# partitionMetric: Compute a distance metric between two partitions of a set In partitionMetric: 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

 `1` ```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. B(i) corresponds to C(i), and the two vectors must be the same length. The data types of B and C must be identical and convertable to a factor data type. See examples below for more information. `C` See B above. `beta` Beta is the nonlinear parameter used to compute the distance metric. See the publication referenced below for full details.

## 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

`as.dist`, `hclust`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```## 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)))) ```

partitionMetric documentation built on May 29, 2017, 4:08 p.m.