Gini = pLp
0
Lp
1
L + pRp
0
Rp
1
R
Now suppose the distance of two examples e1 and e2 is de-
fined only on class information:
δ(e1, e2) = ½
0 if e1 and e2 share the same class
1 otherwise
Then the within-cluster average distance weighted on the
left and right subsets can be written as:
pL
P
ei,ej∈SL
δ(ei
, ej )
|SL|
2
+ pR
P
ei,ej∈SR
δ(ei
, ej )
|SR|
2
= pL
2|S
0
L
||S
1
L
|
|SL|
2
+ pR
2|S
0
R||S
1
R|
|SR|
2
= 2(pLp
0
Lp
1
L + pRp
0
Rp
1
R)
∝ Gini