Package smile.math.kernel
package smile.math.kernel
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 non-negative.
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ClassDescriptionGaussian kernel, also referred as RBF kernel or squared exponential kernel.The hyperbolic tangent kernel on binary sparse data.Laplacian kernel, also referred as exponential kernel.The linear dot product kernel on sparse binary arrays in
int[], which are the indices of nonzero elements.The class of Matérn kernels is a generalization of the Gaussian/RBF.The polynomial kernel on binary sparse data.The Thin Plate Spline kernel on binary sparse data.Dot product kernel depends only on the dot product of x and y.Gaussian kernel, also referred as RBF kernel or squared exponential kernel.Gaussian kernel, also referred as RBF kernel or squared exponential kernel.The Hellinger kernel.The hyperbolic tangent kernel.The hyperbolic tangent kernel.Isotropic kernel.Laplacian kernel, also referred as exponential kernel.Laplacian kernel, also referred as exponential kernel.The linear dot product kernel.The class of Matérn kernels is a generalization of the Gaussian/RBF.The class of Matérn kernels is a generalization of the Gaussian/RBF.MercerKernel<T>Mercer kernel, also called covariance function in Gaussian process.Pearson VII universal kernel.The polynomial kernel.The polynomial kernel.The product kernel takes two kernels and combines them via k1(x, y) * k2(x, y).Gaussian kernel, also referred as RBF kernel or squared exponential kernel.The hyperbolic tangent kernel on sparse data.Laplacian kernel, also referred as exponential kernel.The linear dot product kernel on sparse arrays.The class of Matérn kernels is a generalization of the Gaussian/RBF.The polynomial kernel on sparse data.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)The Thin Plate Spline kernel.The Thin Plate Spline kernel.