Is a Distance Matrix Euclidean?

Confirmation of the Euclidean nature of a distance matrix by the Gower's theorem.
is.euclid is used in summary.dist.

Usage

is.euclid(distmat, plot = FALSE, print = FALSE, tol = 1e-07)
# S3 method for class 'dist'
summary(object, ...)

Arguments

distmat

an object of class 'dist'

plot

a logical value indicating whether the eigenvalues bar plot of the matrix of the term \(-\frac{1}{2} {d_{ij}^2}\) centred by rows and columns should be diplayed

print

a logical value indicating whether the eigenvalues of the matrix of the term \(-\frac{1}{2} {d_{ij}^2}\) centred by rows and columns should be printed

tol

a tolerance threshold : an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue.

object

an object of class 'dist'

...

further arguments passed to or from other methods

Value

returns a logical value indicating if all the eigenvalues are positive or equal to zero

References

Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5–48.

Author

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

Examples

w <- matrix(runif(10000), 100, 100)
w <- dist(w)
summary(w)
#> Class: dist 
#> Distance matrix by lower triangle : d21, d22, ..., d2n, d32, ...
#> Size: 100 
#> Labels: 
#> call: dist(x = w)
#> method: euclidean 
#> Euclidean matrix (Gower 1966): TRUE 
is.euclid (w) # TRUE
#> [1] TRUE
w <- quasieuclid(w) # no correction need in: quasieuclid(w)
#> Warning: Euclidean distance found : no correction need
w <- lingoes(w) # no correction need in: lingoes(w)
#> Warning: Euclidean distance found : no correction need
w <- cailliez(w) # no correction need in: cailliez(w)
#> Warning: Euclidean distance found : no correction need
rm(w)