Kernel trick

In the field of machine learning is a class of algorithms has been developed in recent years that a kernel ( dt core ) make use of to their calculations implicitly perform in a higher-dimensional space. Known algorithms that work with kernels, the support vector machines and kernel PCA.

One speaks in this context by the kernel trick, because applying a linear classifier on non linearklassifizierbare data using this method. This is achieved by transforming the data into a higher dimensional space in which it is hoped that a better linear separability.

Formal definition

Be an input space. A mapping is called kernel if there is a scalar product and a picture in this space with. called feature space or feature space mapping feature or feature map. In practice, the feature space need not be known explicitly because kernel have a simple characterization of the set of Mercer.

Several classes of kernel functions

There are different types of kernels, which can be customized via parameters to the given problem in part:

• Linear kernel
• Polynomial kernel
• RBF kernel

Meanwhile kernel on graphs and strings are defined.