Transformation to make Euclidean a distance matrix

This function computes the smallest positive constant that makes Euclidean a distance matrix and applies it.

Usage

cailliez(distmat, print = FALSE, tol = 1e-07, cor.zero = TRUE)

Arguments

distmat

an object of class dist

print

if TRUE, prints the eigenvalues of the matrix

tol

a tolerance threshold for zero

cor.zero

if TRUE, zero distances are not modified

Value

an object of class dist containing a Euclidean distance matrix.

References

Cailliez, F. (1983) The analytical solution of the additive constant problem. Psychometrika, 48, 305–310.

Legendre, P. and Anderson, M.J. (1999) Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs, 69, 1–24.

Legendre, P., and Legendre, L. (1998) Numerical ecology, 2nd English edition edition. Elsevier Science BV, Amsterdam.

Author

Daniel Chessel
Stéphane Dray stephane.dray@univ-lyon1.fr

Examples

data(capitales)
d0 <- capitales$dist
is.euclid(d0) # FALSE
#> [1] FALSE
d1 <- cailliez(d0, TRUE)
#> Cailliez constant = 2429.87867 
# Cailliez constant = 2429.87867 
is.euclid(d1) # TRUE
#> [1] TRUE
plot(d0, d1)
abline(lm(unclass(d1)~unclass(d0)))

print(coefficients(lm(unclass(d1)~unclass(d0))), dig = 8) # d1 = d + Cte
#> (Intercept) unclass(d0) 
#>   2429.8787      1.0000 
is.euclid(d0 + 2428) # FALSE
#> [1] FALSE
is.euclid(d0 + 2430) # TRUE the smallest constant
#> [1] TRUE