289 Clustering in Central Disorders of Hypersomnolence members of its cluster. Besides, consider all clusters of which pi is not a member, and for each, consider the mean distance between pi and its members. Let b(pi) be the minimum of these mean distances. If a(pi) < b(pi), the silhouette s(pi) = 1 – a(pi) / b(pi) > 0. (This is the preferred case.) If a(pi) = b(pi), the silhouette s(pi) = 0. If a(pi) > b(pi), the silhouette s(pi) = b(pi) / a(pi) – 1 < 0. Although the choice of linkage type affects how clusters form, it does not affect the definition of this outcome measure. Dunn index Like the silhouette, the family of Dunn-like indices attempts to capture the distinctness of the clusters. However, it is not defined on a per-individual basis but for the dataset as a whole. We define the Dunn index (DI) as the ratio between the smallest inter-cluster distance and the largest intra-cluster distance. As such, it is high only if all clusters are compact relative to even the smallest separation between clusters. Note that, due to the inclusion of the inter-cluster distance in the definition, the Dunn index depends on the choice of linkage type. It is defined only when at least one cluster has at least two distinct individuals. Other Dunn-like indices can be defined by quantifying the notion of cluster compactness differently. 9
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