clValid (version 0.7)

stability: Stability Measures

Description

Calculates the stability measures the average proportion of non-overlap (APN), the average distance (AD), the average distance between means (ADM), and the figure of merit (FOM).

Usage

stability(mat, Dist=NULL, del, cluster, clusterDel, method="euclidean")

Arguments

mat

The data matrix of the clustered observations

Dist

The distance matrix (as a matrix or dist object) of the clustered observations. If NULL then method is used with mat to determine the distance matrix.

del

An integer indicating which column was removed

cluster

An integer vector indicating the cluster partitioning based on all the data

clusterDel

An integer vector indicating the cluster partitioning based on the data with column del removed.

method

The metric used to determine the distance matrix. Not used if distance is provided.

Value

Returns a numeric vector with the APN, AD, ADM, and FOM measures corresponding to the particular column that was removed.

Details

The stability measures evaluate the stability of a clustering result by comparing it with the clusters obtained by removing one column at a time. These measures include the average proportion of non-overlap (APN), the average distance (AD), the average distance between means (ADM), and the figure of merit (FOM). The APN, AD, and ADM are all based on the cross-classification table of the original clustering with the clustering based on the removal of one column. The APN measures the average proportion of observations not placed in the same cluster under both cases, while the AD measures the average distance between observations placed in the same cluster under both cases and the ADM measures the average distance between cluster centers for observations placed in the same cluster under both cases. The FOM measures the average intra-cluster variance of the deleted column, where the clustering is based on the remaining (undeleted) columns. In all cases the average is taken over all the deleted columns, and all measures should be minimized. For details see the package vignette.

NOTE: The stability function only calculates these measures for the particular column specified by del removed. To get the overall scores, the user must average the measures corresponding to each removed column.

References

Datta, S. and Datta, S. (2003). Comparisons and validation of statistical clustering techniques for microarray gene expression data. Bioinformatics 19(4): 459-466.

See Also

For a description of the function 'clValid' see clValid.

For a description of the class 'clValid' and all available methods see clValidObj or clValid-class.

For additional help on the other validation measures see connectivity, dunn, BSI, and BHI.

Examples

# NOT RUN {
data(mouse)
express <- mouse[1:25,c("M1","M2","M3","NC1","NC2","NC3")]
rownames(express) <- mouse$ID[1:25]
## hierarchical clustering
Dist <- dist(express,method="euclidean")
clusterObj <- hclust(Dist, method="average")
nc <- 4 ## number of clusters      
cluster <- cutree(clusterObj,nc)

stab <- matrix(0,nrow=ncol(express),ncol=4)
colnames(stab) <- c("APN","AD","ADM","FOM")

## Need loop over all removed samples
for (del in 1:ncol(express)) {
  matDel <- express[,-del]               
  DistDel <- dist(matDel,method="euclidean")
  clusterObjDel <- hclust(DistDel, method="average")
  clusterDel <- cutree(clusterObjDel,nc)
  stab[del,] <- stability(express, Dist, del, cluster, clusterDel)
}
colMeans(stab)

# }