correctionKernelMatrix: Correction of a Kernel (Correlation) Matrix

In CEGO: Combinatorial Efficient Global Optimization

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)

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.

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)

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.

See Also

correctionDefinite, repairConditionsCorrelationMatrix

Examples

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

Example output

[1] FALSE
[1] TRUE
          [,1]      [,2]      [,3]      [,4]      [,5]
[1,] 1.0000000 0.9955780 0.9955780 0.9933607 0.9955780
[2,] 0.9955780 1.0000000 0.9933578 0.9955780 0.9933578
[3,] 0.9955780 0.9933578 1.0000000 0.9955780 0.9933578
[4,] 0.9933607 0.9955780 0.9955780 1.0000000 0.9955780
[5,] 0.9955780 0.9933578 0.9933578 0.9955780 1.0000000

CEGO documentation built on May 14, 2021, 1:08 a.m.