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

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

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

Criterion values corresponding to each proposed number of clusters
in 

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 DaviesBouldin criterion is based on a ratio of withincluster and betweencluster distances. The DaviesBouldin 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 withintobetween 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 jth 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 worstcase withintobetween cluster ratio for cluster i. The optimal clustering solution has the smallest DaviesBouldin index value.
[1] Davies, D. L., and D. W. Bouldin. "A Cluster Separation Measure." IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. PAMI1, No. 2, 1979, pp. 224–227.