Initial Dataset Dimension Reduction Using Principal Component Analysis

Oļegs Užga-Rebrovs, Gaļina Kuļešova

Abstract


Any data in an implicit form contain information of interest to the researcher. The purpose of data analysis is to extract this information. The original data may contain redundant elements and noise, distorting these data to one degree or another. Therefore, it seems necessary to subject the data to preliminary processing. Reducing the dimension of the initial data makes it possible to remove interfering factors and present the data in a form suitable for further analysis. The paper considers an approach to reducing the dimensionality of the original data based on principal component analysis.

Keywords:
Data labels in the space of principal components; data recovery in a space of lower dimension; data transformation into a space of principal components; eigenvectors and eigenvalues of variance/covariance matrix; variance/covariance matrix of data

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References


J. De Mast and B. P. H. Kemper, “Principles of Exploratory Data Analysis in Problem Solving: What Can We Learn from a Well-Known Case?” Quality Engineering, vol. 21, no. 4, pp. 366–375, 2009. https://doi.org/10.1080/08982110903188276

J. W. Tukay, “Analysing data: Sanctification or defective work?” American Psychologist, vol. 24, no. 2, pp. 83–91, 1969. https://doi.org/10.1037/h0027108

J. W. Tukay, Exploratory data analysis. MA: Addison-Wesley, 1977.

J. W. Tukay, “We Need both Exploratory and Confirmatory”, The American Statistician, vol. 34, no. 1, pp. 23–25, 1980. https://doi.org/10.1080/00031305.1980.10482706

J. W. Tukay, “The future of data analysis”, The Annals of Mathematical Statistics, vol. 3, no. 1, pp. 1–67, 1962. https://doi.org/10.1214/aoms/1177704711

H. Y. Cheng, “Exploratory data analysis in the context of data mining and resampling”, Int. Journal of Psychological Research, vol. 3, no. 1, pp. 9–22, 2010. https://doi.org/10.21500/20112084.819

J. T. Behrens, “Principles and procedures of exploratory data analysis”, Psychological Methods, vol. 2, no. 2, pp. 131–160, 1997. https://doi.org/10.1037/1082-989X.2.2.131

H. Y. Cheng “Abduction? Deduction? Induction? Is There Logic of Exploratory Data Analysis?” Annual Meeting of the American Educational Research Association, New Orleans, LA, April 4–8, 28 p., 1991.

B. D. Haig, “An abductive theory of scientific method”, Psychological Methods, vol. 10, no. 4, pp. 371–388, 2005. https://doi.org/10.1037/1082-989X.10.4.371

I. T. Jolliffe, Principal Component Analysis (Second Edition). Springer-Verlag, New York, Berlin Heidelberg, 2002.

J. D. Jackson, A User’s Guide to Principal Component Analysis. John Willey & Sons, Inc., 1991.

L. Ch. Paul, A. Suman and N. Sultan, “Methodological Analysis of Principal Component Analysis (PCA) Method”, Int. Journal of Computational Engineering & Management, vol. 16, issue 2, pp. 32–38, 2013.

P. R. Peres-Neto, D. A. Jackson and K. M. Somers, “How many principal components? stopping rules for determining the numbers of non-trivial axes revisited”, Computational Statistics & Data Analysis, vol. 49, no. 4, pp. 974–997, 2005. https://doi.org/10.1016/j.csda.2004.06.015




DOI: 10.7250/itms-2020-0006

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