smile.math.kernel

Interface MercerKernel<T>

All Known Implementing Classes:

BinarySparseGaussianKernel, BinarySparseHyperbolicTangentKernel, BinarySparseLaplacianKernel, BinarySparseLinearKernel, BinarySparsePolynomialKernel, BinarySparseThinPlateSplineKernel, GaussianKernel, HellingerKernel, HyperbolicTangentKernel, LaplacianKernel, LinearKernel, PearsonKernel, PolynomialKernel, SparseGaussianKernel, SparseHyperbolicTangentKernel, SparseLaplacianKernel, SparseLinearKernel, SparsePolynomialKernel, SparseThinPlateSplineKernel, ThinPlateSplineKernel

public interface MercerKernel<T>

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.

Method Summary

Modifier and Type	Method and Description
double	k(T x, T y) Kernel function.

Method Detail

k

double k(T x,
         T y)

Kernel function.