Ordinary Meeting Organized by the Research Section
Invariant co-ordinate selection
by David E. Tyler (Rutgers University)
Frank Critchley (The Open University),
Lutz Duembgen (University of Berne) and
Hannu Oja (University of Tampere)
Wednesday 17 December 2008, 5pm
RSS Headquarters, 12 Errol Street, London
The paper can be downloaded in advance from:
http://www.rss.org.uk/main.asp?page=1836
Fellows and visitors are invited to make contributions of no
longer than 5 minutes following the reading of the paper. Please
register your interest with the Secretary of the RSS Research
Section Committee ([log in to unmask]) or C. Stovell at
the RSS ([log in to unmask]).
Tea is served at 4:30pm.
For more information, contact Charlotte Stovell at the RSS.
([log in to unmask]).
Summary
A general method for exploring multivariate data by comparing
different estimates of multivariate scatter is presented.
The method is based on the eigenvalue-eigenvector decomposition
of one scatter matrix relative to another. In particular,
it is shown that the eigenvectors can be used to generate an
affine invariant co-ordinate system for the multivariate data.
Consequently, we view this method as a method for invariant
co-ordinate selection. By plotting the data with respect to
this new invariant co-ordinate system, various data structures
can be revealed. For example, under certain independent
components models, it is shown that the invariant co-ordinates
correspond to the independent components. Another example
pertains to mixtures of elliptical distributions. In this case,
it is shown that a subset of the invariant co-ordinates
corresponds to Fisher's linear discriminant subspace, even
though the class identifications of the data points are unknown.
Some illustrative examples are given.
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