partitionMetric {partitionMetric} | R Documentation |
Compute a distance metric between two partitions of a set
Description
Given a set partitioned in two ways, compute a distance metric between the partitions.
Usage
partitionMetric(B, C, beta = 2)
Arguments
B |
B and C are vectors that represents partitions of a single set, with
each element representing a member of the set. See examples below for more information. |
C |
See B above. |
beta |
|
Value
The return value is a nonnegative real number representing the distance between the two partition of the set. Full details are in the paper referenced below.
Author(s)
David Weisman, Dan Simovici
References
David Weisman and Dan Simovici, Several Remarks on the Metric Space of Genetic Codes. International Journal of Data Mining and Bioinformatics, 2012(6).
See Also
Examples
## Define several partitions of a 4-element set
gender <- c('boy', 'girl', 'girl', 'boy')
height <- c('short', 'tall', 'medium', 'tall')
age <- c(7, 6, 5, 4)
## Compute some distances
(dGG <- partitionMetric (gender, gender))
(dGH <- partitionMetric (gender, height))
(dHG <- partitionMetric (height, gender))
(dGA <- partitionMetric (gender, age))
(dHA <- partitionMetric (height, age))
## These properties must hold for any metric
dGG == 0
dGH == dHG
dGA <= dGH + dHA
## Note that the partition names are irrelevant, and only need to be
## self-consistent within each B and C. It follows that these two set
## partitions are identical and have distance 0.
partitionMetric (c(1,8,8), c(7,3,3)) == 0
## Use the set partition to measure amino acid acid sequence differences
## between several alleles of the aryl hydrocarbon receptor.
data(AhRs)
dim(AhRs)
AhRs[,1:10]
distanceMatrix <-
matrix(nrow=nrow(AhRs), ncol=nrow(AhRs), 0,
dimnames=list(rownames(AhRs), rownames(AhRs)))
for (pair in combn(rownames(AhRs), 2, simplify=FALSE)) {
d <- partitionMetric (AhRs[pair[1],], AhRs[pair[2],], beta=1.01)
distanceMatrix[pair[1],pair[2]] <- distanceMatrix[pair[2],pair[1]] <- d
}
hc <- hclust(as.dist(distanceMatrix))
plot(hc,
sub=sprintf('Cophenentic correlation between distances and tree is %0.2f',
cor(as.dist(distanceMatrix), cophenetic(hc))))