Decomposition using Maximum Autocorrelation Factors  Rasmus Larsen
 Abstract  This article presents methods for the analysis and decomposition of
multivariate datasets where a given ordering/structure of the observations or
the variables exist. Examples of such data sets are remote sensing imagery where
observations (pixels) each consisting of a reflectance spectrum are
organised in a twodimensional grid. Another example is biological shape
analysis.
Here each observation (e.g. human bone, cerebral ventricle) is
represented by a number of landmarks the coordinates of which are the
variables.
Here we do not have an ordering of the observations
(individuals).
However, normally we have an ordering of landmarks (variables)
along the contour of the objects.
For the case with observation ordering the maximum autocorrelation
factor (MAF) transform was proposed for multivariate imagery
in~\cite{switzer85}. This corresponds to a Rmode analyse of the data
matrix. We propose to extend this concept to situations with variable
ordering. This corresponds to a Qmode analysis of the data matrix. We denote
this methods QMAF decomposition.
It turns out that in many situations the new variables
resulting from the MAF and the QMAF analyses can be interpreted as a
decomposition of (spatial) frequency.
However, contrary to Fourier decomposition these
new variables are located in frequency as well as location (space,
time, wavelength etc).  Keywords  maximum autocorrelation factors, shape, ordered variables,dered observations  Type  Journal paper [With referee]  Journal  Journal of Chemometrics  Year  2002 Vol. 16 No. 810 pp. 427435  Publisher  John Wiley & Sons  Address  Chichester, West Sussex, UK  Electronic version(s)  [pdf]  BibTeX data  [bibtex]  IMM Group(s)  Image Analysis & Computer Graphics 
