  We propose a Bayesian framework of Gaussian process in order to extend
Fisher's discriminant to classify functional data such as spectra and images.
The probability structure for our extended Fisher's discriminant is explicitly
formulated, and we utilize the smoothness assumptions of functional data as
prior probabilities. Existing methods which directly employ the smoothness
assumption of functional data can be shown as special cases within this
framework given corresponding priors while their estimates of the unknowns are
one-step approximations to the proposed MAP estimates. Empirical results on
various simulation studies and different real applications show that the
proposed method significantly outperforms the other Fisher's discriminant
methods for functional data.
