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Journal articles on the topic 'Principal components'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 June 2025

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1

Sutter, Jon M., John H. Kalivas, and Patrick M. Lang. "Which principal components to utilize for principal component regression." Journal of Chemometrics 6, no. 4 (July 1992): 217–25. http://dx.doi.org/10.1002/cem.1180060406.

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2

Abegaz, Fentaw, Kridsadakorn Chaichoompu, Emmanuelle Génin, David W. Fardo, Inke R. König, Jestinah M. Mahachie John, and Kristel Van Steen. "Principals about principal components in statistical genetics." Briefings in Bioinformatics 20, no. 6 (September 14, 2018): 2200–2216. http://dx.doi.org/10.1093/bib/bby081.

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Abstract Principal components (PCs) are widely used in statistics and refer to a relatively small number of uncorrelated variables derived from an initial pool of variables, while explaining as much of the total variance as possible. Also in statistical genetics, principal component analysis (PCA) is a popular technique. To achieve optimal results, a thorough understanding about the different implementations of PCA is required and their impact on study results, compared to alternative approaches. In this review, we focus on the possibilities, limitations and role of PCs in ancestry prediction, genome-wide association studies, rare variants analyses, imputation strategies, meta-analysis and epistasis detection. We also describe several variations of classic PCA that deserve increased attention in statistical genetics applications.

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3

Haswell, S. J. "Principal Components." Analytica Chimica Acta 309, no. 1-3 (June 1995): 405–6. http://dx.doi.org/10.1016/0003-2670(95)90335-6.

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4

Miyazaki, Haruo, and Youichi Seki. "Principal Components and Principal Clusters." Journal of Information and Optimization Sciences 8, no. 2 (May 1987): 189–99. http://dx.doi.org/10.1080/02522667.1987.10698885.

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5

Fujiwara, Masakazu, Tomohiro Minamidani, Isamu Nagai, and Hirofumi Wakaki. "Principal Components Regression by Using Generalized Principal Components Analysis." JOURNAL OF THE JAPAN STATISTICAL SOCIETY 43, no. 1 (2013): 57–78. http://dx.doi.org/10.14490/jjss.43.57.

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6

Saegusa, Ryo, Hitoshi Sakano, and Shuji Hashimoto. "Nonlinear principal component analysis to preserve the order of principal components." Neurocomputing 61 (October 2004): 57–70. http://dx.doi.org/10.1016/j.neucom.2004.03.004.

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7

Mertens, B. J. A., T. Fearn, and M. Thompson. "Efficient cross-validation of principal components applied to principal component regression." Statistics and Computing 6, no. 2 (June 1996): 178. http://dx.doi.org/10.1007/bf00162530.

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8

Whitlark, David, and George H. Dunteman. "Principal Components Analysis." Journal of Marketing Research 27, no. 2 (May 1990): 243. http://dx.doi.org/10.2307/3172855.

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9

Ammann, Larry P. "Robust Principal Components." Communications in Statistics - Simulation and Computation 18, no. 3 (January 1989): 857–74. http://dx.doi.org/10.1080/03610918908812795.

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10

Franses, Philip Hans, and Eva Janssens. "Spurious principal components." Applied Economics Letters 26, no. 1 (February 2018): 37–39. http://dx.doi.org/10.1080/13504851.2018.1433292.

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11

SINGH, ASHBINDU, and ANDREW HARRISON. "Standardized principal components." International Journal of Remote Sensing 6, no. 6 (June 1985): 883–96. http://dx.doi.org/10.1080/01431168508948511.

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12

Vines, S. K. "Simple principal components." Journal of the Royal Statistical Society: Series C (Applied Statistics) 49, no. 4 (January 2000): 441–51. http://dx.doi.org/10.1111/1467-9876.00204.

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13

Kim, Sung-Hoon, and George H. Dunteman. "Principal Components Analysis." Journal of Educational Statistics 16, no. 2 (1991): 141. http://dx.doi.org/10.2307/1165117.

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14

de la Iglesia, Manuel D., and Esteban G. Tabak. "Principal Dynamical Components." Communications on Pure and Applied Mathematics 66, no. 1 (June 22, 2012): 48–82. http://dx.doi.org/10.1002/cpa.21411.

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15

Lefkovitch, L. P. "Consensus Principal Components." Biometrical Journal 35, no. 5 (1993): 567–80. http://dx.doi.org/10.1002/bimj.4710350506.

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16

Boente, Graciela, Ana M. Pires, and Isabel M. Rodrigues. "Detecting influential observations in principal components and common principal components." Computational Statistics & Data Analysis 54, no. 12 (December 2010): 2967–75. http://dx.doi.org/10.1016/j.csda.2010.01.001.

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17

Mertens, Bart, Tom Fearn, and Michael Thompson. "The efficient cross-validation of principal components applied to principal component regression." Statistics and Computing 5, no. 3 (September 1995): 227–35. http://dx.doi.org/10.1007/bf00142664.

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18

Kim, Bu-Yong, and Myung-Hee Shin. "Procedure for the Selection of Principal Components in Principal Components Regression." Korean Journal of Applied Statistics 23, no. 5 (October 31, 2010): 967–75. http://dx.doi.org/10.5351/kjas.2010.23.5.967.

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19

Artigue, Heidi, Gary Smith, and Zudi Lu. "The principal problem with principal components regression." Cogent Mathematics & Statistics 6, no. 1 (January 1, 2019): 1622190. http://dx.doi.org/10.1080/25742558.2019.1622190.

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20

Shin, Jae-Kyoung, and Yutaka Tanaka. "CROSS-VALIDATORY CHOICE FOR THE NUMBER OF PRINCIPAL COMPONENTS IN PRINCIPAL COMPONENT REGRESSION." Journal of the Japanese Society of Computational Statistics 9, no. 1 (1996): 53–59. http://dx.doi.org/10.5183/jjscs1988.9.53.

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21

Tanaka, Yukata. "Sensitivity analysis in principal component analysis:influence on the subspace spanned by principal components." Communications in Statistics - Theory and Methods 17, no. 9 (January 1988): 3157–75. http://dx.doi.org/10.1080/03610928808829796.

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22

KARAKUZULU, Cihan, İbrahim Halil GÜMÜŞ, Serkan GÜLDAL, and Mustafa YAVAŞ. "Determining The Number of Principal Components with Schur's Theorem in Principal Component Analysis." Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 12, no. 2 (February 23, 2023): 299–306. http://dx.doi.org/10.17798/bitlisfen.1144360.

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Principal Component Analysis is a method for reducing the dimensionality of datasets while also limiting information loss. It accomplishes this by producing uncorrelated variables that maximize variance one after the other. The accepted criterion for evaluating a Principal Component’s (PC) performance is λ_j/tr(S) where tr(S) denotes the trace of the covariance matrix S. It is standard procedure to determine how many PCs should be maintained using a predetermined percentage of the total variance. In this study, the diagonal elements of the covariance matrix are used instead of the eigenvalues to determine how many PCs need to be considered to obtain the defined threshold of the total variance. For this, an approach which uses one of the important theorems of majorization theory is proposed. Based on the tests, this approach lowers the computational costs.

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23

Ekvall, Karl Oskar. "Targeted principal components regression." Journal of Multivariate Analysis 190 (July 2022): 104995. http://dx.doi.org/10.1016/j.jmva.2022.104995.

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24

Oksanen, E. H. "Principal components in econometrics." Communications in Statistics - Theory and Methods 17, no. 8 (January 1988): 2507–32. http://dx.doi.org/10.1080/03610928808829759.

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25

Hörmann, Siegfried, Łukasz Kidziński, and Marc Hallin. "Dynamic functional principal components." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 77, no. 2 (July 18, 2014): 319–48. http://dx.doi.org/10.1111/rssb.12076.

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26

Meister, J., and W. H. E. Schwarz. "Principal Components of Ionicity." Journal of Physical Chemistry 98, no. 33 (August 1994): 8245–52. http://dx.doi.org/10.1021/j100084a048.

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27

GONZALEZPINTO, A. "Principal components of mania." Journal of Affective Disorders 76, no. 1-3 (September 2003): 95–102. http://dx.doi.org/10.1016/s0165-0327(02)00070-8.

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28

Voegtlin, Thomas. "Recursive principal components analysis." Neural Networks 18, no. 8 (October 2005): 1051–63. http://dx.doi.org/10.1016/j.neunet.2005.07.005.

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29

Maronna, Ricardo A., Fernanda Méndez, and Víctor J. Yohai. "Robust nonlinear principal components." Statistics and Computing 25, no. 2 (December 11, 2013): 439–48. http://dx.doi.org/10.1007/s11222-013-9442-0.

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30

Benko, Michal, Wolfgang Härdle, and Alois Kneip. "Common functional principal components." Annals of Statistics 37, no. 1 (February 2009): 1–34. http://dx.doi.org/10.1214/07-aos516.

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31

Diaz-Garcia, J. A., and R. A. Perez-Agamez. "Principal components under singularity." International Mathematical Forum 2 (2007): 1093–103. http://dx.doi.org/10.12988/imf.2007.07094.

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32

Peña, Daniel, and Victor J. Yohai. "Generalized Dynamic Principal Components." Journal of the American Statistical Association 111, no. 515 (July 2, 2016): 1121–31. http://dx.doi.org/10.1080/01621459.2015.1072542.

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33

Umali, Jennifer, and Erniel Barrios. "Nonparametric Principal Components Regression." Communications in Statistics - Simulation and Computation 43, no. 7 (January 2014): 1797–810. http://dx.doi.org/10.1080/03610918.2012.744046.

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34

Al-Ibrahim, A. H., and Noriah M. Al-Kandari. "Stability of principal components." Computational Statistics 23, no. 1 (August 10, 2007): 153–71. http://dx.doi.org/10.1007/s00180-007-0082-8.

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35

Maćkiewicz, Andrzej, and Waldemar Ratajczak. "Principal components analysis (PCA)." Computers & Geosciences 19, no. 3 (March 1993): 303–42. http://dx.doi.org/10.1016/0098-3004(93)90090-r.

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36

Yendle, Peter W., and Halliday J. H. MacFie. "Discriminant principal components analysis." Journal of Chemometrics 3, no. 4 (September 1989): 589–600. http://dx.doi.org/10.1002/cem.1180030407.

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37

Richman, Michael B. "Rotation of principal components." Journal of Climatology 6, no. 3 (1986): 293–335. http://dx.doi.org/10.1002/joc.3370060305.

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38

Vanella, Patrizio. "Stochastic Forecasting of Demographic Components Based on Principal Component." Athens Journal of Sciences 5, no. 3 (August 31, 2018): 223–45. http://dx.doi.org/10.30958/ajs.5-3-2.

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39

Chapman, R. M., and J. W. Mccrary. "EP Component Identification and Measurement by Principal Components-Analysis." Brain and Cognition 27, no. 3 (April 1995): 288–310. http://dx.doi.org/10.1006/brcg.1995.1024.

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40

Chapman, Robert M., John W. McCrary, R. M. Chapman, and J. W. Mccrary. "EP Component Identification and Measurement by Principal Components-Analysis." Brain and Cognition 28, no. 3 (August 1995): 342. http://dx.doi.org/10.1006/brcg.1995.1262.

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41

Kim, Bu-Yong. "A Criterion for the Selection of Principal Components in the Robust Principal Component Regression." Communications for Statistical Applications and Methods 18, no. 6 (November 30, 2011): 761–70. http://dx.doi.org/10.5351/ckss.2011.18.6.761.

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42

Cristina, O. Chávez Chong, E. Sánchez García Jesús, and DelaCerda Gastélum José. "Análisis de componentes principales funcionales en series de tiempo económicas (Analysis of principal functional components in economic time series)." GECONTEC: Revista Internacional de Gestión del Conocimiento y la Tecnología 3, no. 2 (December 16, 2015): 13–25. https://doi.org/10.5281/zenodo.7080829.

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Resumen El análisis de datos funcionales ha cobrado gran relevancia en los últimos años, convirtiéndose en un importante campo de investigación en la Estadística. El primer método considerado para procesar este tipo de datos fue el de las componentes principales. En este trabajo se considera la extensión del método de las componentes principales clásicas (ACP) al caso funcional (ACPF), algunas propiedades interesantes que aparecen y otras que se conservan al realizar dicha extensión, así como su aplicación el procesamiento de datos reales económicos y una breve explicación de algunas bibliotecas que realizan el análisis de componentes principales funcionales.  English abstract The functional data analysis has gained relevance over the last years becoming an important statistics investigation field. The first method used to process this data type was the principal components analysis (PCA). In this paper, an extension of the classical principal components analysis (PCA) to the functional method (FPCA) is considered, as well as some interesting properties that appear and others that remain with it. Furthermore, its application in the processing of real economic data and some previous work that analyze functional principal components are explained.

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43

Oja, Erkki. "Principal components, minor components, and linear neural networks." Neural Networks 5, no. 6 (November 1992): 927–35. http://dx.doi.org/10.1016/s0893-6080(05)80089-9.

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44

Hancock, Peter J. B. "Evolving faces from principal components." Behavior Research Methods, Instruments, & Computers 32, no. 2 (June 2000): 327–33. http://dx.doi.org/10.3758/bf03207802.

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45

Boudou, Alain, and Sylvie Viguier-Pla. "Principal components analysis and cyclostationarity." Journal of Multivariate Analysis 189 (May 2022): 104875. http://dx.doi.org/10.1016/j.jmva.2021.104875.

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46

Greer, Kieran. "Exemplars can Reciprocate Principal Components." WSEAS TRANSACTIONS ON COMPUTERS 20 (April 21, 2021): 30–38. http://dx.doi.org/10.37394/23205.2021.20.4.

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This paper presents a clustering algorithm that is an extension of the Category Trees algorithm. Category Trees is a clustering method that creates tree structures that branch on category type and not feature. The development in this paper is to consider a secondary order of clustering that is not the category to which the data row belongs, but the tree, representing a single classifier, that it is eventually clustered with. Each tree branches to store subsets of other categories, but the rows in those subsets may also be related. This paper is therefore concerned with looking at that second level of clustering between the category subsets, to try to determine if there is any consistency over it. It is argued that Principal Components may be a related and reciprocal type of structure, and there is an even bigger question about the relation between exemplars and principal components, in general. The theory is demonstrated using the Portugal Forest Fires dataset as a case study. The Category Trees are then combined with other Self-Organising algorithms from the author and it is suggested that they all belong to the same family type, which is an Entropy-style of classifier. Some analysis of classifier types is also presented.

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47

Bahashwan, Ameerah O., Zakiah I. Kalantan, and Samia A. Adham. "Double gamma principal components analysis." Applied Mathematical Sciences 12, no. 11 (2018): 523–33. http://dx.doi.org/10.12988/ams.2018.8455.

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48

Bensen, Jeannette T., Leslie A. Lange, Carl D. Langefeld, Bao-Li Chang, Eugene R. Bleecker, Deborah A. Meyers, and Jianfeng Xu. "Exploring pleiotropy using principal components." BMC Genetics 4, Suppl 1 (2003): S53. http://dx.doi.org/10.1186/1471-2156-4-s1-s53.

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49

Bair, Eric, Trevor Hastie, Debashis Paul, and Robert Tibshirani. "Prediction by Supervised Principal Components." Journal of the American Statistical Association 101, no. 473 (March 2006): 119–37. http://dx.doi.org/10.1198/016214505000000628.

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50

Calmon, Flavio du Pin, Ali Makhdoumi, Muriel Medard, Mayank Varia, Mark Christiansen, and Ken R. Duffy. "Principal Inertia Components and Applications." IEEE Transactions on Information Theory 63, no. 8 (August 2017): 5011–38. http://dx.doi.org/10.1109/tit.2017.2700857.

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