clustering 평가 방법 (RI, rand index)

Rand Index (RI)

adjusted rand index는 클러스터의 타깃값을 아는 경우에 사용하는 평가 방법 (supervised inference?)

 

given $S = {o_1, ..., o_n}$, S의 두개의 partition이 존재.

1. $X={X_1, ..., X_r}$ a partition of $S$ into $r$ subset
2. $Y={Y_1, ..., Y_r}$ a partition of $S$ into $s$ subset

• ${\displaystyle a}$, the number of pairs of elements in $S$ that are in the same subset in $X$ and in the same subset in $Y$
• ${\displaystyle b}$, the number of pairs of elements in $S$ that are in different subsets in $X$ and in different subsets in $Y$
• ${\displaystyle c}$, the number of pairs of elements in $S$ that are in the same subset in $X$ and in different subsets in $Y$
• ${\displaystyle d}$, the number of pairs of elements in $S$ that are in different subsets in $X$ and in the same subset in $Y$

	$X_{same}$	$X_{diff}$
$Y_{same}$	a	d
$Y_{diff}$	c	b

$$ R = {a + b \over a+ b+ c+ d} = {a + b \over {n \choose k}}$$

 

Rand Index를 measure of the percentage of correct decisions로 볼 수 있음

$$RI = {TP + TN \over TP+FP+FN+TN}$$

 

 

Reference

• https://scikit-learn.org/stable/modules/generated/sklearn.metrics.adjusted_rand_score.html
• https://en.wikipedia.org/wiki/Rand_index​