cailliez function

Transformation to make Euclidean a distance matrix

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

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

Returns

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(s)

Daniel Chessel

Stéphane Dray stephane.dray@univ-lyon1.fr

Examples

data(capitales)
d0 <- capitales$dist
is.euclid(d0) # FALSE
d1 <- cailliez(d0, TRUE)
# Cailliez constant = 2429.87867 
is.euclid(d1) # TRUE
plot(d0, d1)
abline(lm(unclass(d1)~unclass(d0)))
print(coefficients(lm(unclass(d1)~unclass(d0))), dig = 8) # d1 = d + Cte
is.euclid(d0 + 2428) # FALSE
is.euclid(d0 + 2430) # TRUE the smallest constant