correctionKernelMatrix: Correction of a Kernel (Correlation) Matrix

Description

Convert a non-PSD kernel matrix with chosen approach so that it becomes a PSD matrix. Optionally, the resulting matrix is enforced to have values between -1 and 1 and a diagonal of 1s, with the repair parameter. That means, it is (optionally) converted to a valid correlation matrix. Essentially, this is a combination of correctionDefinite with repairConditionsCorrelationMatrix.

Usage

correctionKernelMatrix(mat, method = "flip", repair = TRUE, tol = 1e-08)

Value

list with corrected kernel matrix mat, isPSD (boolean, whether original matrix was PSD), transformation matrix A, the matrix of eigenvectors (U) and the transformation vector (a)

Arguments

mat: symmetric kernel matrix
method: string that specifies method for correction: spectrum clip "clip", spectrum flip "flip", nearest definite matrix "near", spectrum square"square", spectrum diffusion "diffusion".
repair: boolean, whether or not to use condition repair, so that elements between -1 and 1, and the diagonal values are 1.
tol: torelance value. Eigenvalues between -tol and tol are assumed to be zero.

References

Martin Zaefferer and Thomas Bartz-Beielstein. (2016). Efficient Global Optimization with Indefinite Kernels. Parallel Problem Solving from Nature-PPSN XIV. Accepted, in press. Springer.

Examples

Run this code

x <- list(c(2,1,4,3),c(2,4,3,1),c(4,2,1,3),c(4,3,2,1),c(1,4,3,2))
D <- distanceMatrix(x,distancePermutationInsert)
K <- exp(-0.01*D)
is.PSD(K) #matrix should not be PSD
K <- correctionKernelMatrix(K)$mat
is.PSD(K) #matrix should now be CNSD
K