# How to compute FN and TN explicitly?

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

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

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 !

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: $${17\choose 2}-40=96$$

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