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There are several threads discussing clustering analysis of a distance matrix and they dismiss use of the k-means algorithm. Here are two examples:

However, it is hard to come by an intuitive (and ideally visual) explanation why it is wrong to apply k-means to a distance matrix. It will be really helpful is someone can explain this.

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    $\begingroup$ Your first link makes the basic point that you cannot calculate a mean without values to average. So it suggested $k$-mediods instead $\endgroup$
    – Henry
    Commented Jun 10, 2021 at 17:18
  • $\begingroup$ My answer to the question in the first link says that it is possible (and how) to apply k-means to a distance matrix and that it is implied that the distances are euclidean. $\endgroup$
    – ttnphns
    Commented Jun 13, 2021 at 10:13

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