# Partition Comparison Indices

### Description

This function computes several partition comparison indices.

### Usage

1 | ```
pci(x1, x2)
``` |

### Arguments

`x1` |
a factor |

`x2` |
a factor |

### Details

This function computes indices of similarity between two factors representing the cluster partition of *n* items. The two vectors must be of the same length. Let *n11* be the number of item pairs that occur in the same cluster in both partitions `x1`

and `x2`

, *n00* the number of item pairs that occur in differenct clusters in both partitions, *n10* the number of item pairs that occur in the same cluster in partition `x1`

but in different clusters in parition `x2`

, and *n01* the number of item pairs that occur in different clusters in partition `x1`

but in the same cluster in partition `x2`

. The Rand index is given by

*(n11+n00)/(n11+n00+n01+n10).*

The Fowlkes and Mallows index is given by

*n11/sqrt((n11+n10)*(n11+n01)).*

The Wallace indices are respectively given by

*n11/(n11+n10), and n11/(n11+n01).*

The Jaccard index is given by

*n11/(n11+n01+n10).*

### Value

A named vector with the following elements:

`R` |
Rand index |

`FM` |
Fowlkes and Mallows index |

`W10` |
Wallace 10 index |

`W01` |
Wallace 01 index |

`J` |
Jaccard index |

### Author(s)

Matt Shotwell

### References

Rand, W. (1971) Objective Criteria for the Evaluation of Clustering Methods. Journal of the American Statistical Association 66:846-850

Fowlkes, E. B. and Mallows, C. L. (1983) A Method for Comparing Two Hierarchical Clusterings. Journal of the American Statistical Association 78:553-569

Wallace, D. L. (1983) A Method for Comparing Two Hierarchical Clusterings: comment. Journal of the American Statistical Association 78:569-576