Documentation |
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.
eva = evalclusters(x,clust,'Silhouette') creates a silhouette criterion clustering evaluation object.
eva = evalclusters(x,clust,'Silhouette',Name,Value) creates a silhouette criterion clustering evaluation object using additional options specified by one or more name-value pair arguments.
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 ith point, Si, is defined as
Si = (bi-ai)/ max(ai,bi)
where ai is the average distance from the ith point to the other points in the same cluster as i, and bi is the minimum average distance from the ith 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 well-matched to its own cluster, and poorly-matched 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.