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When would I use each and when would they give me the same results?

Luis
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    `When would I use each`: oserve their differences http://stats.stackexchange.com/q/195446/3277. `when would they give me the same results?` I by results you mean the best clustering partition you arrive at based on the agglomaration history - then, obviously, same results will be given by the data with very strongly separated, clear clusters. – ttnphns Jul 20 '16 at 07:33

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Single link - You link two clusters based on the minimum distance between 2 elements. A drawback of this method is that it tends to produce long thin clusters since you make the link based on only 2 points.

Complete link - You link two clusters based on the max distance between 2 elements. Opposite problem with single link. Clusters tend to be overly conservative.

Average link - Instead of making a decision based on a single pair of elements, you take the distance between every pair of elements.

When in doubt, use average link for hierarchical clustering if your computation allows it!