correctionDistanceMatrix: Correction of a Distance Matrix

Description

Convert (possibly non-euclidean or non-metric) distance matrix with chosen approach so that it becomes a CNSD matrix. Optionally, the resulting matrix is enforced to have positive elements and zero diagonal, with the repair parameter. Essentially, this is a combination of functions correctionDefinite or correctionCNSD with repairConditionsDistanceMatrix.

Usage

correctionDistanceMatrix(
  mat,
  type = "NSD",
  method = "flip",
  repair = TRUE,
  tol = 1e-08
)

Value

list with corrected distance matrix mat, isCNSD (boolean, whether original matrix was CNSD) and transformation matrix A.

Arguments

mat: symmetric distance matrix
type: string that specifies type of correction: "CNSD","NSD" to enforce CNSD or NSD matrices respectively.
method: string that specifies method for correction: spectrum clip "clip", spectrum flip "flip", nearest definite matrix "near", spectrum square"square", spectrum diffusion "diffusion", feature embedding "feature".
repair: boolean, whether or not to use condition repair, so that elements are positive, and diagonal is zero.
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)
is.CNSD(D) #matrix should not be CNSD
D <- correctionDistanceMatrix(D)$mat
is.CNSD(D) #matrix should now be CNSD
D