Principal component analysis (PCA) allows us to summarize a set of variables with a smaller number of representative features that collectively explain most of the variability in the original data set. PCA projects the observations described by \(n\) variables into orthogonal, and thus by definition uncorrelated, features/variables. The new set of synthetic variables is equal in number to the original set. However, the first synthetic variable represents as much of the common variation of the original variables as possible, the second variable represents as much of the residual variation as possible, and so forth.

PCA is particularly powerful in dealing with multicollinearity and observations that outnumber the variables \((m>n)\), and it is widely used for explanatory data analysis, outlier detection and as a data pre-processing technique for predictive modelling. The figure below outlines the analysis workflow.

PCA workflow

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Citation

The E-Learning project SOGA-R was developed at the Department of Earth Sciences by Kai Hartmann, Joachim Krois and Annette Rudolph. You can reach us via mail by soga[at]zedat.fu-berlin.de.

You may use this project freely under the Creative Commons Attribution-ShareAlike 4.0 International License.

Please cite as follow: Hartmann, K., Krois, J., Rudolph, A. (2023): Statistics and Geodata Analysis using R (SOGA-R). Department of Earth Sciences, Freie Universitaet Berlin.