## the class of objects 'kdist' (K distance matrices)

### Description

An object of class kdist is a list of distance matrices observed on the same individuals

### Usage

kdist(..., epsi = 1e-07, upper = FALSE)


### Arguments

 ... a sequence of objects of the class kdist. epsi a tolerance threshold to test if distances are Euclidean (Gower's theorem) using \frac{\lambda_n}{\lambda_1} is larger than -epsi. upper a logical value indicating whether the upper of a distance matrix is used (TRUE) or not (FALSE).

### Details

The attributs of a 'kdist' object are:
names: the names of the distances
size: the number of points between distances are known
labels: the labels of points
euclid: a logical vector indicating whether each distance of the list is Euclidean or not.
call: a call order
class: object 'kdist'

### Value

returns an object of class 'kdist' containing a list of semidefinite matrices.

### Author(s)

Daniel Chessel
Anne B Dufour dufour@biomserv.univ-lyon1.fr

### References

Gower, J. C. (1966) Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–338.

### Examples

# starting from a list of matrices
data(yanomama)
lapply(yanomama,class)
kd1 = kdist(yanomama)
print(kd1)

# giving the correlations of Mantel's test
cor(as.data.frame(kd1))
pairs(as.data.frame(kd1))

# starting from a list of objects 'dist'
data(friday87)
fri.w <- ktab.data.frame(friday87$fau, friday87$fau.blo,
tabnames = friday87$tab.names) fri.kd = lapply(1:10, function(x) dist.binary(fri.w[[x]],2)) names(fri.kd) = friday87$tab.names
unlist(lapply(fri.kd,class)) # a list of distances
fri.kd = kdist(fri.kd)
fri.kd
s.corcircle(dudi.pca(as.data.frame(fri.kd), scan = FALSE)$co) # starting from several distances data(ecomor) d1 <- dist.binary(ecomor$habitat, 1)
d2 <- dist.prop(ecomor$forsub, 5) d3 <- dist.prop(ecomor$diet, 5)
d4 <- dist.quant(ecomor$morpho, 3) d5 <- dist.taxo(ecomor$taxo)
ecomor.kd <- kdist(d1, d2, d3, d4, d5)
names(ecomor.kd) = c("habitat", "forsub", "diet", "morpho", "taxo")
class(ecomor.kd)
s.corcircle(dudi.pca(as.data.frame(ecomor.kd), scan = FALSE)$co) data(bsetal97) X <- prep.fuzzy.var(bsetal97$biol, bsetal97$biol.blo) w1 <- attr(X, "col.num") w2 <- levels(w1) w3 <- lapply(w2, function(x) dist.quant(X[,w1==x], method = 1)) names(w3) <- names(attr(X, "col.blocks")) w3 <- kdist(list = w3) s.corcircle(dudi.pca(as.data.frame(w3), scan = FALSE)$co)

data(rpjdl)
w1 = lapply(1:10, function(x) dist.binary(rpjdl$fau, method = x)) w2 = c("JACCARD", "SOCKAL_MICHENER", "SOCKAL_SNEATH_S4", "ROGERS_TANIMOTO") w2 = c(w2, "CZEKANOWSKI", "S9_GOWER_LEGENDRE", "OCHIAI", "SOKAL_SNEATH_S13") w2 <- c(w2, "Phi_PEARSON", "S2_GOWER_LEGENDRE") names(w1) <- w2 w3 = kdist(list = w1) w4 <- dudi.pca(as.data.frame(w3), scan = FALSE)$co
w4


### Worked out examples


> ### Name: kdist
> ### Title: the class of objects 'kdist' (K distance matrices)
> ### Aliases: kdist c.kdist print.kdist [.kdist as.data.frame.kdist
> ### Keywords: multivariate
>
> ### ** Examples
>
> # starting from a list of matrices
> data(yanomama)
> lapply(yanomama,class)
$geo [1] "matrix"$gen
[1] "matrix"

$ant [1] "matrix" > kd1 = kdist(yanomama) > print(kd1) List of distances matrices call: kdist(yanomama) class: kdist number of distances: 3 size: 19 labels: [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10" "11" "12" "13" "14" "15" [16] "16" "17" "18" "19" geo: non euclidean distance gen: non euclidean distance ant: non euclidean distance > > # giving the correlations of Mantel's test > cor(as.data.frame(kd1)) geo gen ant geo 1.0000000 0.5098684 0.8428053 gen 0.5098684 1.0000000 0.2995506 ant 0.8428053 0.2995506 1.0000000 > pairs(as.data.frame(kd1))  > > # starting from a list of objects 'dist' > data(friday87) > fri.w <- ktab.data.frame(friday87$fau, friday87$fau.blo, + tabnames = friday87$tab.names)
> fri.kd = lapply(1:10, function(x) dist.binary(fri.w[[x]],2))
> names(fri.kd) = friday87$tab.names > unlist(lapply(fri.kd,class)) # a list of distances Hemiptera Odonata Trichoptera Ephemeroptera Coleoptera "dist" "dist" "dist" "dist" "dist" Diptera Hydracarina Malacostraca Mollusca Oligochaeta "dist" "dist" "dist" "dist" "dist" > fri.kd = kdist(fri.kd) > fri.kd List of distances matrices call: kdist(fri.kd) class: kdist number of distances: 10 size: 16 labels: [1] "Q" "P" "R" "J" "E" "C" "D" "K" "B" "A" "G" "M" "L" "F" "H" "N" Hemiptera: euclidean distance Odonata: euclidean distance Trichoptera: euclidean distance Ephemeroptera: euclidean distance Coleoptera: euclidean distance Diptera: euclidean distance Hydracarina: euclidean distance Malacostraca: euclidean distance Mollusca: euclidean distance Oligochaeta: euclidean distance > s.corcircle(dudi.pca(as.data.frame(fri.kd), scan = FALSE)$co)

>
> # starting from several distances
> data(ecomor)
> d1 <- dist.binary(ecomor$habitat, 1) > d2 <- dist.prop(ecomor$forsub, 5)
> d3 <- dist.prop(ecomor$diet, 5) > d4 <- dist.quant(ecomor$morpho, 3)
> d5 <- dist.taxo(ecomor$taxo) > ecomor.kd <- kdist(d1, d2, d3, d4, d5) > names(ecomor.kd) = c("habitat", "forsub", "diet", "morpho", "taxo") > class(ecomor.kd) [1] "kdist" > s.corcircle(dudi.pca(as.data.frame(ecomor.kd), scan = FALSE)$co)

>
> data(bsetal97)
> X <- prep.fuzzy.var(bsetal97$biol, bsetal97$biol.blo)
17 missing data found in block 1
14 missing data found in block 2
28 missing data found in block 3
8 missing data found in block 4
5 missing data found in block 5
19 missing data found in block 6
10 missing data found in block 7
5 missing data found in block 8
2 missing data found in block 9
12 missing data found in block 10
> w1 <- attr(X, "col.num")
> w2 <- levels(w1)
> w3 <- lapply(w2, function(x) dist.quant(X[,w1==x], method = 1))
> names(w3) <- names(attr(X, "col.blocks"))
> w3 <- kdist(list = w3)
> s.corcircle(dudi.pca(as.data.frame(w3), scan = FALSE)$co)  > > data(rpjdl) > w1 = lapply(1:10, function(x) dist.binary(rpjdl$fau, method = x))
> w2 = c("JACCARD", "SOCKAL_MICHENER", "SOCKAL_SNEATH_S4", "ROGERS_TANIMOTO")
> w2 = c(w2, "CZEKANOWSKI", "S9_GOWER_LEGENDRE", "OCHIAI", "SOKAL_SNEATH_S13")
> w2 <- c(w2, "Phi_PEARSON", "S2_GOWER_LEGENDRE")
> names(w1) <- w2
> w3 = kdist(list = w1)
> w4 <- dudi.pca(as.data.frame(w3), scan = FALSE)\$co
> w4
Comp1       Comp2
JACCARD           -0.9791013 -0.18151963
SOCKAL_MICHENER   -0.8693893  0.48952277
SOCKAL_SNEATH_S4  -0.9673038 -0.17757093
ROGERS_TANIMOTO   -0.8760634  0.48095455
CZEKANOWSKI       -0.9811773 -0.18245217
S9_GOWER_LEGENDRE -0.8693893  0.48952277
OCHIAI            -0.9801507 -0.18304997
SOKAL_SNEATH_S13  -0.9882272 -0.12063315
Phi_PEARSON       -0.9955160 -0.03143543
S2_GOWER_LEGENDRE -0.8342624 -0.49634908
>
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