io.github.mandar2812.dynaml.kernels
MahalanobisKernel
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package kernels
Returns the kernel multiplied by a positive constant: k_new = k*c
Returns the kernel multiplied by a positive constant: k_new = k*c
Create composite kernel k = k1 * k2
Create composite kernel k = k1 * k2
The kernel to multiply to the current one.
The kernel k defined above.
Create composite kernel k = k1 + k2
Create composite kernel k = k1 + k2
param otherKernel The kernel to add to the current one. return The kernel k defined above.
Construct the kronecker product kernel
Construct the kronecker product kernel
Construct a 2 layer kernel K = k1 > rbf
Construct a 2 layer kernel K = k1 > rbf
Get a pipeline which when given a particular configuration of hyper-parameters returns this kernel function set with that configuration.
Get a pipeline which when given a particular configuration of hyper-parameters returns this kernel function set with that configuration.
Builds an approximate nonlinear feature map which corresponds to an SVM Kernel.
Builds an approximate nonlinear feature map which corresponds to an SVM Kernel. This is done using the Nystrom method i.e. approximating the eigenvalues and eigenvectors of the Kernel matrix of some data set.
For each data point, calculate m dimensions of the feature map where m is the number of eigenvalues/vectors obtained from the Eigen Decomposition.
phi_i(x) = (1/sqrt(eigenvalue(i)))*Sum(k, 1, m, K(k, x)*eigenvector(i)(k))
The Eigenvalue decomposition calculated from the kernel matrix of the prototype subset.
The prototype subset.
The dataset on which the feature map is to be applied.
Mahalanobis kernel is an anisotropic generalization of the RBF Kernel, its definition is based on the so called Mahalanobis distance between two vectors x and y.
K(x,y) = h*exp(-(x - y)T . M . (x - y))
In this implementation the symmetric positive semi-definite matrix M is assumed to be diagonal.