Decomposition of spectra using maximum autocorrelation factors

This paper addresses the problem of generating a low dimensional representation of the variation present in a set of spectra, e.g. reflection spectra recorded from a series of objects. The resulting low dimensional description may subseque ntly be input through variable selection schemes into classification or regression type analyses.

A featured method for low dimensional representation of multivariate datasets is Hotellings principal components transform. We will extend the use of principal components analysis incorporating new information into the algorithm. This new information consists of the fact that given a spectrum we have a natura ln order of the input \$\backslash\$underline{variables}.

This is similar to Switzers maximum au tocorrelation factors, where a natural order of \$\backslash\$underline{observations} (pixels) in multispectral images is utilized. However, in order to utilize an ordering of the input \$\backslash\$underline{variables} we need a non-trivial reformulation of the maximum autocorrelation problem in Q-mode.

We call the resulting transformation for Q-MAF. The resulting new variables can be interpreted as a frequency ecomposition of the spectra. But contrary to ordinary Fourier decomposition these new variables are located in frequency as well as well wavelength. The proposed algorithm is tested on 100 samples of NIR spectra of wheat.