2
$\begingroup$

I try to understand Precision and Recall:

I have the following definitions: $P= \frac{TP}{TP + FP}$ and $R=\frac{TP}{FP+FN}$

This are the definitions for TP etc.:

True Positive (TP): when similar points are assigned to the same communities

True Negative (TN): when dissimilar points are assigned to different communities

False Negative (FN): when similar points are assigned to different communities

False Positive (FP): when dissimilar points are assigned to the same communities

There is an example I don't understand: I have two Clusters. The first one has 5 crosses and 1 circle. The second one includes 6 circles and 2 crosses.

1: [cross, cross, cross, cross, cross, circle]

2: [cross, cross, circle, circle, circle, circle, circle, circle]

Now I have this calculation I don't understand:

$TP = \binom{5}{2} + \binom{6}{2} + 1 = 26$

$FP = (5*1) + (6*2) = 17$

$FN = (5*2) + (6*1) = 16$

$TN = (6*5) + (2*1) = 32$

I think I can understand the last three. But the first one is a miracle for me. Can anyone explain me how to calculate TP?

Thank you so much!

$\endgroup$
1
$\begingroup$

The $5 \choose 2$ is the number of pairs of crosses in cluster 1, the $6\choose 2$ is the number of pairs of circles in cluster 2, $1={2 \choose 2}$ is the number of pairs of crosses in cluster 2, and there are ${1 \choose 2}=0$ pairs of circles in cluster 1

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ Thank yo uvery much. Just one other question: If there would be three clusters and in this third one there would be no cross, how would I compute "FN" ? $FN= (5*2*0) + \dots$ or would I skip the zero. Thanks. $\endgroup$ – mathNewbie Jan 6 '15 at 20:37
  • $\begingroup$ I don't know what happens with three communities at all. I just could see where the numbers you asked about came from. $\endgroup$ – Ross Millikan Jan 6 '15 at 21:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.