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I am self studying hierarchical clustering and got confused about the concept of linkage, could anyone explain what does it mean? what role does it play in what type of clustering? Any input will be helpful, thanks!

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    $\begingroup$ Hierarchical agglomerative clustering (HAC) stepwisely combines objects in greater and greater, wrt frequency inside, clusters. There arises question how a distance between clusters should be defined. Between two single objects the distance is plain: it's the distance between them in the input distance matrix. But what is the distance between an object and a 2-object cluster? What's the distance between 2-object cluster and 3-object cluster? It could be defined in various ways. And it is what "linkage method" is about. Just take some text on HAC and learn more about it. Also, browse this site. $\endgroup$
    – ttnphns
    Commented Mar 21, 2016 at 19:57
  • $\begingroup$ @ttnphns thank you so much! now this makes a lot more sense. $\endgroup$
    – Jing
    Commented Mar 21, 2016 at 20:12

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Linkage is how you compute the distance between clusters in hierarchical clustering. So linkage is a part of hierarchical clustering.

  • minimum of pairwise distances = single linkage
  • maximum of pairwise distance = complete linkage
  • average of the pairwise distances = average linkage (there are two; depending on how you weight the averages)

For 1-element clusters, all the linkages reduce to the regular point-to-point distance. So they only matter for clusters.

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