Bayesian Fisher's Discriminant for Functional Data
This work addresses classification challenges for functional data in fields like spectroscopy and imaging, but it is incremental as it builds upon existing Fisher's discriminant methods.
The authors tackled the problem of classifying functional data like spectra and images by proposing a Bayesian Gaussian process framework to extend Fisher's discriminant, resulting in a method that significantly outperforms other Fisher's discriminant approaches in simulations and real applications.
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.