eigen2hat: Calculate the hat matrix from an eigen decomposition
In xnet: Two-Step Kernel Ridge Regression for Network Predictions

Description Usage Arguments Details Value

These functions calculate either the hat matrix, the mapping matrix or the original (kernel) matrix for a two-step kernel ridge regression, based on the eigendecomposition of the kernel matrix.

eigen2hat(eigen, val, lambda)

eigen2map(eigen, val, lambda)

eigen2matrix(eigen, val)

`eigen`	a matrix with the eigenvectors.
`val`	an numeric vector with the eigenvalues.
`lambda`	a single numeric value for the hyperparameter lambda

For the hat matrix, this boils down to:

UΣ(Σ + λ I)^{-1} U^{T}

For the map matrix, this is :

U(Σ + λ I)^{-1} U^{T}

with U the matrix with eigenvectors, Σ a diagonal matrix with the eigenvalues on the diagonal, I the identity matrix and λ the hyperparameter linked to this kernel. The internal calculation is optimized to avoid having to invert a matrix. This is done using the fact that Σ is a diagonal matrix.

a numeric matrix representing either the hat matrix (eigen2hat), the map matrix (eigen2map) or the original matrix (eigen2matrix)

xnet documentation built on Feb. 4, 2020, 9:10 a.m.