Decomposition of spectra using maximum autocorrelation factors  Rasmus Larsen
 Abstract  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 \underline{variables}. This is similar to Switzers maximum au
tocorrelation factors, where a natural order of \underline{observations} (pixels) in multispectral images is utilized. However, in order to utilize an ordering of the input \underline{variables} we need a nontrivial reformulation of the maximum autocorrelation problem in Qmode. We call the resulting transformation for QMAF. 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.  Keywords  maximum autocorrelation factors, chemometrics, shape analysis  Type  Conference paper [With referee]  Conference  7th Scandinavian Symposium on Chemometrics, 1923 August, Copenhagen , Denmark  Editors   Year  2001  Electronic version(s)  [pdf]  BibTeX data  [bibtex]  IMM Group(s)  Image Analysis & Computer Graphics 
