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Principal components analysis (PCA) is based conventially on the eigenvector decomposition (EVD). Mean-centering the input data prior to the eigenanalysis is treated as an integral part of the algorithm. It ensures that the first principal component is proportional to the maximum variance of the input data. Equivalent to EVD, but numerically more robust, is the singular value decomposition (SVD). Mean-centered data subjected to SVD, yield transformation coefficients identical to EVD. Nevertheless, mean-centering is optional in SVD. Avoiding to center the input data, results in generic first component that mainly reflects their mean. This may, however, detect more accurately distinct clusters in PCA-based change detection applications.

Remote sensing of burned areas via PCA, Part 1; centering, scaling and EVD vs SVD