April 2013
Intermediate to advanced
1164 pages
39h 37m
English
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13.3 Relationship Between FVC-FLSMA and LCMV, TCIMF, and CEM
Recalling the LCMV in Chang (2002b) and Chang (2003a), its weighting matrix (11.16) in Chang (2003a) or (6) in Chang (2002b) is given by
where the matrix C is the constraint matrix and R is the data correlation matrix.
Now, let I be the 
identity matrix and express it as
where 1l is the lth p-dimensional unit vector specified by 
. By means of (13.20), we can rewrite (13.17) as
Comparing (13.21) to the LCMV-generated weighting matrix specified by (13.19), an immediate finding is that the FVC-FLSMA-generated weighting matrix given by (13.21) has the same form as does (13.19) with the within-class scatter matrix SW and I in the FVC-FLSMA corresponding to R and the constraint matrix C in the LCMV, respectively, where the constraint matrix I used in (13.21) is exactly the same p constraints 
used in (13.8)
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