hopach (version 2.32.0)

labelstomss: Functions to compute silhouettes and split silhouettes

Description

Silhouettes measure how well an element belongs to its cluster, and the average silhouette measures the strength of cluster membership overall. The Median (or Mean) Split Silhouette (MSS) is a measure of cluster heterogeneity. Given a partitioning of elements into groups, the MSS algorithm considers each group separately and computes the split silhouette for that group, which evaluates evidence in favor of further splitting the group. If the median (or mean) split silhouette over all groups in the partition is low, the groups are homogeneous.

Usage

labelstomss(labels, dist, khigh = 9, within = "med", between = "med", 
hierarchical = TRUE)
msscheck(dist, kmax = 9, khigh = 9, within = "med", between = "med", 
    force = FALSE, echo = FALSE, graph = FALSE)
silcheck(data, kmax = 9, diss = FALSE, echo = FALSE, graph = FALSE)

Arguments

labels

vector of cluster labels for each element in the set.

dist

numeric distance matrix containing the pair wise distances between all elements. All values must be numeric and missing values are not allowed.

data

a data matrix. Each column corresponds to an observation, and each row corresponds to a variable. In the gene expression context, observations are arrays and variables are genes. All values must be numeric. Missing values are ignored. In silcheck, data may also be a distance matrix or dissimilarity object if the argument diss=TRUE.

khigh

integer between 1 and 9 specifying the maximum number of children for each cluster when computing MSS.

kmax

integer between 1 and 9 specifying the maximum number of clusters to consider. Can be different from khigh, though typically these are the same value.

within

character string indicating how to compute the split silhouette for each cluster. The available options are "med" (median over all elements in the cluster) or "mean" (mean over all elements in the cluster).

between

character string indicating how to compute the MSS over all clusters. The available options are "med" (median over all clusters) or "mean" (mean over all clusters). Recommended to use the same value as within.

hierarchical

logical indicating if 'labels' should be treated as encoding a hierarchical tree, e.g. from HOAPCH.

force

indicator of whether to require at least 2 clusters, if FALSE (default), one cluster is considered.

echo

indicator of whether to print the selected number of clusters and corresponding MSS.

graph

indicator of whether to generate a plot of MSS (or average silhouette in silcheck) versus number of clusters.

diss

indicator of whether data is a dissimilarity matrix (or dissimilarity object), as in the pam function of the cluster package. If TRUE then data will be considered as a dissimilarity matrix. If FALSE, then data will be considered as a data matrix (observations by variables).

Value

• For labelstomss, the median (or mean or combination) split silhouette, depending on the values of within and between. For msscheck, a vector with first component the chosen number of clusters (minimizing MSS) and second component the corresponding MSS.

  For silcheck, a vector with first component the chosen number of clusters (maximizing average silhouette) and second component the corresponding average silhouette.

Details

The Median (and mean) Split Silhouette (MSS) criteria is defined in paper107 listed in the references (below). This criteria is based on the criteria function 'silhouette', proposed by Kaufman and Rousseeuw (1990). While average silhouette is a good global measure of cluster strength, MSS was developed to be more "aggressive" for finding small, homogeneous clusters in large data sets. MSS is a measure of average cluster homogeneity. The Median version is more robust than the Mean.

References

http://www.bepress.com/ucbbiostat/paper107/

http://www.stat.berkeley.edu/~laan/Research/Research_subpages/Papers/jsmpaper.pdf

Kaufman, L. and Rousseeuw, P.J. (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.

See Also

pam, hopach, distancematrix

Examples

mydata<-rbind(cbind(rnorm(10,0,0.5),rnorm(10,0,0.5),rnorm(10,0,0.5)),cbind(rnorm(15,5,0.5),rnorm(15,5,0.5),rnorm(15,5,0.5)))
mydist<-distancematrix(mydata,d="cosangle") #compute the distance matrix.

#pam
result1<-pam(mydata,k=2)
result2<-pam(mydata,k=5)
labelstomss(result1$clust,mydist,hierarchical=FALSE)
labelstomss(result2$clust,mydist,hierarchical=FALSE)

#hopach
result3<-hopach(mydata,dmat=mydist)
labelstomss(result3$clustering$labels,mydist)
labelstomss(result3$clustering$labels,mydist,within="mean",between="mean")