If they belong to the same partition T and

they also in the same cluster C, in that case, this is a true positive.

For example, we look at this case.

The definition is the true positive is a number of such cases, okay?

For example, for any two points x sub i and x sub j,

if they have the same true partition label and

they also have the same cluster label, that means they belong

to the same cluster, then that's the case of true positive.

For example, we just look at this case.

For these two blue points, they belong to the same

ground truth T2 and also they belong to the same cluster C2.

That's true positive.

Okay.

Then what is false negative?

False negative means they have the same ground-truth partition label,

but on the other hand they are not in the same cluster.

For example, you just look at these two brown points.

They have the same ground-truth T1, but they belong to different, clusters.

So that's the false negative case.

Well, what is false positive?

False positive means they actually have different partition label,

but they are in the same cluster.

For example, just look at this blue one and this brown one.

They actually do not have the same partition label but

they are in the same cluster, okay.

What is true negative?

True negative pairs actually means that they do not have the same

partition label but they are also not in the same cluster.

For example, if you look at this black one and this blue one.

These two points, they do not have the same partition label,

but they are also not in the same cluster.

So that's a good case.

Then we see how we can calculate the four measures.

First, given n points in the data sets, the possible pairs you need to examine,

actually the n chooses two, so that's the reason you have this formula.

Then for the true positive case is you get all the, the partitions and

the clusters, if they agree to each other, that's the case you have n i j,

you choose any, these case you choose any two, you get that many cases.