Wojtek J. Krzanowski
University of Exeter
Multivariate measurements are often made in either a spatial or a temporal context.
Examples of the former occur in environmental reconnaissance programs that are
carried out in many countries, where measurements are taken on a large set of
different chemical elements at various locations throughout the study area.
An example of the latter occurs in industrial process control, where a range
of output measures is monitored on a regular basis, such as daily or weekly,
across a period of time.
Principal component analysis (PCA) is often used on such data sets to identify
important combinations of the original variables, either as a focus for more
detailed study or to explain any significant outcomes shown up by omnibus tests.
However, while PCA and related projection techniques from the standard multivariate
repertoire are optimal under independence of observations and random sampling,
they are not explicitly designed to address or to exploit the strong
auto-correlation and cross-correlation structures that are often present
in multivariate spatial or temporal data. Consequently their use may produce
In this talk, several alternative projection techniques that are tailored to
multivariate spatial and temporal data will be introduced and described.
Like PCA these methods linearly transform the original variables into
uncorrelated components, but instead of maximising variance these components
are designed to have particular spatial or temporal properties. They can thus
be viewed as optimal components to use in a spatial or temporal setting.
The technical derivation of the methods will be presented, their general
performances and properties will be demonstrated via simulation results,
and their specific applications will be illustrated on several real data sets.
The advantages of the new methods over the more traditional ones such as PCA
will be highlighted in these examples.