lingoes {ade4}R Documentation

Transformation of a Distance Matrix for becoming Euclidean

Description

transforms a distance matrix in a Euclidean one.

Usage

lingoes(distmat, print = FALSE)

Arguments

distmat an object of class dist
print if TRUE, prints the eigenvalues of the matrix

Details

The function uses the smaller positive constant k which transforms the matrix of sqrt(dij² + 2*k) in an Euclidean one

Value

returns an object of class dist with a Euclidean distance

Author(s)

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

References

Lingoes, J.C. (1971) Some boundary conditions for a monotone analysis of symmetric matrices. Psychometrika, 36, 195–203.

Examples

data(capitales)
d0 <- as.dist(capitales$df)
is.euclid(d0) # FALSE
d1 <- lingoes(d0, TRUE)
# Lingoes constant = 2120982
is.euclid(d1) # TRUE
plot(d0, d1)
x0 <- sort(unclass(d0))
lines(x0, sqrt(x0^2 + 2 * 2120982), lwd = 3)
 
is.euclid(sqrt(d0^2 + 2 * 2120981), tol = 1e-10) # FALSE
is.euclid(sqrt(d0^2 + 2 * 2120982), tol = 1e-10) # FALSE
is.euclid(sqrt(d0^2 + 2 * 2120983), tol = 1e-10) 
    # TRUE the smaller constant

Worked out examples


> library(ade4)
> ### Name: lingoes
> ### Title: Transformation of a Distance Matrix for becoming Euclidean
> ### Aliases: lingoes
> ### Keywords: array multivariate
> 
> ### ** Examples
> 
> data(capitales)
> d0 <- as.dist(capitales$df)
> is.euclid(d0) # FALSE
[1] FALSE
> d1 <- lingoes(d0, TRUE)
Lingoes constant = 2120982 
> # Lingoes constant = 2120982
> is.euclid(d1) # TRUE
[1] TRUE
> plot(d0, d1)
> x0 <- sort(unclass(d0))
> lines(x0, sqrt(x0^2 + 2 * 2120982), lwd = 3)
> 
> is.euclid(sqrt(d0^2 + 2 * 2120981), tol = 1e-10) # FALSE
[1] FALSE
> is.euclid(sqrt(d0^2 + 2 * 2120982), tol = 1e-10) # FALSE
[1] FALSE
> is.euclid(sqrt(d0^2 + 2 * 2120983), tol = 1e-10) 
[1] TRUE
>     # TRUE the smaller constant
> 
> 
> 
> 

[Package ade4 Index]