Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis
Tonatiuh Pena-Centeno and Neil Lawrence
University of Sheffield, Sheffield, U.K..
In this paper we consider a Bayesian interpretation of Fisher's discriminant. By relating Rayleigh's
coefficient to a likelihood function and through the
choice of a suitable prior we use Bayes' rule to
infer a posterior distribution over
projections. Through the use of a Gaussian process
prior we show the equivalence of our model to a
regularised kernel Fisher's discriminant. A key
advantage of our approach is the facility to
determine kernel parameters and the regularisation
coefficient through optimisation of the marginalised
likelihood of the data.