analogue (version 0.4-0)

distance: Flexibly calculate dissimilarity or distance measures

Description

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, 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)

Arguments

x

data frame or matrix containing the training set samples.

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.

Value

• A matrix of dissimilarities where columns are the samples in "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.

concept

• dissimilarity
• dissimilarity coefficient
• similarity

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.

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.

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)

## 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