edist {energy}R Documentation

E-distance

Description

Returns the E-distances (energy statistics) between clusters.

Usage

 edist(x, sizes, distance = FALSE, ix = 1:sum(sizes), alpha = 1)

Arguments

x data matrix of pooled sample or Euclidean distances
sizes vector of sample sizes
distance logical: if TRUE, x is a distance matrix
ix a permutation of the row indices of x
alpha distance exponent

Details

A vector containing the pairwise two-sample multivariate E-statistics for comparing clusters or samples is returned. The e-distance between clusters is computed from the original pooled data, stacked in matrix x where each row is a multivariate observation, or from the distance matrix x of the original data, or distance object returned by dist. The first sizes[1] rows of the original data matrix are the first sample, the next sizes[2] rows are the second sample, etc. The permutation vector ix may be used to obtain e-distances corresponding to a clustering solution at a given level in the hierarchy.

The e-distance between two clusters C_i, C_j of size n_i, n_j proposed by Szekely and Rizzo (2003) is the e-distance e(C_i,C_j), defined by

e(S_i, S_j) = (n_i n_j)(n_i+n_j)[2M_(ij)-M_(ii)-M_(jj)],

where

M_{ij} = 1/(n_i n_j) sum[1:n_i, 1:n_j] ||X_(ip) - X_(jq)||^a,

|| || denotes Euclidean norm, a= alpha, and X_(ip) denotes the p-th observation in the i-th cluster. The exponent alpha should be in the interval (0,2].

Value

A object of class dist containing the lower triangle of the e-distance matrix of cluster distances corresponding to the permutation of indices ix is returned.

Author(s)

Maria L. Rizzo mrizzo @ bgnet.bgsu.edu and Gabor J. Szekely gabors @ bgnet.bgsu.edu

References

Szekely, G. J. and Rizzo, M. L. (2005) Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method, Journal of Classification 22(2) 151-183.
http://dx.doi.org/10.1007/s00357-005-0012-9

Szekely, G. J. and Rizzo, M. L. (2004) Testing for Equal Distributions in High Dimension, InterStat, November (5).

Szekely, G. J. (2000) Technical Report 03-05, E-statistics: Energy of Statistical Samples, Department of Mathematics and Statistics, Bowling Green State University.

See Also

energy.hclust eqdist.etest ksample.e

Examples

 ## compute e-distances for 3 samples of iris data
 data(iris)
 edist(iris[,1:4], c(50,50,50))


 ## compute e-distances from vector of group labels
 d <- dist(matrix(rnorm(100), nrow=50))
 g <- cutree(energy.hclust(d), k=4)
 edist(d, sizes=table(g), ix=rank(g, ties.method="first"))
 

[Package energy version 1.1-0 Index]