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Suppose that we have the following clusters ( output of some clustering algorithm ) based on 3 classes : enter image description here

Source : Source link

The source explains how to calculate TP+FP and TP explicitly as following :

enter image description here

I'm confused about how to calculate TN+FN and TN , I'm wanting to know how to calculate those measures ( using the same logic of Combinations ) ?

Thank you in advance for help !

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For FNs (d: diamond), you take pairs of different clusters that should have been in the same cluster:

  • 5x in C1 and 1x in C2 --> 5
  • 5x in C1 and 2x in C3 --> 10
  • 2x in C3 and 1x in C2 --> 2
  • 1o in C1 and 4o in C2 --> 4
  • 1d in C2 and 3d in C3 --> 3

which sums up to 24.

The FN+TN is (TP+FP) subtracted from the total number of combinations: $${17\choose 2}-40=96$$

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  • $\begingroup$ thank you a lot for your precious help ! $\endgroup$ – Tou Mou Aug 14 at 18:59
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    $\begingroup$ I accepted your answer. Your answer clarified plenty of things for me. Thank you a lot for the valuable help! $\endgroup$ – Tou Mou Aug 15 at 18:44

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