E-cient Leave-One-Out Cross-Validationof KernelFisherDiscriminant Classiflers
Gavin C. Cawley, Nicola L. C. Talbot · 2005
Mika et al. [1] apply the \kernel trick to obtain a non-linear variant of Fisher’s linear discriminant analysis method, demonstrating state-of-the-art performance on a range of benchmark datasets. We show that leave-one-out cross-validation of kernel Fisher discriminant classiflers can be implemented with a computational complexity of only O(‘ 3 ) operations rather than the O(‘ 4 ) of a na˜‡ve implementation, where ‘ is the number of training patterns. Leave-one-out cross-validation then becomes an attractive means of model selection in large-scale applications of kernel Fisher discriminant analysis, being signiflcantly faster than conventional k-fold cross-validation procedures commonly used.