hybridHclust (version 1.0-5)

eisenCluster: An implementation of Eisen's hierarchical clustering

Description

Bottom-up clustering in which each cluster is represented by the mean vector for observations in the cluster.

Usage

eisenCluster(x, method, compatible = TRUE, verbose = FALSE)

Arguments

x

Data matrix, whose rows we wish to cluster

method

How should distance between points (and centres) be calculated? Choices include “euclidean”,“squared.euclidean”, “correlation”,“uncentered.correlation”. For “euclidean” and “squared.euclidean”, unexpected behaviour can result, since data points are replaced by their cluster centres, the overall variance in the data will decrease.

compatible

Flag for whether cluster merging should be done as in Eisen's cluster algorithm. If compatible=TRUE, then when two clusters are merged, a weighted average of the mean vectors for each of the two clusters is used. If compatible=F, then the original data are averaged to obtain the new centre. When x does not contain missing values, these two options generate the same result. If there are missing values, they will differ. Using the original data makes more sense when there are missing values, since the weights won't account for the missing value pattern.

verbose

Prints iteration number if TRUE

Value

A hclust object. The definition of distance between 2 clusters as the distance between their means can result in a non-monotone dendrogram (e.g., if A, B, C are vertices of an equilateral triangle with side lengths 1, A joins B at distance 1, then C joins AB at distance 0.866). Non-monotone distances are coerced to be monotone before the object is returned. This can yeild dendrograms which seem to join more than 2 points at one height.The “trueheight” component contains actual heights before they were forced to be monotone.

Details

The main difference between this algorithm and hclust(...,method='centroid') is the manner in which missing values are handled. Here, original rows are merged at each step, taking means after omitting missing observations.

Missing values are permitted, and can be handled in the same manner as in Eisen's package. This is perhaps the main reason the current implementation might be used: to reproduce the clusterings found from Eisen's code when there are missing values. When two clusters are merged, missing values can be handled in two ways (controlled by the compatible flag): (1) new cluster centres can be calculated using means of all original observations in the clusters, or (2) new cluster centres can be calculated using a weighted average of the means of the two clusters being joined. Although Eisen's cluster software uses (2), it seems less desirable in situations where observations are missing in some dimensions only, since the presence of missing values will cause the wrong weights to be used when updating centres. Subsequent averaging of clusters centres will ignore the missingness patterns in the cluster means. Option (2) is included to enable clusters identical to Eisen's to be produced.

Examples

set.seed(101)
x <- matrix(rnorm(500),5,100)
x <- rbind(x,x[rep(1,4),]+matrix(rnorm(400),4,100))
x <- rbind(x,x[2:5,]+matrix(rnorm(400),4,100))
par(mfrow=c(1,2))
image(1-cor(t(x)),main='correlation distances',zlim=c(0,2),col=gray(1:100/101))
e1 <- eisenCluster(x,'correlation')
plot(e1)