Decomposition using Maximum Autocorrelation Factors

Rasmus Larsen

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 two-dimensional 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 R-mode analyse of the data
matrix. We propose to extend this concept to situations with variable
ordering. This corresponds to a Q-mode analysis of the data matrix. We denote
this methods Q-MAF decomposition.
It turns out that in many situations the new variables
resulting from the MAF and the Q-MAF 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).
Keywordsmaximum autocorrelation factors, shape, ordered variables,dered observations
TypeJournal paper [With referee]
JournalJournal of Chemometrics
Year2002    Vol. 16    No. 8-10    pp. 427-435
PublisherJohn Wiley & Sons