Package smile.math.kernel
Interface MercerKernel<T>
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- All Superinterfaces:
java.io.Serializable
- All Known Implementing Classes:
GaussianKernel
public interface MercerKernel<T> extends java.io.Serializable
A Mercer Kernel is a kernel that is positive semi-definite. When a kernel is positive semi-definite, one may exploit the kernel trick, the idea of implicitly mapping data to a high-dimensional feature space where some linear algorithm is applied that works exclusively with inner products. Assume we have some mapping Φ from an input space X to a feature space H, then a kernel k(u, v) = <Φ(u), Φ(v)> may be used to define the inner product in feature space H.Positive definiteness in the context of kernel functions also implies that a kernel matrix created using a particular kernel is positive semi-definite. A matrix is positive semi-definite if its associated eigenvalues are nonnegative.
- Author:
- Haifeng Li
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description double
k(T x, T y)
Kernel function.
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