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

Abstract

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. In remote sensing, PCA transforms multi-spectral bands into a new coordinate system. The first, among the transformed components, contain the variance of unchanged landscape features. Succeeding components may contain an enhanced variance of changed features. Such is the case of burned surfaces appearing as distinct clusters in multitemporal composites. Within this framework, a non-centered SVD may increase the spectral separability of burned clusters among other features in some of the higher order principal components.