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Principal Component Analysis versus Factor Analysis

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
Strony
35--88
Opis fizyczny
Bibliogr. 21 poz., tab., wykr.
Twórcy
  • Warsaw School of Computer Science
Bibliografia
  • [1] Z. Gniazdowski, “New Interpretation of Principal Components Analysis,” Zeszyty Naukowe WWSI, vol. 11, no. 16, pp. 43-65, 2017. [Online]. Available: https://www.doi.org/10.26348/znwwsi.16.43
  • [2] P. Francuz and R. Mackiewicz, Liczby nie wiedzą, skąd pochodzą. Przewodnik po metodologii i statystyce nie tylko dla psychologów. Lublin: Wydawnictwo KUL, 2007.
  • [3] Z. Gniazdowski, “Geometric interpretation of a correlation,” Zeszyty Naukowe WWSI, vol. 7, no. 9, pp. 27-35, 2013. [Online]. Available: https://www.doi.org/10.26348/znwwsi.9.27
  • [4] J. Legras, Praktyczne metody analizy numerycznej. Wydawnictwa Naukowo-Techniczne, 1974.
  • [5] D. T. Larose, Data mining methods & models. John Wiley & Sons, 2006.
  • [6] E. Mooi, M. Sarstedt, and I. Mooi-Reci, “Principal Component and Factor Analysis,” in Market Research: The Process, Data, and Methods Using Stata. Singapore: Springer Singapore, 2018, pp. 265-311. [Online]. Available: https://doi.org/10.1007/978-981-10-5218-7_8
  • [7] B. Thompson, Exploratory and confirmatory factor analysis: Understanding concepts and applications. Washington, DC: American Psychological Association, 2004.
  • [8] R. A. Fisher, “The use of multiple measurements in taxonomic problems,” Annals of eugenics, vol. 7, no. 2, pp. 179-188, 1936. [Online]. Available: https://doi.org/10.1111/j.1469-1809.1936.tb02137.x
  • [9] S. Ertel, Factor analysis-Healing an ailing model. Universitätsverlag Göttingen, 2013.
  • [10] C. F. Hofacker, Mathematical marketing. New South Network Services, 2007.
  • [11] A. Phakiti, “Exploratory factor analysis,” in The Palgrave handbook of applied linguistics research methodology. Springer, 2018, pp. 423-457.
  • [12] H. F. Kaiser, “The varimax criterion for analytic rotation in factor analysis,” Psychometrika, vol. 23, no. 3, pp. 187-200, 1958. [Online]. Available: https://doi.org/10.1007/BF02289233
  • [13] H. Abdi, “Factor rotations in factor analyses,” in Encyclopedia for Research Methods for the Social Sciences. Thousand Oaks, CA: Sage, 2003, pp. 792-795.
  • [14] M. Loève, “Elementary Probability Theory,” in Probability Theory I. New York, NY: Springer New York, 1977, pp. 1-52. [Online]. Available: https://doi.org/10.1007/978-1-4684-9464-8_1
  • [15] R. K. Pace and R. Barry, “Sparse spatial autoregressions,” Statistics & Probability Letters, vol. 33, no. 3, pp. 291-297, 1997. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S016771529600140X
  • [16] R. K. Pace and R. Barry, “Data from: Sparse spatial autoregressions,” 1999. [Online]. Available: http://lib.stat.cmu.edu/datasets/houses.zip
  • [17] Z. Gniazdowski and D. Kaliszewski, “On the clustering of correlated random variables,” Zeszyty Naukowe WWSI, vol. 12, no. 18, pp. 45-114, 2018. [Online]. Available: https://www.doi.org/10.26348/znwwsi.18.45
  • [18] J. W. Poelstra, N. Vijay, M. Hoeppner, and J. B. Wolf, “Transcriptomics of colour patterning and coloration shifts in crows,” Molecular ecology, vol. 24, no. 18, pp. 4617-4628, 2015.
  • [19] J. W. Poelstra, N. Vijay, M. P. Höppner, and J. B. W. Wolf, “Data from: Transcriptomics of colour patterning and colouration shifts in crows,” 2015. [Online]. Available: https://doi.org/10.5061/dryad.hv333
  • [20] J. Gerritsma, R. Onnink, and A. Versluis, “Yacht Hydrodynamics,” UCI Machine Learning Repository, 2013. [Online]. Available: https://archive.ics.uci.edu/ml/datasets/YachtHydrodynamics
  • [21] O. Akbilgic, “Istanbul Stock Exchange,” UCI Machine Learning Repository, 2013. [On-line]. Available: https://archive.ics.uci.edu/ml/datasets/ISTANBULSTOCKEXCHANGE
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d210093f-81b8-4c03-bb13-acca19358a1d
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