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The silhouette score is specialized for measuring cluster quality when the clusters are convex-shaped, and may not perform well if the data clusters have irregular shapes or are of varying sizes. [3] The silhouette can be calculated with any distance metric, such as the Euclidean distance or the Manhattan distance.
The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]
The Dunn index, introduced by Joseph C. Dunn in 1974, is a metric for evaluating clustering algorithms. [1] [2] This is part of a group of validity indices including the Davies–Bouldin index or Silhouette index, in that it is an internal evaluation scheme, where the result is based on the clustered data itself.
Similar to other clustering evaluation metrics such as Silhouette score, the CH index can be used to find the optimal number of clusters k in algorithms like k-means, where the value of k is not known a priori. This can be done by following these steps: Perform clustering for different values of k.
The Davies–Bouldin index (DBI), introduced by David L. Davies and Donald W. Bouldin in 1979, is a metric for evaluating clustering algorithms. [1] This is an internal evaluation scheme, where the validation of how well the clustering has been done is made using quantities and features inherent to the dataset.
In statistics, Gower's distance between two mixed-type objects is a similarity measure that can handle different types of data within the same dataset and is particularly useful in cluster analysis or other multivariate statistical techniques.
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The Hopkins statistic (introduced by Brian Hopkins and John Gordon Skellam) is a way of measuring the cluster tendency of a data set. [1] It belongs to the family of sparse sampling tests.