Nearest CNSD matrix
This function
implements the alternating projection algorithm by Glunt et al. (1990) to calculate the nearest conditionally
negative semi-definite (CNSD) matrix (or: the nearest Euclidean distance matrix).
The function is similar to the nearPD function from the Matrix package,
which implements a very similar algorithm for finding the nearest Positive Semi-Definite (PSD) matrix.
nearCNSD( x, eig.tol = 1e-08, conv.tol = 1e-08, maxit = 1000, conv.norm.type = "F" )
x |
symmetric matrix, to be turned into a CNSD matrix. |
eig.tol |
eigenvalue torelance value. Eigenvalues between |
conv.tol |
convergence torelance value. The algorithm stops if the norm of the difference between two iterations is below this value. |
maxit |
maximum number of iterations. The algorithm stops if this value is exceeded, even if not converged. |
conv.norm.type |
type of norm, by default the F-norm (Frobenius). See |
list with:
matnearestCNSD matrix
normFF-norm between original and resulting matrices
iterationsthe number of performed
rel.tolthe relative value used for the tolerance convergence criterion
convergeda boolean that records whether the algorithm
Glunt, W.; Hayden, T. L.; Hong, S. and Wells, J. An alternating projection algorithm for computing the nearest Euclidean distance matrix, SIAM Journal on Matrix Analysis and Applications, SIAM, 1990, 11, 589-600
# example using Insert distance with permutations: 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) print(D) is.CNSD(D) nearD <- nearCNSD(D) print(nearD) is.CNSD(nearD$mat) # or example matrix from Glunt et al. (1990): D <- matrix(c(0,1,1,1,0,9,1,9,0),3,3) print(D) is.CNSD(D) nearD <- nearCNSD(D) print(nearD) is.CNSD(nearD$mat) # note, that the resulting values given by Glunt et al. (1990) are 19/9 and 76/9
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