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SUMMARY:Invariant Coordinate Selection revisited:  Fisher Symmetry and Sym
 metric Component Analysis - Frank Critchley\, Open University
DTSTART:20140228T160000Z
DTEND:20140228T170000Z
UID:TALK50326@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Tyler et al. (2009) introduced invariant coordinate selection\
 , or ICS\, as a general method for exploring affine invariant features of 
 multivariate data by comparing different estimates of multivariate scatter
 . Together with Critchley et al. (2006)\, they report examples of the meth
 od performing well for a wide range of problems\, extending beyond the lim
 its of existing theoretical support. Motivated by this\, we provide comple
 mentary ICS theory based on the relevant symmetry group. A _Fisher symmetr
 y_ condition is introduced for which elliptical symmetry is not required\,
  yet under which a subset of the invariant coordinates is shown to corresp
 ond to Fisher’s linear discriminant subspace\, class identifications of 
 data points remaining unknown. Again\, a _Symmetric Component Analysis_ mo
 del is introduced in which independence is not required\, yet under which 
 the invariant coordinates are seen to correspond to the symmetric componen
 ts. Illustrative examples are given. Further developments are briefly indi
 cated.
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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