Is a Distance Matrix Euclidean ?

Description

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

Usage

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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 -1/2 dij² centred by rows and columns should be diplayed

print

a logical value indicating whether the eigenvalues of the matrix of the term -1/2 dij² 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

Author(s)

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

References

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

Examples

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w <- matrix(runif(10000), 100, 100)
w <- dist(w)
summary(w)
is.euclid (w) # TRUE
w <- quasieuclid(w) # no correction need in: quasieuclid(w)
w <- lingoes(w) # no correction need in: lingoes(w)
w <- cailliez(w) # no correction need in: cailliez(w)
rm(w)

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