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

Tonatiuh Peña-Centeno
Neil D. Lawrence, University of Sheffield

#### Abstract

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.

  @TechReport{pena-fbd-tech04, title = {Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis}, author = {Tonatiuh Peña-Centeno and Neil D. Lawrence}, year = {2004}, institution = {The University of Sheffield, Department of Computer Science}, number = {CS-04-13}, month = {00}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2004-01-01-pena-fbd-tech04.md}, url = {http://inverseprobability.com/publications/pena-fbd-tech04.html}, abstract = {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.}, key = {Pena:fbd-tech04}, linkpsgz = {ftp://ftp.dcs.shef.ac.uk/home/neil/bfdPaper.ps.gz}, linksoftware = {http://inverseprobability.com/bfd/}, group = {shefml} }
 %T Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis %A Tonatiuh Peña-Centeno and Neil D. Lawrence %B %D %F pena-fbd-tech04 %P -- %R %U http://inverseprobability.com/publications/pena-fbd-tech04.html %N CS-04-13 %X 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. 
 TY - CPAPER TI - Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis AU - Tonatiuh Peña-Centeno AU - Neil D. Lawrence PY - 2004/01/01 DA - 2004/01/01 ID - pena-fbd-tech04 SP - EP - UR - http://inverseprobability.com/publications/pena-fbd-tech04.html AB - 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. ER - 
 Peña-Centeno, T. & Lawrence, N.D.. (2004). Optimising Kernel Parameters and Regularisation Coefficients for Non-linear Discriminant Analysis.(CS-04-13):-