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