Rand.index {matchFeat}

Rand Index of Agreement Between Two Partitions

Description

Calculates the Rand Index between two partitions of a set

Usage

Rand.index(x, y)

Arguments

x

first partition vector

y

second partition vector

Details

The two vectors x and y must have equal length. Given a set S and two partitions X and Y of S, the Rand index is the proportion of pairs of elements in S (out of all pairs) that are either concordant in both X and Y (i.e., they belong to the same member of X and to the same member of Y) or discordant (i.e., not concordant) in both X and Y.

Value

The Rand index (not adjusted for chance)

References

W. M. Rand (1971). "Objective criteria for the evaluation of clustering methods"
https://en.wikipedia.org/wiki/Rand_index

Examples

## Example 1
x <- sample.int(3, 20, replace = TRUE)
y <- sample.int(3, 20, replace = TRUE)
table(x,y)
Rand.index(x,y)

## Example 2
data(optdigits)
label <- optdigits$label 
m <- length(unique(label)) # 10 
n <- length(unique(optdigits$unit)) # 100
dim(label) <- c(m,n)
p <- ncol(optdigits$x) # 64
x <- array(t(optdigits$x),c(p,m,n))
## Permute data and labels to make problem harder
for (i in 1:n) {
	sigma <- sample.int(m)
	x[,,i] <- x[,sigma,i]
	label[,i] <- label[sigma,i]
}
## Compare Rand indices of matching methods
Rand.index(match.bca(x)$cluster, label)
Rand.index(match.rec(x)$cluster, label)
Rand.index(match.template(x)$cluster, label)
Rand.index(match.kmeans(x)$cluster, label)