Global Environmental Risk

By Jeanne X. Kasperson; Roger Kasperson | Go to book overview

Appendix E:
Principal-component
analysis

A brief introduction to principal-component analysis 1
Principal-component analysis (PCA) is a method for expressing multidimensional data as new variables that are mutually uncorrelated, linear combinations of the original variables. These new variables are called principal components (PCs). The specific aims of performing PCA on data are as follows:
1. Reducing dimensionality. If some variables are correlated, then the effective dimensionality may be decreased by expressing their information content in their PCs. If the first few PCs account for most of the variation in the original data, then the rest of the PCs may be neglected, reducing the effective dimensionality of the problem.
2. Arranging variables into meaningful groups. It may be possible to interpret or assign meaning to the set of variables contributing significantly to the more important PCs. The PCs may also be rotated to maximize the difference in loadings between variables. Rotation modifies the PCs without altering their underlying structure, to allow easier determination of the significant variables in each PC and better interpretation.
3. Discarding redundant variables. Some variables may be redundant and may therefore be discarded. PCA gives a method for systematically identifying variables with the least contribution to the overall variability in the data.

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