Bagged Clustering

Cluster the data in x using the bagged clustering algorithm. A partitioning cluster algorithm such as kmeans is run repeatedly on bootstrap samples from the original data. The resulting cluster centers are then combined using the hierarchical cluster algorithm hclust.

Usage

bclust(x, centers=2, iter.base=10, minsize=0,
       dist.method="euclidean",
       hclust.method="average", base.method="kmeans",
       base.centers=20, verbose=TRUE,
       final.kmeans=FALSE, docmdscale=FALSE,
       resample=TRUE, weights=NULL, maxcluster=base.centers, ...)
hclust.bclust(object, x, centers, dist.method=object$dist.method,
              hclust.method=object$hclust.method, final.kmeans=FALSE,
              docmdscale = FALSE, maxcluster=object$maxcluster)
# S3 method for class 'bclust'
plot(x, maxcluster=x$maxcluster, main, ...)
centers.bclust(object, k)
clusters.bclust(object, k, x=NULL)

Arguments

x: Matrix of inputs (or object of class "bclust" for plot).
centers, k: Number of clusters.
iter.base: Number of runs of the base cluster algorithm.
minsize: Minimum number of points in a base cluster.
dist.method: Distance method used for the hierarchical clustering, see dist for available distances.
hclust.method: Linkage method used for the hierarchical clustering, see hclust for available methods.
base.method: Partitioning cluster method used as base algorithm.
base.centers: Number of centers used in each repetition of the base method.
verbose: Output status messages.
final.kmeans: If TRUE, a final kmeans step is performed using the output of the bagged clustering as initialization.
docmdscale: Logical, if TRUE a cmdscale result is included in the return value.
resample: Logical, if TRUE the base method is run on bootstrap samples of x, else directly on x.
weights: Vector of length nrow(x), weights for the resampling. By default all observations have equal weight.
maxcluster: Maximum number of clusters memberships are to be computed for.
object: Object of class "bclust".
main: Main title of the plot.
...: Optional arguments top be passed to the base method in bclust, ignored in plot.

Details

First, iter.base bootstrap samples of the original data in x are created by drawing with replacement. The base cluster method is run on each of these samples with base.centers centers. The base.method must be the name of a partitioning cluster function returning a list with the same components as the return value of kmeans.

This results in a collection of iter.base * base.centers centers, which are subsequently clustered using the hierarchical method hclust. Base centers with less than minsize points in there respective partitions are removed before the hierarchical clustering.

The resulting dendrogram is then cut to produce centers clusters. Hence, the name of the argument centers is a little bit misleading as the resulting clusters need not be convex, e.g., when single linkage is used. The name was chosen for compatibility with standard partitioning cluster methods such as kmeans.

A new hierarchical clustering (e.g., using another hclust.method) re-using previous base runs can be performed by running hclust.bclust on the return value of bclust.

Value

bclust and hclust.bclust return objects of class "bclust" including the components

hclust: Return value of the hierarchical clustering of the collection of base centers (Object of class "hclust").
cluster: Vector with indices of the clusters the inputs are assigned to.
centers: Matrix of centers of the final clusters. Only useful, if the hierarchical clustering method produces convex clusters.
allcenters: Matrix of all iter.base * base.centers centers found in the base runs.

Author

Friedrich Leisch

References

Friedrich Leisch. Bagged clustering. Working Paper 51, SFB “Adaptive Information Systems and Modeling in Economics and Management Science”, August 1999. doi:10.57938/9b129f95-b53b-44ce-a129-5b7a1168d832

Examples

data(iris)
bc1 <- bclust(iris[,1:4], 3, base.centers=5)
#> Committee Member: 1(1) 2(1) 3(1) 4(1) 5(1) 6(1) 7(1) 8(1) 9(1) 10(1)
#> Computing Hierarchical Clustering
plot(bc1)


table(clusters.bclust(bc1, 3))
#> 
#>  1  2  3 
#> 72 50 28 
centers.bclust(bc1, 3)
#>          [,1]     [,2]     [,3]     [,4]
#> [1,] 5.919204 2.763804 4.426290 1.456563
#> [2,] 5.022182 3.454259 1.458944 0.247232
#> [3,] 7.078234 3.142672 5.959044 2.114061