# Computes the Rand similarity index of two clusterings of the same data set under the assumption that the two clusterings are independent.

### Description

For two clusterings of the same data set, this function calculates the Rand similarity coefficient of the clusterings from the comemberships of the observations. Basically, the comembership is defined as the pairs of observations that are clustered together.

### Usage

1 | ```
rand_indep(labels1, labels2)
``` |

### Arguments

`labels1` |
a vector of |

`labels2` |
a vector of |

### Details

To calculate the Rand index, we compute the 2x2 contingency table, consisting of the following four cells:

- n_11
the number of observation pairs where both observations are comembers in both clusterings

- n_10
the number of observation pairs where the observations are comembers in the first clustering but not the second

- n_01
the number of observation pairs where the observations are comembers in the second clustering but not the first

- n_00
the number of observation pairs where neither pair are comembers in either clustering

The Rand similarity index is defined as:

*R =
\frac{n_{11} + n_{00}}{n_{11} + n_{10} + n_{01} +
n_{00}}*

.

To compute the contingency table, we use the
`comembership_table`

function.

### Value

the Rand index for the two sets of cluster labels

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
## Not run:
# We generate K = 3 labels for each of n = 10 observations and compute the
# Rand similarity index between the two clusterings.
set.seed(42)
K <- 3
n <- 10
labels1 <- sample.int(K, n, replace = TRUE)
labels2 <- sample.int(K, n, replace = TRUE)
rand_indep(labels1, labels2)
# Here, we cluster the \code{\link{iris}} data set with the K-means and
# hierarchical algorithms using the true number of clusters, K = 3.
# Then, we compute the Rand similarity index between the two clusterings.
iris_kmeans <- kmeans(iris[, -5], centers = 3)$cluster
iris_hclust <- cutree(hclust(dist(iris[, -5])), k = 3)
rand_indep(iris_kmeans, iris_hclust)
## End(Not run)
``` |