Random projections in reducing the dimensionality of climate simulation data

Random projection (RP) is a dimensionality reduction method that has been earlier applied to high-dimensional data sets, for instance, in image processing. This study presents experimental results of RP applied to simulated global surface temperature data. Principal component analysis (PCA) is utilised to analyse how RP preserves structures when the original data set is compressed down to 10% or 1% of its original volume. Our experiments show that, although information is naturally lost in RP, the main spatial patterns (the principal component loadings) and temporal signatures (spectra of the principal component scores) can nevertheless be recovered from the randomly projected low-dimensional subspaces. Our results imply that RP could be used as a pre-processing step before analysing the structure of high-dimensional climate data sets having many state variables, time steps and spatial locations.