13.4 Relationship Between FVC-FLSMA and OSP

If we replace in (13.12) with defined in (2.86), then the resulting weight vector becomes the least squares OSP (LSOSP) in Tu et al. (1997) and Chang (2003a):

(13.23)

With this interpretation, FVC-FLSMA can be considered as a discriminant analysis version of OSP. Additionally, is also idempotent. We can define a linear transformation by and where r is an image pixel vector. The resulting image with pixel vectors described by is called the -whitened hyperspectral image. Let be the -whitened lth class mean defined by . Equation (13.23) is reduced to

(13.24)

where and for . If we further let , (13.24) is reduced to , which is exactly the same matched filter used by LSOSP with the matched signature specified by the desired signature .