Documentation |
Package: clustering.evaluation
Superclasses: clustering.evaluation.ClusterCriterion
Davies-Bouldin criterion clustering evaluation object
clustering.evaluation.DaviesBouldinEvaluation is an object consisting of sample data, clustering data, and Davies-Bouldin criterion values used to evaluate the optimal number of clusters. Create a Davies-Bouldin criterion clustering evaluation object using evalclusters.
eva = evalclusters(x,clust,'DaviesBouldin') creates a Davies-Bouldin criterion clustering evaluation object.
eva = evalclusters(x,clust,'DaviesBouldin',Name,Value) creates a Davies-Bouldin 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 Davies-Bouldin criterion is based on a ratio of within-cluster and between-cluster distances. The Davies-Bouldin index is defined as
$$DB=\frac{1}{k}{\displaystyle \sum _{i=1}^{k}{\mathrm{max}}_{j\ne i}\left\{{D}_{i,j}\right\},}$$
where D_{i,j} is the within-to-between cluster distance ratio for the ith and jth clusters. In mathematical terms,
$${D}_{i,j}=\frac{\left({\overline{d}}_{i}+{\overline{d}}_{j}\right)}{{d}_{i,j}}.$$
$${\overline{d}}_{i}$$ is the average distance between each point in the ith cluster and the centroid of the ith cluster. $${\overline{d}}_{j}$$ is the average distance between each point in the ith cluster and the centroid of the jth cluster. $${d}_{i,j}$$ is the Euclidean distance between the centroids of the ith and jth clusters.
The maximum value of D_{i,j} represents the worst-case within-to-between cluster ratio for cluster i. The optimal clustering solution has the smallest Davies-Bouldin index value.