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I have this idea where I want to compute the number of clusters in subsets of the full dataset and compare this number with the total number of clusters for the full dataset as a metric for the diversity of the subset of data. For example, if the full dataset has 20 clusters and a subset of the dataset contains 10 clusters, than the "diversity score" would be 0.50. However, one problem here is that I don't know if it necessarily the case that this number is bounded by 0 and 1. It could be possible that there are more clusters in the data subset, correct?

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    $\begingroup$ It is not clear whether your $10$ clusters are a subset of your $20$ clusters. If they are then clearly the ratio is in $[0,1]$ $\endgroup$
    – Henry
    Jul 2, 2021 at 16:25
  • $\begingroup$ Exactly! So is it the case that the 10 clusters are a subset of the 20 clusters? Or is this not necessarily a requirement? I believe this certainly could happen, but more likely would not. Correct? $\endgroup$
    – Evan
    Jul 8, 2021 at 19:02
  • $\begingroup$ I meant that is is not clear whether you decided that the $10$ clusters must be a subset of the $20$ clusters by seeing which of the $20$ clusters had elements of the subset. In that case then clearly the ratio is in [0,1]. Or whether you had some undescribed method for deciding the number of clusters for each set (ignoring what was decided for other set), in which case the ratio could be almost anything rational $\endgroup$
    – Henry
    Jul 8, 2021 at 20:29

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