a way to obtain Euclidean distance matrices

Usage

kdisteuclid(obj, method = c("lingoes", "cailliez", "quasi"))

Arguments

obj: an object of class kdist
method: a method to convert a distance matrix in a Euclidean one

Value

returns an object of class kdist with all distances Euclidean.

References

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

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

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

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

Author

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

Examples

w <- c(0.8, 0.8, 0.377350269, 0.8, 0.377350269, 0.377350269) # see ref.
w <- kdist(w)
w1 <- c(kdisteuclid(kdist(w), "lingoes"), kdisteuclid(kdist(w), "cailliez"), 
  kdisteuclid(kdist(w), "quasi"))
#> [1] "Lingoes constant = 0.0532050808642207"
#> [1] "Cailliez constant = 0.20000000044866"
#> [1] "First ev = 0.32 Last ev = -0.0532050808642197"
print(w, print = TRUE)
#> List of distances matrices
#> call: kdist(w)
#> class: kdist
#> number of distances: 1
#> size: 4
#> labels:
#> [1] "1" "2" "3" "4"
#> w: non euclidean distance
#>   1         2         3         4
#> 1                                
#> 2 0.8000000                      
#> 3 0.8000000 0.8000000            
#> 4 0.3773503 0.3773503 0.3773503  
#> 
print(w1, print = TRUE)
#> List of distances matrices
#> call: c.kdist(kdisteuclid(kdist(w), "lingoes"), kdisteuclid(kdist(w), 
#>     "cailliez"), kdisteuclid(kdist(w), "quasi"))
#> class: kdist
#> number of distances: 3
#> size: 4
#> labels:
#> [1] "1" "2" "3" "4"
#> list(c(0.863950323646239, 0.863950323646239, 0.49880195192362, 0.863950323646239, 0.49880195192362, 0.49880195192362)).w: euclidean distance
#>   1         2         3         4
#> 1                                
#> 2 0.8639503                      
#> 3 0.8639503 0.8639503            
#> 4 0.4988020 0.4988020 0.4988020  
#> 
#> list(c(1.00000000044866, 1.00000000044866, 0.57735026944866, 1.00000000044866, 0.57735026944866, 0.57735026944866)).w: euclidean distance
#>   1         2         3         4
#> 1                                
#> 2 1.0000000                      
#> 3 1.0000000 1.0000000            
#> 4 0.5773503 0.5773503 0.5773503  
#> 
#> list(c(0.8, 0.8, 0.461880215351701, 0.8, 0.461880215351701, 0.461880215351701)).w: euclidean distance
#>   1         2         3         4
#> 1                                
#> 2 0.8000000                      
#> 3 0.8000000 0.8000000            
#> 4 0.4618802 0.4618802 0.4618802  
#> 

data(eurodist)
par(mfrow = c(1, 3))
eu1 <- kdist(eurodist) # an object of class 'dist'
plot(data.frame(unclass(c(eu1, kdisteuclid(eu1, "quasi")))), asp = 1)
#> [1] "First ev = 19538377.0895428 Last ev = -2251844.33173616"
title(main = "Quasi")
abline(0,1)
plot(data.frame(unclass(c(eu1, kdisteuclid(eu1, "lingoes")))), asp = 1)
#> [1] "Lingoes constant = 2251844.33173616"
title(main = "Lingoes")
abline(0,1)
plot(data.frame(unclass(c(eu1, kdisteuclid(eu1, "cailliez")))), asp = 1)
#> [1] "Cailliez constant = 2132.67849519795"
title(main = "Cailliez")
abline(0,1)