Package smile.math.kernel

Mercer kernels.

See: Description

Interface Summary

Interface	Description
DotProductKernel	Dot product kernel depends only on the dot product of x and y.
IsotropicKernel	Isotropic kernel.
MercerKernel<T>	Mercer kernel, also called covariance function in Gaussian process.

Class Summary

Class	Description
BinarySparseGaussianKernel	Gaussian kernel, also referred as RBF kernel or squared exponential kernel.
BinarySparseHyperbolicTangentKernel	The hyperbolic tangent kernel on binary sparse data.
BinarySparseLaplacianKernel	Laplacian kernel, also referred as exponential kernel.
BinarySparseLinearKernel	The linear dot product kernel on sparse binary arrays in int[], which are the indices of nonzero elements.
BinarySparseMaternKernel	The class of Matérn kernels is a generalization of the Gaussian/RBF.
BinarySparsePolynomialKernel	The polynomial kernel on binary sparse data.
BinarySparseThinPlateSplineKernel	The Thin Plate Spline kernel on binary sparse data.
Gaussian	Gaussian kernel, also referred as RBF kernel or squared exponential kernel.
GaussianKernel	Gaussian kernel, also referred as RBF kernel or squared exponential kernel.
HellingerKernel	The Hellinger kernel.
HyperbolicTangent	The hyperbolic tangent kernel.
HyperbolicTangentKernel	The hyperbolic tangent kernel.
Laplacian	Laplacian kernel, also referred as exponential kernel.
LaplacianKernel	Laplacian kernel, also referred as exponential kernel.
LinearKernel	The linear dot product kernel.
Matern	The class of Matérn kernels is a generalization of the Gaussian/RBF.
MaternKernel	The class of Matérn kernels is a generalization of the Gaussian/RBF.
PearsonKernel	Pearson VII universal kernel.
Polynomial	The polynomial kernel.
PolynomialKernel	The polynomial kernel.
ProductKernel<T>	The product kernel takes two kernels and combines them via k1(x, y) * k2(x, y).
SparseGaussianKernel	Gaussian kernel, also referred as RBF kernel or squared exponential kernel.
SparseHyperbolicTangentKernel	The hyperbolic tangent kernel on sparse data.
SparseLaplacianKernel	Laplacian kernel, also referred as exponential kernel.
SparseLinearKernel	The linear dot product kernel on sparse arrays.
SparseMaternKernel	The class of Matérn kernels is a generalization of the Gaussian/RBF.
SparsePolynomialKernel	The polynomial kernel on sparse data.
SparseThinPlateSplineKernel	The Thin Plate Spline kernel on sparse data.
SumKernel<T>	The sum kernel takes two kernels and combines them via k1(x, y) + k2(x, y)
ThinPlateSpline	The Thin Plate Spline kernel.
ThinPlateSplineKernel	The Thin Plate Spline kernel.

Package smile.math.kernel Description

Mercer kernels. 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.