distance
Flexibly calculate dissimilarity or distance measures
Flexibly calculates distance or dissimilarity measures between a
training set 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.
- Keywords
- multivariate, methods
Usage
distance(x, ...)## S3 method for class 'default':
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, ...)
## S3 method for class 'join':
distance(x, \dots)
Arguments
- x
- data frame or matrix containing the training set samples, or
and object of class
join
. - y
- data frame or matrix containing the fossil or test set samples.
- method
- character; which choice of dissimilarity coefficient to use. One of the listed options. See Details below.
- fast
- logical; should fast versions of the dissimilarities be calculated? See details below.
- weights
- numeric; vector of weights for each descriptor.
- R
- numeric; vector of ranges for each descriptor.
- ...
- arguments passed to other methods
Details
A range of dissimilarity coefficients can be used to calculate dissimilarity between samples. The following are currently available:
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 method
s "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.
Value
- A matrix of dissimilarities where columns are the samples in
y
and the rows the samples inx
. Ify
is not provided then a square, symmetric matrix of pairwise sample dissimilarities for the training setx
is returned.The dissimilarity coefficient used (
method
) is returned as attribute"method"
.
Note
The dissimilarities are calculated in native R code. As such, other
implementations (see See Also below) will be quicker. This is done for
one main reason - it is hoped to allow a user defined function to be
supplied as argument "method"
to allow for user-extension of
the available coefficients.
The other advantage of distance
over other implementations, is
the simplicity of calculating only the required pairwise sample
dissimilarities between each fossil sample (y
) and each
training set sample (x
). To do this in other implementations,
you would need to merge the two sets of samples, calculate the full
dissimilarity matrix and then subset it to achieve similar results.
concept
- dissimilarity
- dissimilarity coefficient
- similarity
warning
For method = "mixed"
it is essential that a factor in x
and y
have the same levels in the two data frames. Previous
versions of analogue would work even if this was not the case, which
will have generated incorrect dissimilarities for method =
"mixed"
for cases where factors for a given species had different
levels in x
to y
.
distance
now checks for matching levels for each species
(column) recorded as a factor. If the factor for any individual
species has different levels in x
and y
, an error will
be issued.
References
Faith, D.P., Minchin, P.R. and Belbin, L. (1987) Compositional dissimilarity as a robust measure of ecological distance. Vegetatio 69, 57--68. Gavin, D.G., Oswald, W.W., Wahl, E.R. and Williams, J.W. (2003) A statistical approach to evaluating distance metrics and analog assignments for pollen records. Quaternary Research 60, 356--367.
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.
See Also
vegdist
in package daisy
in package dist
provide comparable functionality for the
case of missing y
and are implemented in compiled code, so
will be faster.
Examples
## 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)
## Using distance on an object of class join
dists <- distance(join(train, fossil))
str(dists)
## 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 coefficient