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Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis AbstractIn 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.
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