Abstract
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Model selection in kernel linear discriminant analysis
(KLDA) refers to the selection of appropriate parameters of a
kernel function and the regularizer. By following the principle
of maximum information preservation, this paper formulates the
model selection problem as a problem of selecting an optimal
kernel-induced space in which different classes are maximally
separated from each other. A scatter-matrix-based criterion is developed
to measure the “goodness” of a kernel-induced space, and
the kernel parameters are tuned by maximizing this criterion. This
criterion is computationally efficient and is differentiable with respect
to the kernel parameters. Compared with the leave-one-out
(LOO) or -fold cross validation (CV), the proposed approach
can achieve a faster model selection, especially when the number
of training samples is large or when many kernel parameters
need to be tuned. To tune the regularization parameter in the
KLDA, our criterion is used together with the method proposed
by Saadi et al. (2004). Experiments on benchmark data sets verify
the effectiveness of this model selection approach.