"x" and a fossil or test set "y". If
"y" is not supplied then the pairwise dissimilarities between
samples in the training set, "x", are calculated.distance(x, y, method = c("euclidean", "SQeuclidean",
"chord", "SQchord", "bray", "chi.square",
"SQchi.square", "information", "chi.distance",
"manhattan", "kendall", "gower", "alt.gower",
"mixed"),
fast = TRUE,
weights = NULL, R = NULL)"y" and the rows the samples in "x". If "y" is
not provided then a square, symmetric matrix of pairwise sample
dissimilarities for the training set "x" is returned. euclidean
$d_{jk} = \sqrt{\sum_i (x_{ij}-x_{ik})^2}$
SQeuclidean
$d_{jk} = \sum_i (x_{ij}-x_{ik})^2$
chord
$d_{jk} = \sqrt{\sum_i
(\sqrt{x_{ij}}-\sqrt{x_{ik}})^2}$
SQchord
$d_{jk} = \sum_i (\sqrt{x_{ij}}-\sqrt{x_{ik}})^2$
bray
$d_{jk} = \frac{\sum_i |x_{ij} - x_{ik}|}{\sum_i (x_{ij} +
x_{ik})}$
chi.square
$d_{jk} = \sqrt{\sum_i \frac{(x_{ij} - x_{ik})^2}{x_{ij} +
x_{ik}}}$
SQchi.square
$d_{jk} = \sum_i \frac{(x_{ij} - x_{ik})^2}{x_{ij} +
x_{ik}}$
information
$d_{jk} = \sum_i (p_{ij}log(\frac{2p_{ij}}{p_{ij} + p_{ik}})
+ p_{ik}log(\frac{2p_{ik}}{p_{ij} + p_{ik}}))$
chi.distance
$d_{jk} = \sqrt{\sum_i (x_{ij}-x_{ik})^2 / (x_{i+} /
x_{++})}$
manhattan
$d_{jk} = \sum_i (|x_{ij}-x_{ik}|)$
kendall
$d_{jk} = \sum_i MAX_i - minimum(x_{ij}, x_{ik})$
gower
$d_{jk} = \sum_i\frac{|p_{ij} -
p_{ik}|}{R_i}$
alt.gower
$d_{jk} = \sqrt{2\sum_i\frac{|p_{ij} -
p_{ik}|}{R_i}}$
where $R_i$ is the range of proportions for
descriptor (variable) $i$
mixed
$d_{jk} = \frac{\sum_{i=1}^p w_{i}s_{jki}}{\sum_{i=1}^p
w_{i}}$
where $w_i$ is the weight for descriptor $i$ and
$s_{jki}$ is the similarity
between samples $j$ and $k$ for descriptor (variable)
$i$.
}
Argument fast determines whether fast C versions of some of the
dissimilarity coefficients are used. The fast versions make use of
dist for methods "euclidean",
"SQeuclidean", "chord", "SQchord", and
vegdist for method == "bray". These
fast versions are used only when x is supplied, not when
y is also supplied. Future versions of distance will
include fast C versions of all the dissimilary coefficients and for
cases where y is supplied.
Kendall, D.G. (1970) A mathematical approach to seriation. Philosophical Transactions of the Royal Society of London - Series B 269, 125--135.
Legendre, P. and Legendre, L. (1998) Numerical Ecology, 2nd English Edition. Elsevier Science BV, The Netherlands. Overpeck, J.T., Webb III, T. and Prentice I.C. (1985) Quantitative interpretation of fossil pollen spectra: dissimilarity coefficients and the method of modern analogues. Quaternary Research 23, 87--108. Prentice, I.C. (1980) Multidimensional scaling as a research tool in Quaternary palynology: a review of theory and methods. Review of Palaeobiology and Palynology 31, 71--104.
vegdist in package vegan,
daisy in package cluster, and
dist provide comparable functionality for the
case of missing "y" and are implemented in compiled code, so
will be faster.## simple example using dummy data
train <- data.frame(matrix(abs(runif(200)), ncol = 10))
rownames(train) <- LETTERS[1:20]
colnames(train) <- as.character(1:10)
fossil <- data.frame(matrix(abs(runif(100)), ncol = 10))
colnames(fossil) <- as.character(1:10)
rownames(fossil) <- letters[1:10]
## calculate distances/dissimilarities between train and fossil
## samples
test <- distance(train, fossil)
## using a different coefficient, chi-square distance
test <- distance(train, fossil, method = "chi.distance")
## calculate pairwise distances/dissimilarities for training
## set samples
test2 <- distance(train)
## calculate Gower's general coefficient for mixed data
## first, make a couple of variables factors
fossil[,4] <- factor(sample(rep(1:4, length = 10), 10))
train[,4] <- factor(sample(rep(1:4, length = 20), 20))
## now fit the mixed coefficient
test3 <- distance(train, fossil, "mixed")
## Example from page 260 of Legendre & Legendre (1998)
x1 <- t(c(2,2,NA,2,2,4,2,6))
x2 <- t(c(1,3,3,1,2,2,2,5))
Rj <- c(1,4,2,4,1,3,2,5) # supplied ranges
distance(x1, x2, method = "mixed", R = Rj)
## note this gives 1 - 0.66 (not 0.66 as the answer in
## Legendre & Legendre) as this is expressed as a
## distance whereas Legendre & Legendre describe the
## coefficient as similarity coefficientRun the code above in your browser using DataLab