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Journal articles on the topic 'Principal component analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 June 2025

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1

Barros, António S., and Douglas N. Rutledge. "Segmented principal component transform–principal component analysis." Chemometrics and Intelligent Laboratory Systems 78, no. 1-2 (July 2005): 125–37. http://dx.doi.org/10.1016/j.chemolab.2005.01.003.

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2

Gewers, Felipe L., Gustavo R. Ferreira, Henrique F. De Arruda, Filipi N. Silva, Cesar H. Comin, Diego R. Amancio, and Luciano Da F. Costa. "Principal Component Analysis." ACM Computing Surveys 54, no. 4 (May 2021): 1–34. http://dx.doi.org/10.1145/3447755.

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Principal component analysis (PCA) is often applied for analyzing data in the most diverse areas. This work reports, in an accessible and integrated manner, several theoretical and practical aspects of PCA. The basic principles underlying PCA, data standardization, possible visualizations of the PCA results, and outlier detection are subsequently addressed. Next, the potential of using PCA for dimensionality reduction is illustrated on several real-world datasets. Finally, we summarize PCA-related approaches and other dimensionality reduction techniques. All in all, the objective of this work is to assist researchers from the most diverse areas in using and interpreting PCA.

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3

Richards, Larry E., and I. T. Jolliffe. "Principal Component Analysis." Journal of Marketing Research 25, no. 4 (November 1988): 410. http://dx.doi.org/10.2307/3172953.

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4

Lever, Jake, Martin Krzywinski, and Naomi Altman. "Principal component analysis." Nature Methods 14, no. 7 (July 2017): 641–42. http://dx.doi.org/10.1038/nmeth.4346.

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5

Timmerman, Marieke E. "Principal Component Analysis." Journal of the American Statistical Association 98, no. 464 (December 2003): 1082–83. http://dx.doi.org/10.1198/jasa.2003.s308.

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6

Goodall, Colin. "Principal Component Analysis." Technometrics 30, no. 3 (August 1988): 351–52. http://dx.doi.org/10.1080/00401706.1988.10488412.

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7

Wold, Svante, Kim Esbensen, and Paul Geladi. "Principal component analysis." Chemometrics and Intelligent Laboratory Systems 2, no. 1-3 (August 1987): 37–52. http://dx.doi.org/10.1016/0169-7439(87)80084-9.

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8

Law, John, and I. T. Jolliffe. "Principal Component Analysis." Statistician 36, no. 4 (1987): 432. http://dx.doi.org/10.2307/2348864.

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9

Hess, Aaron S., and John R. Hess. "Principal component analysis." Transfusion 58, no. 7 (May 6, 2018): 1580–82. http://dx.doi.org/10.1111/trf.14639.

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10

Bro, Rasmus, and Age K. Smilde. "Principal component analysis." Anal. Methods 6, no. 9 (2014): 2812–31. http://dx.doi.org/10.1039/c3ay41907j.

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11

Abdi, Hervé, and Lynne J. Williams. "Principal component analysis." Wiley Interdisciplinary Reviews: Computational Statistics 2, no. 4 (June 30, 2010): 433–59. http://dx.doi.org/10.1002/wics.101.

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12

Guo, Hao, Kurt J. Marfurt, and Jianlei Liu. "Principal component spectral analysis." GEOPHYSICS 74, no. 4 (July 2009): P35—P43. http://dx.doi.org/10.1190/1.3119264.

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Spectral decomposition methods help illuminate lateral changes in porosity and thin-bed thickness. For broadband data, an interpreter might generate 80 or more somewhat redundant amplitude and phase spectral components spanning the usable seismic bandwidth at [Formula: see text] intervals. Large numbers of components can overload not only the interpreter but also the display hardware. We have used principal component analysis to reduce the multiplicity of spectral data and enhance the most energetic trends inside the data. Each principal component spectrum is mathematically orthogonal to other spectra, with the importance of each spectrum being proportional to the size of its corresponding eigenvalue. Principal components are ideally suited to identify geologic features that give rise to anomalous moderate- to high-amplitude spectra. Unlike the input spectral magnitude and phase components, the principal component spectra are not direct indicators of bed thickness. By combining the variability of multiple components, principal component spectra highlight stratigraphic features that can be interpreted using a seismic geomorphology workflow. By mapping the three largest principal components using the three primary colors of red, green, and blue, we could represent more than 80% of the spectral variance with a single image. We have applied and validated this workflow using a broadband data volume containing channels draining an unconformity, which was acquired over the Central Basin Platform, Texas, U.S.A. Principal component analysis reveals a channel system with only a few output data volumes. The same process provides the interpreter with flexibility to remove any unwanted high-amplitude geologic trends or random noise from the original spectral components by eliminating those principal components that do not aid in delineation of prospective features with their interpretation during the reconstruction process.

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13

Jiang, Hansi. "Modularity Component Analysis versus Principal Component Analysis." American Journal of Applied Mathematics 4, no. 2 (2016): 99. http://dx.doi.org/10.11648/j.ajam.20160402.15.

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14

O., P. Sheoran, Kumar Vinay, Poonia Hemant, and Malik Komal. "Principal Component Analysis - Online Statistical Analysis Tool." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 3 (February 29, 2020): 3050–54. https://doi.org/10.35940/ijeat.C6014.029320.

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An online module to deal with PCA has been developed in ASP scripting language based on Server-Client Architecture. The module produces descriptive statistics via subprogram Descriptive Stats, computes eigenvalues and eigenvector using MxEigen Jacobisub-program, order eigenvector through MxEigsrtsub-program and finally produces eigenvalues, eigenvectors, output loadings and components scores through Output Eigenval, Output Loadings, Output Scoressub-programs. A user friendly interface has been developed for entering or pasting the data, entering various parameters such as number of variables, number of observations and selection of covariance/correlation matrix. A complete procedure for how to perform principal component has also been provided in help file

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15

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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16

Moller, R., and A. Konies. "Coupled Principal Component Analysis." IEEE Transactions on Neural Networks 15, no. 1 (January 2004): 214–22. http://dx.doi.org/10.1109/tnn.2003.820439.

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17

Hu, Yu-Pin, and Ruey S. Tsay. "Principal Volatility Component Analysis." Journal of Business & Economic Statistics 32, no. 2 (April 3, 2014): 153–64. http://dx.doi.org/10.1080/07350015.2013.818006.

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18

Tipping, Michael E., and Christopher M. Bishop. "Probabilistic Principal Component Analysis." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61, no. 3 (August 1999): 611–22. http://dx.doi.org/10.1111/1467-9868.00196.

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19

Zou, Hui, Trevor Hastie, and Robert Tibshirani. "Sparse Principal Component Analysis." Journal of Computational and Graphical Statistics 15, no. 2 (June 2006): 265–86. http://dx.doi.org/10.1198/106186006x113430.

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20

Lloyd, Seth, Masoud Mohseni, and Patrick Rebentrost. "Quantum principal component analysis." Nature Physics 10, no. 9 (July 27, 2014): 631–33. http://dx.doi.org/10.1038/nphys3029.

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21

Kao, Yi-Hao, and Benjamin Van Roy. "Directed Principal Component Analysis." Operations Research 62, no. 4 (August 2014): 957–72. http://dx.doi.org/10.1287/opre.2014.1290.

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22

Akinduko, A. A., and A. N. Gorban. "Multiscale principal component analysis." Journal of Physics: Conference Series 490 (March 11, 2014): 012081. http://dx.doi.org/10.1088/1742-6596/490/1/012081.

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23

Jie Luo, Bo Hu, Xie-Ting Ling, and Ruey-Wen Liu. "Principal independent component analysis." IEEE Transactions on Neural Networks 10, no. 4 (July 1999): 912–17. http://dx.doi.org/10.1109/72.774259.

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24

Wiesel, A., and A. O. Hero. "Decomposable Principal Component Analysis." IEEE Transactions on Signal Processing 57, no. 11 (November 2009): 4369–77. http://dx.doi.org/10.1109/tsp.2009.2025806.

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25

Gupta, Ajay, and Adrian Barbu. "Parameterized principal component analysis." Pattern Recognition 78 (June 2018): 215–27. http://dx.doi.org/10.1016/j.patcog.2018.01.018.

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26

Li, TianJiang, and Qiang Du. "Abstract principal component analysis." Science China Mathematics 56, no. 12 (August 29, 2013): 2783–98. http://dx.doi.org/10.1007/s11425-013-4715-9.

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27

Candès, Emmanuel J., Xiaodong Li, Yi Ma, and John Wright. "Robust principal component analysis?" Journal of the ACM 58, no. 3 (May 2011): 1–37. http://dx.doi.org/10.1145/1970392.1970395.

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28

Liwicki, Stephan, Georgios Tzimiropoulos, Stefanos Zafeiriou, and Maja Pantic. "Euler Principal Component Analysis." International Journal of Computer Vision 101, no. 3 (September 5, 2012): 498–518. http://dx.doi.org/10.1007/s11263-012-0558-z.

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29

Fearn, Tom. "Probabilistic Principal Component Analysis." NIR news 25, no. 3 (May 2014): 23. http://dx.doi.org/10.1255/nirn.1439.

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30

Sando, Keishi, and Hideitsu Hino. "Modal Principal Component Analysis." Neural Computation 32, no. 10 (October 2020): 1901–35. http://dx.doi.org/10.1162/neco_a_01308.

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Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and various robust PCA methods have been proposed. It has been shown that the robustness of many statistical methods can be improved using mode estimation instead of mean estimation, because mode estimation is not significantly affected by the presence of outliers. Thus, this study proposes a modal principal component analysis (MPCA), which is a robust PCA method based on mode estimation. The proposed method finds the minor component by estimating the mode of the projected data points. As a theoretical contribution, probabilistic convergence property, influence function, finite-sample breakdown point, and its lower bound for the proposed MPCA are derived. The experimental results show that the proposed method has advantages over conventional methods.

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31

Nounou, Mohamed N., Bhavik R. Bakshi, Prem K. Goel, and Xiaotong Shen. "Bayesian principal component analysis." Journal of Chemometrics 16, no. 11 (2002): 576–95. http://dx.doi.org/10.1002/cem.759.

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32

Aflalo, Yonathan, and Ron Kimmel. "Regularized principal component analysis." Chinese Annals of Mathematics, Series B 38, no. 1 (January 2017): 1–12. http://dx.doi.org/10.1007/s11401-016-1061-6.

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33

Gniazdowski, Zenon. "Principal Component Analysis versus Factor Analysis." Zeszyty Naukowe WWSI 15, no. 24 (August 18, 2021): 35——88. https://doi.org/10.26348/znwwsi.24.35.

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The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed. The problem of determining the number of principal components in PCA and factors in FA was discussed in detail. A new criterion for determining the number of factors and principal components is discussed, which will allow to present most of the variance of each of the analyzed primary variables. An efficient algorithm for determining the number of factors in FA, which complies with this criterion, was also proposed. This algorithm was adapted to find the number of principal components in PCA. It was also proposed to modify the PCA algorithm using a new method of determining the number of principal components. The obtained results were discussed.

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34

Hassani, Sahar, Harald Martens, El Mostafa Qannari, and Achim Kohler. "Degrees of freedom estimation in Principal Component Analysis and Consensus Principal Component Analysis." Chemometrics and Intelligent Laboratory Systems 118 (August 2012): 246–59. http://dx.doi.org/10.1016/j.chemolab.2012.05.015.

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35

Li, Zhaokai, Zihua Chai, Yuhang Guo, Wentao Ji, Mengqi Wang, Fazhan Shi, Ya Wang, Seth Lloyd, and Jiangfeng Du. "Resonant quantum principal component analysis." Science Advances 7, no. 34 (August 2021): eabg2589. http://dx.doi.org/10.1126/sciadv.abg2589.

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Principal component analysis (PCA) has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the principal components of it, i.e., the eigenvectors of the density matrix with the largest eigenvalues. However, because of the substantial resource requirement, its experimental implementation remains challenging. Here, we develop a resonant analysis algorithm with minimal resource for ancillary qubits, in which only one frequency-scanning probe qubit is required to extract the principal components. In the experiment, we demonstrate the distillation of the first principal component of a 4 × 4 density matrix, with an efficiency of 86.0% and a fidelity of 0.90. This work shows the speedup ability of quantum algorithm in dimension reduction of data and thus could be used as part of quantum artificial intelligence algorithms in the future.

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36

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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37

prakash, Mr S. Om, and Gokila S. "Principal Component Analysis - A Survey." IJARCCE 7, no. 8 (August 30, 2018): 63–66. http://dx.doi.org/10.17148/ijarcce.2018.7814.

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38

McLean, Robert A. "Immunization Using Principal Component Analysis." CFA Digest 27, no. 3 (August 1997): 32–33. http://dx.doi.org/10.2469/dig.v27.n3.112.

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39

Chun, Young-Jae, Kyoung-Su Oh, and Sung-Hyun Cho. "Photomosaics Using Principal Component Analysis." Journal of Korea Game Society 11, no. 1 (February 28, 2011): 139–46. http://dx.doi.org/10.7583/jkgs.2011.11.1.139.

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40

Adamu, Nuraddeen, Samaila Abdullahi, and Sani Musa. "Online Stochastic Principal Component Analysis." Caliphate Journal of Science and Technology 4, no. 1 (February 10, 2022): 101–8. http://dx.doi.org/10.4314/cajost.v4i1.13.

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This paper studied Principal Component Analysis (PCA) in an online. The problem is posed as a subspace optimization problem and solved using gradient based algorithms. One such algorithm is the Variance-Reduced PCA (VR-PCA). The VR-PCA was designed as an improvement to the classical online PCA algorithm known as the Oja’s method where it only handled one sample at a time. The paper developed Block VR-PCA as an improved version of VR-PCA. Unlike prominent VR-PCA, the Block VR-PCA was designed to handle more than one dimension in subspace optimization at a time and it showed good performance. The Block VR-PCA and Block Oja method were compared experimentally in MATLAB using synthetic and real data sets, their convergence results showed Block VR-PCA method appeared to achieve a minimum steady state error than Block Oja method. Keywords: Online Stochastic; Principal Component Analysis; Block Variance-Reduced; Block Oja

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41

Everitt, B. S., and P. M. Kroonenberg. "Three-Mode Principal Component Analysis." Biometrics 42, no. 1 (March 1986): 224. http://dx.doi.org/10.2307/2531268.

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42

Barber, Joel R., and Mark L. Copper. "Immunization Using Principal Component Analysis." Journal of Portfolio Management 23, no. 1 (October 31, 1996): 99–105. http://dx.doi.org/10.3905/jpm.1996.409574.

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43

TAKANE, Yoshio. "ON CONSTRAINED PRINCIPAL COMPONENT ANALYSIS." Kodo Keiryogaku (The Japanese Journal of Behaviormetrics) 19, no. 1 (1992): 29–39. http://dx.doi.org/10.2333/jbhmk.19.29.

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44

Gortler, Jochen, Thilo Spinner, Dirk Streeb, Daniel Weiskopf, and Oliver Deussen. "Uncertainty-Aware Principal Component Analysis." IEEE Transactions on Visualization and Computer Graphics 26, no. 1 (January 2020): 822–31. http://dx.doi.org/10.1109/tvcg.2019.2934812.

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45

Tharwat, Alaa. "Principal component analysis - a tutorial." International Journal of Applied Pattern Recognition 3, no. 3 (2016): 197. http://dx.doi.org/10.1504/ijapr.2016.079733.

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46

Tharwat, Alaa. "Principal component analysis - a tutorial." International Journal of Applied Pattern Recognition 3, no. 3 (2016): 197. http://dx.doi.org/10.1504/ijapr.2016.10000630.

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47

Vidal, R., Yi Ma, and S. Sastry. "Generalized principal component analysis (GPCA)." IEEE Transactions on Pattern Analysis and Machine Intelligence 27, no. 12 (December 2005): 1945–59. http://dx.doi.org/10.1109/tpami.2005.244.

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48

Shou, Haochang, Vadim Zipunnikov, Ciprian M. Crainiceanu, and Sonja Greven. "Structured functional principal component analysis." Biometrics 71, no. 1 (October 18, 2014): 247–57. http://dx.doi.org/10.1111/biom.12236.

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49

Lin, Zhenhua, Liangliang Wang, and Jiguo Cao. "Interpretable functional principal component analysis." Biometrics 72, no. 3 (December 18, 2015): 846–54. http://dx.doi.org/10.1111/biom.12457.

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50

Sang, Peijun, Liangliang Wang, and Jiguo Cao. "Parametric functional principal component analysis." Biometrics 73, no. 3 (March 10, 2017): 802–10. http://dx.doi.org/10.1111/biom.12641.

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