:10.1037/0033-2909.103.2.276 · Cited by 496 · see citing works
Centering and scaling in component analysis
Bro, R., & Smilde, A. K. (2003) · Journal of Chemometrics · doi:10.1002/cem.773 · Cited by 445 · see citing works
Self-citationPrincipal Components and Factor Analysis: Part I—Principal Components
Jackson, J. E. (1980) · Journal of Quality Technology · doi:10.1080/00224065.1980.11980967 · Cited by 376 · see citing works
Robust Estimation of Dispersion Matrices and Principal Components
Devlin, S. J., Gnanadesikan, R., & Kettenring, J. R. (1981) · Journal of the American Statistical Association · doi:10.1080/01621459.1981.10477654 · Cited by 373 · see citing works
Missing data methods in PCA and PLS: Score calculations with incomplete observations
Nelson, P. R. C., Taylor, P. A., & MacGregor, J. F. (1996) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(96)00007-x · Cited by 361 · see citing works
Cross-validation of component models: A critical look at current methods
河野, 麻., Kjeldahl, K., Smilde, A. K., & Kiers, H. A. L. (2008) · Analytical and Bioanalytical Chemistry · doi:10.1007/s00216-007-1790-1 · Cited by 341 · see citing works
Self-citationFrontier, S. (1976) · Journal of Experimental Marine Biology and Ecology · doi:10.1016/0022-0981(76)90076-9 · Cited by 303 · see citing works
Maximum likelihood principal component analysis
Wentzell, P. D., Andrews, D. T., Hamilton, D. C., Faber, K., & Kowalski, B. R. (1997) · Journal of Chemometrics · doi:10.1002/(sici)1099-128x(199707)11:4 · Cited by 236 · see citing works
Bro, R. (2003) · Analytica Chimica Acta · doi:10.1016/s0003-2670(03)00681-0 · Cited by 225 · see citing works
Self-citationRaman Spectra of Biological Samples: A Study of Preprocessing Methods
Afseth, N. K., Segtnan, V. H., & Wold, J. P. (2006) · Applied Spectroscopy · doi:10.1366/000370206779321454 · Cited by 206 · see citing works
Walczak, B., & Massart, D. L. (2001) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(01)00131-9 · Cited by 202 · see citing works
Partitioning of interaction in analysis of variance
Mandel, J. (1969) · Journal of Research of the National Bureau of Standards Section B Mathematical Sciences · doi:10.6028/jres.073b.031 · Cited by 167 · see citing works
Robust methods for multivariate data analysis
Møller, S. F., von Frese, J., & Bro, R. (2005) · Journal of Chemometrics · doi:10.1002/cem.962 · Cited by 162 · see citing works
Self-citationMissing values in principal component analysis
Grung, B., & Manne, R. (1998) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(98)00031-8 · Cited by 160 · see citing works
Dealing with missing data: Part II
Walczak, B., & Massart, D. L. (2001) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(01)00132-0 · Cited by 159 · see citing works
Robustness and Outlier Detection in Chemometrics
Rousseeuw, P. J., Debruyne, M., Engelen, S., & Mia Hubert, B. (2006) · Critical Reviews in Analytical Chemistry · doi:10.1080/10408340600969403 · Cited by 156 · see citing works
Derivative Preprocessing and Optimal Corrections for Baseline Drift in Multivariate Calibration
Brown, C. D., Vega‐Montoto, L., & Wentzell, P. D. (2000) · Applied Spectroscopy · doi:10.1366/0003702001950571 · Cited by 148 · see citing works
Least squares optimization in multivariate analysis
Berge, T. J. (2005) · DSWO Press eBooks · Cited by 141 · see citing works
Nomikos, P. (1996) · ISA Transactions · doi:10.1016/s0019-0578(96)00035-3 · Cited by 131 · see citing works
A Proposal for Handling Missing Data
Gleason, T. C., & Staelin, R. (1975) · Psychometrika · doi:10.1007/bf02291569 · Cited by 125 · see citing works
de Noord, O. E. (1994) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/0169-7439(93)e0065-c · Cited by 101 · see citing works
Maximum likelihood fitting using ordinary least squares algorithms
Bro, R., Sidiropoulos, N. D., & Smilde, A. K. (2002) · Journal of Chemometrics · doi:10.1002/cem.734 · Cited by 97 · see citing works
Self-citationPardo, M., Niederjaufner, G., Benussi, G., et al. (2000) · Sensors and Actuators B Chemical · doi:10.1016/s0925-4005(00)00499-8 · Cited by 96 · see citing works
Classification of archaeological artifacts by applying pattern recognition to trace element data
Kowalski, B. R., Schatzki, T. F., & Stross, F. H. (1972) · Analytical Chemistry · doi:10.1021/ac60321a002 · Cited by 93 · see citing works
Bootstrap based confidence limits in principal component analysis — A case study
Babamoradi, H., van den Berg, F. W. J., & Rinnan, Å. (2012) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2012.10.007 · Cited by 91 · see citing works
Comparing a new algorithm with the classic methods for estimating the number of factors
Henry, R. C., Park, E. S., & Spiegelman, C. H. (1999) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(99)00015-5 · Cited by 90 · see citing works
Andrews, D. T., & Wentzell, P. D. (1997) · Analytica Chimica Acta · doi:10.1016/s0003-2670(97)00270-5 · Cited by 85 · see citing works
Timmerman, M. E., Kiers, H. A. L., & Smilde, A. K. (2006) · British Journal of Mathematical and Statistical Psychology · doi:10.1348/000711006x109636 · Cited by 84 · see citing works
Self-citationDecompositions and Biplots in Three-Way Correspondence Analysis
Carlier, A., & Kroonenberg, P. M. (1996) · Psychometrika · doi:10.1007/bf02294344 · Cited by 71 · see citing works
Ballabio, D., Skov, T., Leardi, R., et al. (2008) · Journal of Chemometrics · doi:10.1002/cem.1173 · Cited by 64 · see citing works
Multiblock variance partitioning: A new approach for comparing variation in multiple data blocks
Skov, T., Ballabio, D., & Bro, R. (2008) · Analytica Chimica Acta · doi:10.1016/j.aca.2008.03.045 · Cited by 64 · see citing works
Self-citationClassification models: Discriminant analysis, SIMCA, CART
Frank, I. E., & Lanteri, S. (1989) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/0169-7439(89)80052-8 · Cited by 61 · see citing works
A method of robust multivariate outlier replacement
Hoo, K. A., Tvarlapati, K. J., Piovoso, M. J., et al. (2002) · Computers & Chemical Engineering · doi:10.1016/s0098-1354(01)00734-7 · Cited by 56 · see citing works
Robust principal component analysis by projection pursuit
Xie, Y., Wang, J., Liang, Y., Sun, L., Song, X., & Yu, R. (1993) · Journal of Chemometrics · doi:10.1002/cem.1180070606 · Cited by 53 · see citing works
Robust PCA and normal region in multivariate statistical process monitoring
Chen, J., Bandoni, J. A., & Romagnoli, J. A. (1996) · AIChE Journal · doi:10.1002/aic.690421228 · Cited by 49 · see citing works
Development of Robust Multivariate Calibration Models
Thomas, E. V., & Ge, N. (2000) · Technometrics · doi:10.1080/00401706.2000.10485996 · Cited by 39 · see citing works
Cross-Validation for Choosing the Number of Important Components in Principal Component Analysis
Krzanowski, W. J., & Kline, P. (1995) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3002_2 · Cited by 37 · see citing works
Chemometrics and Chemoinformatics
Lavine, B. K. (2005) · ACS symposium series · doi:10.1021/bk-2005-0894 · Cited by 29 · see citing works
Sufficient conditions for unique solutions within a certain class of curve resolution models
Smilde, A. K., Hoefsloot, H. C. J., Kiers, H. A. L., et al. (2001) · Journal of Chemometrics · doi:10.1002/cem.685 · Cited by 29 · see citing works
Self-citationOutliers and robust procedures in some chemometric applications
Singh, A. K. (1996) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/0169-7439(95)00087-9 · Cited by 26 · see citing works
Test of linear trend in eigenvalues of a covariance matrix with application to data analysis
Bentler, P. M., & Yuan, K. (1996) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1996.tb01090.x · Cited by 25 · see citing works
Tests for Linear Trend in the Smallest Eigenvalues of the Correlation Matrix
Bentler, P. M., & Yuan, K. (1998) · Psychometrika · doi:10.1007/bf02294771 · Cited by 25 · see citing works
Principal component analysis of dissolution data with missing elements
Adams, E., Walczak, B., Vervaet, C., et al. (2002) · International Journal of Pharmaceutics · doi:10.1016/s0378-5173(01)00966-8 · Cited by 24 · see citing works
The geometry of multivariate object preprocessing
Deming, S. N., Palasota, J. A., & Nocerino, J. M. (1993) · Journal of Chemometrics · doi:10.1002/cem.1180070506 · Cited by 18 · see citing works
Gower, J. C. (1995) · doi:10.1093/oso/9780198522850.003.0012 · Cited by 17 · see citing works
Trimmed object projections: a nonparametric robust latent-structure decomposition method
Hove, H., Liang, Y., & Kvalheim, O. M. (1995) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/0169-7439(95)80005-t · Cited by 17 · see citing works
Outlier detection by robust alternating regression
Ukkelberg, Å., & Borgen, O. S. (1993) · Analytica Chimica Acta · doi:10.1016/0003-2670(93)80460-3 · Cited by 16 · see citing works
Hassani, S., Martens, H. A., Qannari, E. M., et al. (2012) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2012.05.015 · Cited by 14 · see citing works
Degrees of freedom for the residuals of a principal component analysis — A clarification
Faber, N. M. (2008) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2008.04.006 · Cited by 7 · see citing works
Are all varieties of PCA the same? A reply to Cadima & Jolliffe
ten Berge, J. M. F., & Kiers, H. A. L. (1997) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1997.tb01152.x · Cited by 6 · see citing works
A New Principal Component Analysis Method Based on Robust Diagnosis
Chen, W., Cui, H., & Liang, Y. (1996) · Analytical Letters · doi:10.1080/00032719608001511 · Cited by 5 · see citing works
Flagged first, then by citations
Research works printed but not linked: 4
- K. Pearson, On lines and planes of closest t to points in space, Philos. Mag., 1901, 2, 559-572.
- R. Bro, N. D. Sidiropoulos and A. K. Smilde, Maximum likelihood tting using simple least squares algorithms, J. Chemom., 2002, 16(8-10), 387-400.
- S. Frontier, Étude de la decroissance des valeurs propers dans une analyze en composantes principales: comparison avec le modèle de baton brisé, J. Exp. Mar. Biol. Ecol., 1976, 25, 67-75.
- P. Nomikos, Detection and diagnosis of abnormal batch operations based on multiway principal component analysis, ISA Trans., 1996, 35, 259-266.
Cited by
Sorted by citations
Machine learning for internet of things data analysis: a survey
Mahdavinejad, M. S., Rezvan, M., Barekatain, M., Adibi, P., Barnaghi, P., & Sheth, A. P. (2018) · Digital Communications and Networks · doi:10.1016/j.dcan.2017.10.002 · Cited by 921 · see citing works
Azam, Z., Islam, M. M., & Huda, M. N. (2023) · IEEE Access · doi:10.1109/access.2023.3296444 · Cited by 265 · see citing works
Reactivity of cellulose during hydrothermal carbonization of lignocellulosic biomass
Volpe, M., Messineo, A., Mäkelä, M., Barr, M. R., Volpe, R., Corrado, C., & Fiori, L. (2020) · Fuel Processing Technology · doi:10.1016/j.fuproc.2020.106456 · Cited by 145 · see citing works
Pan, L., Zhang, P., Daengngam, C., Peng, S., & Chongcheawchamnan, M. (2022) · Journal of Raman Spectroscopy · doi:10.1002/jrs.6225 · Cited by 116 · see citing works
Revolutionizing finance: The synergy of fintech, digital adoption, and innovation
Rizvi, S. K. A., Rahat, B., Naqvi, B., & Umar, M. (2024) · Technological Forecasting and Social Change · doi:10.1016/j.techfore.2023.123112 · Cited by 83 · see citing works
Predicting adverse drug reactions of combined medication from heterogeneous pharmacologic databases
Zheng, Y., Peng, H., Zhang, X., Zhao, Z., Yin, J., & Li, J. (2018) · BMC Bioinformatics · doi:10.1186/s12859-018-2520-8 · Cited by 33 · see citing works
Application of principal component analysis to newborn screening for congenital adrenal hyperplasia
Lasarev, M. R., Bialk, E. R., Allen, D. B., & Held, P. K. (2020) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/clinem/dgaa371 · Cited by 19 · see citing works
Ravi, M., Kaur, K., Wright, C., Bawn, M., & Cutillo, L. (2025) · International Journal of Educational Technology in Higher Education · doi:10.1186/s41239-025-00557-7 · Cited by 12 · see citing works
AI-enabled Parkinson's disease screening using smile videos
Adnan, T., Islam, M. S., Lee, S., Wasifur Rahman Chowdhury, E. M., Tithi, S. D., Noshin, K., Islam, M. R., Sarker, I., Rahman, M. S., Schneider, R. B., et al. (2025) · NEJM AI · doi:10.1056/aioa2400950 · Cited by 5 · see citing works
Zhou, T., Rodríguez-Barrios, S., Ruisánchez, I., & Rivera-Gil, P. (2025) · Biosensors and Bioelectronics · doi:10.1016/j.bios.2025.117897 · Cited by 4 · see citing works
- Authors
- Bro, R., & Smilde, A. K.
- Affiliations
- University of Copenhagen (DK)
- Venue
- Anal. Methods
- Publisher
- Royal Society of Chemistry (RSC)
- Published
- 2014
- Volume
- 6
- Issue
- 9
- Pages
- 2812-2831
- ISSN
- 1759-9660 (ISSN-L)
- 1759-9679
- OpenAlex
- W2763148304
- Cited by
- 3,038
- References
- 72
- Citations by year
- 2026: 251 · 2025: 352 · 2024: 445 · 2023: 435 · 2022: 343 · 2021: 281 · 2020: 254 · 2019: 210 · 2018: 180 · 2017: 120 · 2016: 94 · 2015: 53 · 2014: 12
- FWCI
- 83.34
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- cc-by-nc
- Locations
- Analytical Methods (publishedVersion, cc-by-nc)
- UvA-DARE (University of Amsterdam) (publishedVersion, other-oa)
- Research at the University of Copenhagen (University of Copenhagen) (publishedVersion)
- Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
- Topics
- Physical Sciences › Chemistry › Analytical Chemistry › Spectroscopy and Chemometric Analyses
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- principal component analysis, chemometrics, dimensionality reduction, multivariate analysis
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review