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 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). | | Keywords | maximum autocorrelation factors, shape, ordered variables,dered observations | | Type | Journal paper [With referee] | | Journal | Journal of Chemometrics | | Year | 2002 Vol. 16 No. 8-10 pp. 427-435 | | Publisher | John Wiley & Sons | | Address | Chichester, West Sussex, UK | | Electronic version(s) | [pdf] | | BibTeX data | [bibtex] | | IMM Group(s) | Image Analysis & Computer Graphics |
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