Maximum autocorrelation factors (MAF) and whitened principal components analysis are gaining popularity as tools for exploratory analysis of hyperspectral images. This paper shows that the two approaches are mathematically identical when signal and noise (clutter) are defined similarly. It also shows that the MAF metaphor can be generalized to encompass a wide variety of signal processing objectives referred to generically as maximum signal factors while retaining the interpretability of principal components analysis. A subspace projection approximation of the data prior to decomposition is also introduced, which reduces computational memory requirements. For the hyperspectral images studied, it was demonstrated to bring more signal of interest into the first factor as compared with the approach that did not use the subspace approximation. Also, it is expected to significantly reduce the number of scores images needed to be inspected during exploratory analysis. Copyright © 2014 John Wiley & Sons, Ltd.