Package: clustering.evaluation
Superclasses: clustering.evaluation.ClusterCriterion
Silhouette criterion clustering evaluation object
clustering.evaluation.SilhouetteEvaluation
is
an object consisting of sample data, clustering data, and silhouette
criterion values used to evaluate the optimal number of data clusters.
Create a silhouette criterion clustering evaluation object using evalclusters
.
creates
a silhouette criterion clustering evaluation object.eva
= evalclusters(x
,clust
,'Silhouette')
creates
a silhouette criterion clustering evaluation object using additional
options specified by one or more namevalue pair arguments.eva
= evalclusters(x
,clust
,'Silhouette',Name,Value
)

Clustering algorithm used to cluster the input data, stored
as a valid clustering algorithm name or function handle. If the clustering
solutions are provided in the input, 

Prior probabilities for each cluster, stored as valid prior probability name. 

Silhouette values corresponding to each proposed number of clusters
in 

Name of the criterion used for clustering evaluation, stored as a valid criterion name. 

Criterion values corresponding to each proposed number of clusters
in 

Distance measure used for clustering data, stored as a valid distance measure name. 

List of the number of proposed clusters for which to compute criterion values, stored as a vector of positive integer values. 

Logical flag for excluded data, stored as a column vector of
logical values. If 

Number of observations in the data matrix 

Optimal number of clusters, stored as a positive integer value. 

Optimal clustering solution corresponding to 

Data used for clustering, stored as a matrix of numerical values. 
addK  Evaluate additional numbers of clusters 
compact  Compact clustering evaluation object 
plot  Plot clustering evaluation object criterion values 
The silhouette value for each point is a measure of how similar
that point is to points in its own cluster, when compared to points
in other clusters. The silhouette value for the i
th
point, Si
, is defined as
Si = (biai)/ max(ai,bi)
where ai
is the average distance from the i
th
point to the other points in the same cluster as i
,
and bi
is the minimum average distance from the i
th
point to points in a different cluster, minimized over clusters.
The silhouette value ranges from 1 to +1.
A high silhouette value indicates that i
is wellmatched
to its own cluster, and poorlymatched to neighboring clusters. If
most points have a high silhouette value, then the clustering solution
is appropriate. If many points have a low or negative silhouette value,
then the clustering solution may have either too many or too few clusters.
The silhouette clustering evaluation criterion can be used with any
distance metric.
[1] Kaufman L. and P. J. Rouseeuw. Finding Groups in Data: An Introduction to Cluster Analysis. Hoboken, NJ: John Wiley & Sons, Inc., 1990.
[2] Rouseeuw, P. J. "Silhouettes: a graphical aid to the interpretation and validation of cluster analysis." Journal of Computational and Applied Mathematics. Vol. 20, No. 1, 1987, pp. 53–65.