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**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

where *D*_{i,j} is the
within-to-between cluster distance ratio for the *i*th
and *j*th clusters. In mathematical terms,

is the average distance between
each point in the *i*th cluster and the centroid
of the *i*th cluster.
is the average distance between
each point in the *i*th cluster and the centroid
of the *j*th cluster.
is the Euclidean distance between
the centroids of the *i*th and *j*th
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.

[1] Davies, D. L., and D. W. Bouldin. "A Cluster Separation
Measure." *IEEE Transactions on Pattern Analysis
and Machine Intelligence*. Vol. PAMI-1, No. 2, 1979, pp.
224–227.

`clustering.evaluation.CalinskiHarabaszEvaluation` | `clustering.evaluation.GapEvaluation` | `clustering.evaluation.SilhouetteEvaluation` | `evalclusters`

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