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.

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)

Details

A range of dissimilarity coefficients can be used to calculate dissimilarity between samples. The following are currently available:

ll{ 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.

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 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.

Aliases

• distance
• distance.default
• distance.join

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