Evolutionary Kernel Learning

In kernel-based learning algorithms the kernel function determines the scalar product and thereby the metric in the feature space in which the learning algorithm operates. The kernel is usually not adapted by the kernel method itself. Choosing the right kernel function is crucial for the training accuracy and generalization capabilities of the learning machine. It may also influence the runtime and storage complexity during learning and application. Finding an appropriate kernel is a model selection problem. The kernel function is selected from an a priori fixed class. When a parameterized family of kernel functions is considered, kernel adaptation reduces to finding an appropriate parameter vector. In practice, the most frequently used method to determine these values is grid search. In simple grid search the parameters are varied independently with a fixed step-size through a range of values and the performance of every combination is measured. Because of its computational complexity, grid search is only suitable for the adjustment of a few parameters. Further, the choice of the discretization of the search space may be crucial. Gradient-based approaches are perhaps the most elaborate techniques for adapting real-valued kernel parameters, see [1, 2] and references therein. To use these methods, however, the class of kernel functions must have a differentiable structure. They are also not directly applicable if the score function for assessing the parameter performance is not differentiable. This excludes some reasonable performance measures. Evolutionary kernel learning does not suffer from these limitations. Additionally it allows for