Package smile.math.kernel

Mercer kernels.

See: Description

Interface Summary

Interface	Description
KernelMatrix	A kernel matrix of dataset is the array of k(xi, xj).
MercerKernel<T>	A Mercer Kernel is a kernel that is positive semi-definite.

Class Summary

Class	Description
BinarySparseGaussianKernel	The Gaussian Mercer Kernel.
BinarySparseHyperbolicTangentKernel	The hyperbolic tangent kernel.
BinarySparseLaplacianKernel	The Laplacian Kernel.
BinarySparseLinearKernel	The linear dot product kernel on sparse binary arrays in int[], which are the indices of nonzero elements.
BinarySparsePolynomialKernel	The polynomial kernel.
BinarySparseThinPlateSplineKernel	The Thin Plate Spline Kernel.
GaussianKernel	The Gaussian Mercer Kernel.
HellingerKernel	The Hellinger Mercer Kernel.
HyperbolicTangentKernel	The hyperbolic tangent kernel.
LaplacianKernel	The Laplacian Kernel.
LinearKernel	The linear dot product kernel.
PearsonKernel	The Pearson Mercer Kernel.
PolynomialKernel	The polynomial kernel.
SparseGaussianKernel	The Gaussian Mercer Kernel.
SparseHyperbolicTangentKernel	The hyperbolic tangent kernel.
SparseLaplacianKernel	The Laplacian Kernel.
SparseLinearKernel	The linear dot product kernel on sparse arrays.
SparsePolynomialKernel	The polynomial kernel.
SparseThinPlateSplineKernel	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.