The precision define is for this particular matching what you want to see

is for precision T sub i what you want to find is

what's a maximum y matching this particular cluster then divide

by the number of total number of points in this cluster so

in that sense your precision actually is the same as purity.

That means if you get a fraction of C sub i from the majority partition of C sub j.

Then the j's partition contains a max number of

points from C sub i then you get this formula.

For this formula, you get this the precision and the purity,

actually this one is the same.

You will get 30/50, 20/25 and 25/25.

Okay, that's the precision, what about recall?

Recall actually is the fraction of the points in the partition

shared in common with cluster C sub i.

Simply says, if you assign T3 to C1,

what you want to see is you've got a 30 but

T3 actually got 35 granted you only capture 30.

That means you're recall is 30 over 35.

That's exactly, you probably can see the formula.

Similarly, for the second partition if you assign

ground truths T2 to C2, what you can see is,

you only get 20/40 so your recall is 20/40.

Similarly for the third one when you assign

the ground truth of T1 to C3 you get 25/25.

That means the fraction of the point in this partition share in

common with the cluster C sub i, then you get this recall.