2002
Royal Statistical Society Conference, University of Plymouth, 2-6 September

Keynote
paper in session on “Future perspectives in statistical image analysis”

**Spatio-temporal analysis including
multi-objective orthogonalisation and independent component analysis**

Allan
Aasbjerg Nielsen

Technical University of
Denmark

Richard Petersens Plads,
Building 321

DK-2800
Kongens Lyngby, Denmark

aa@imm.dtu.dk, http://www.imm.dtu.dk/~aa/

The
talk will deal with a number of methods for (*orthogonal) transformation of multivariate data including*

* *

*principal components,**principal factors,**(multi-set) canonical variates,**maximum autocorrelation factors,**minimum noise fractions,**projection pursuit, and**independent components.*

* *

All
these methods are useful in exploratory multivariate data analysis where we
consider the observed data as indirect measurements of underlying, latent
structures or factors that cannot be observed directly. Some of the methods are specifically suited
for data that vary spatially or temporally and some can be tailored to perform
multi-objective orthogonalisation of for instance both spatial and temporal
autocorrelation in spatio-temporal data.
Recently, independent component analysis (ICA) has emerged. ICA can be seen as an interesting extension
to principal component analysis (PCA) specifically suited for non-Gaussian
latent factors. Similarities and
differences between more classical methods such as PCA and ICA will be
described. Application examples of the
transformations will be given. The data
used in the examples include

- global sea surface temperatures from
satellite,
- spectral data from air- and space-borne
optical scanners, and
- image data from scanning electron
microscope energy dispersive spectroscopy also known as x-ray mapping.

Also,
examples on application of some of the methods mentioned to change detection in
bi-temporal, multivariate data will be given.
Finally, non-linear extensions to some of the methods will be described
very briefly.