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I want to know whether Agglomerative Hierarchical clustering draws non-convex cluster boundaries. From sklearn's comparing diff clustering algorithm experiment it seems like Agglomerative clustering can form non-convex clustering even though it is a distance based method. I don't understand how that's possible.sklearn experiment

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    $\begingroup$ My suggestion is to develop your intuition by drawing a few points on a piece of paper in a non-convex configuration and apply the hierarchical clustering algorithm. Do this a few times for different configurations; depending on the spacing of the points and the clusters, you'll find that sometimes you achieve a nice clustering and sometimes you don't. $\endgroup$
    – Sycorax
    Commented Oct 21, 2019 at 13:09
  • $\begingroup$ The below page provides a wonderful example of how non-convex clustering is achieved using a single-link agglomerative method and K-Means https://pafnuty.wordpress.com/2013/08/14/non-convex-sets-with-k-means-and-hierarchical-clustering/ $\endgroup$
    – Narasim Y
    Commented Mar 25, 2021 at 6:09

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Yes, it produces non-convex clusters.

You have an example in your screenshot.

But also no: it does not "draw cluster boundaries". There is no concept of a cluster boundary in hierarchical clustering. Clusters are just sets of points.

In particular single-linkage tends to form "chains" that can be non-convex. Since it uses nearest neighbors only, it ignores the overall shape of the cluster.

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Firstly there is no concept of cluster boundry in hierarchical clustering. Yes, so why it creates non convex clusters is because, it uses neareast neighbours methods for linkage. So the shape of cluster does not matter.

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