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 rizzo@math.ohiou.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) (in press).

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 1.0-3 Index]