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Kernel Methods for Pattern Analysis by Nello Cristianini, John Shawe-Taylor

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3

Properties of kernels

As we have seen in Chapter 2, the use of kernel functions provides a powerful and principled way of detecting nonlinear relations using well-understood linear algorithms in an appropriate feature space. The approach decouples the design of the algorithm from the specification of the feature space. This inherent modularity not only increases the flexibility of the approach, it also makes both the learning algorithms and the kernel design more amenable to formal analysis. Regardless of which pattern analysis algorithm is being used, the theoretical properties of a given kernel remain the same. It is the purpose of this chapter ...

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