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CATEGORIES:Statistics
SUMMARY:Invariant Coordinate Selection revisited: Fisher
Symmetry and Symmetric Component Analysis - Frank
Critchley\, Open University
DTSTART;TZID=Europe/London:20140228T160000
DTEND;TZID=Europe/London:20140228T170000
UID:TALK50326AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/50326
DESCRIPTION:Tyler et al. (2009) introduced invariant coordinat
e selection\, or ICS\, as a general method for exp
loring affine invariant features of multivariate d
ata by comparing different estimates of multivaria
te scatter. Together with Critchley et al. (2006)\
, they report examples of the method performing we
ll for a wide range of problems\, extending beyond
the limits of existing theoretical support. Motiv
ated by this\, we provide complementary ICS theory
based on the relevant symmetry group. A _Fisher s
ymmetry_ condition is introduced for which ellipti
cal symmetry is not required\, yet under which a s
ubset of the invariant coordinates is shown to cor
respond to Fisherâ€™s linear discriminant subspace\,
class identifications of data points remaining un
known. Again\, a _Symmetric Component Analysis_ mo
del is introduced in which independence is not req
uired\, yet under which the invariant coordinates
are seen to correspond to the symmetric components
. Illustrative examples are given. Further develop
ments are briefly indicated.
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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