Computes the prediction strength of a clustering of a dataset into different numbers of components. The prediction strength is defined according to Tibshirani and Walther (2005), who recommend to choose as optimal number of cluster the largest number of clusters that leads to a prediction strength above 0.8 or 0.9. See details.
Various clustering methods can be used, see argument
clustermethod. In Tibshirani and Walther (2005), only
classification to the nearest centroid is discussed, but more methods
are offered here, see argument classification.
prediction.strength(xdata, Gmin=2, Gmax=10, M=50,
clustermethod=kmeansCBI,
classification="centroid", centroidname = NULL,
cutoff=0.8,nnk=1,
distances=inherits(xdata,"dist"),count=FALSE,...)
# S3 method for predstr
print(x, ...)prediction.strength gives out an object of class
predstr, which is a
list with components
list of vectors of length M with relative
frequencies of correct predictions (clusterwise minimum). Every list
entry refers to a certain number of clusters.
means of predcorr for all numbers of
clusters.
optimal number of clusters.
see above.
a string identifying the clustering method.
see above.
see above.
data (something that can be coerced into a matrix).
integer. Minimum number of clusters. Note that the
prediction strength for 1 cluster is trivially 1, which is
automatically included if GMin>1. Therefore GMin<2 is
useless.
integer. Maximum number of clusters.
integer. Number of times the dataset is divided into two halves.
an interface function (the function name, not a
string containing the name, has to be provided!). This defines the
clustering method. See the "Details"-section of clusterboot
and kmeansCBI for the format. Clustering methods for
prediction.strength must have a k-argument for the number of
clusters, must operate on n times p data matrices
and must otherwise follow the specifications in
clusterboot
Note that prediction.strength won't work
with CBI-functions that implicitly already estimate the number of
clusters such as pamkCBI; use claraCBI
if you want to run it for pam/clara clustering.
string.
This determines how non-clustered points are classified to given
clusters. Options are explained in classifnp and
classifdist, the latter for dissimilarity data.
Certain classification methods are connected to certain clustering
methods. classification="averagedist" is recommended for
average linkage, classification="centroid" is recommended for
k-means, clara and pam (with distances it will work with
claraCBI only), classification="knn" with
nnk=1 is recommended for single linkage and
classification="qda" is recommended for Gaussian mixtures
with flexible covariance matrices.
string. Indicates the name of the component of
CBIoutput$result that contains the cluster centroids in case of
classification="centroid", where CBIoutput is the
output object of clustermethod. If clustermethod is
kmeansCBI or claraCBI, centroids are recognised
automatically if centroidname=NULL. If
centroidname=NULL and distances=FALSE, cluster means
are computed as the cluster centroids.
numeric between 0 and 1. The optimal number of clusters
is the maximum one with prediction strength above cutoff.
number of nearest neighbours if
classification="knn", see classifnp.
logical. If TRUE, data will be interpreted as
dissimilarity matrix, passed on to clustering methods as
"dist"-object, and classifdist will be used for
classification.
logical. TRUE will print current number of
clusters and simulation run number on the screen.
object of class predstr.
arguments to be passed on to the clustering method.
Christian Hennig christian.hennig@unibo.it https://www.unibo.it/sitoweb/christian.hennig/en/
The prediction strength for a certain number of clusters k under a
random partition of the dataset in halves A and B is defined as
follows. Both halves are clustered with k clusters. Then the points of
A are classified to the clusters of B. In the original paper
this is done by assigning every
observation in A to the closest cluster centroid in B (corresponding
to classification="centroid"), but other methods are possible,
see classifnp. A pair of points A in
the same A-cluster is defined to be correctly predicted if both points
are classified into the same cluster on B. The same is done with the
points of B relative to the clustering on A. The prediction strength
for each of the clusterings is the minimum (taken over all clusters)
relative frequency of correctly predicted pairs of points of that
cluster. The final mean prediction strength statistic is the mean over
all 2M clusterings.
Tibshirani, R. and Walther, G. (2005) Cluster Validation by Prediction Strength, Journal of Computational and Graphical Statistics, 14, 511-528.
kmeansCBI, classifnp
options(digits=3)
set.seed(98765)
iriss <- iris[sample(150,20),-5]
prediction.strength(iriss,2,3,M=3)
prediction.strength(iriss,2,3,M=3,clustermethod=claraCBI)
# The examples are fast, but of course M should really be larger.
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