Principal component transform — Outer product analysis in the PCA context

Outer product analysis is a method that permits the combination of two spectral domains with the aim of emphasizing co-evolutions of spectral regions. This data fusion technique consists in the product of all combinations of the variables that define each spectral domain. The main issue concerning the application of this technique is the very wide data matrix obtained which can be very hard to handle with multivariate techniques such as PCA or PLS, due to computer resources constraints. The present work presents an alternative way to perform outer product analysis in the PCA context without incurring into high demands on computational resources. This works shows that by decomposing each spectral domain with PCA and performing the outer product on the recovered scores, one can obtain the same results as if one calculated the outer product in the original variable space, but using much less computational resources. The results show that this approach will make possible to apply outer product analysis to very wide domains.