<s>
The	O
Rand	B-General_Concept
index	I-General_Concept
or	O
Rand	B-General_Concept
measure	I-General_Concept
(	O
named	O
after	O
William	O
M	O
.	O
Rand	O
)	O
in	O
statistics	O
,	O
and	O
in	O
particular	O
in	O
data	B-Algorithm
clustering	I-Algorithm
,	O
is	O
a	O
measure	O
of	O
the	O
similarity	O
between	O
two	O
data	B-Algorithm
clusterings	I-Algorithm
.	O
</s>
<s>
A	O
form	O
of	O
the	O
Rand	B-General_Concept
index	I-General_Concept
may	O
be	O
defined	O
that	O
is	O
adjusted	O
for	O
the	O
chance	O
grouping	O
of	O
elements	O
,	O
this	O
is	O
the	O
adjusted	O
Rand	B-General_Concept
index	I-General_Concept
.	O
</s>
<s>
From	O
a	O
mathematical	O
standpoint	O
,	O
Rand	B-General_Concept
index	I-General_Concept
is	O
related	O
to	O
the	O
accuracy	O
,	O
but	O
is	O
applicable	O
even	O
when	O
class	O
labels	O
are	O
not	O
used	O
.	O
</s>
<s>
The	O
Rand	B-General_Concept
index	I-General_Concept
,	O
,	O
is	O
:	O
</s>
<s>
Similarly	O
,	O
one	O
can	O
also	O
view	O
the	O
Rand	B-General_Concept
index	I-General_Concept
as	O
a	O
measure	O
of	O
the	O
percentage	O
of	O
correct	O
decisions	O
made	O
by	O
the	O
algorithm	O
.	O
</s>
<s>
The	O
Rand	B-General_Concept
index	I-General_Concept
has	O
a	O
value	O
between	O
0	O
and	O
1	O
,	O
with	O
0	O
indicating	O
that	O
the	O
two	O
data	B-Algorithm
clusterings	I-Algorithm
do	O
not	O
agree	O
on	O
any	O
pair	O
of	O
points	O
and	O
1	O
indicating	O
that	O
the	O
data	B-Algorithm
clusterings	I-Algorithm
are	O
exactly	O
the	O
same	O
.	O
</s>
<s>
The	O
Rand	B-General_Concept
index	I-General_Concept
can	O
also	O
be	O
viewed	O
through	O
the	O
prism	O
of	O
binary	O
classification	O
accuracy	O
over	O
the	O
pairs	O
of	O
elements	O
in	O
.	O
</s>
<s>
The	O
adjusted	O
Rand	B-General_Concept
index	I-General_Concept
is	O
the	O
corrected-for-chance	O
version	O
of	O
the	O
Rand	B-General_Concept
index	I-General_Concept
.	O
</s>
<s>
Traditionally	O
,	O
the	O
Rand	B-General_Concept
Index	I-General_Concept
was	O
corrected	O
using	O
the	O
Permutation	O
Model	O
for	O
clusterings	O
(	O
the	O
number	O
and	O
size	O
of	O
clusters	O
within	O
a	O
clustering	O
are	O
fixed	O
,	O
and	O
all	O
random	O
clusterings	O
are	O
generated	O
by	O
shuffling	O
the	O
elements	O
between	O
the	O
fixed	O
clusters	O
)	O
.	O
</s>
<s>
For	O
example	O
,	O
consider	O
that	O
in	O
K-means	B-Algorithm
the	O
number	O
of	O
clusters	O
is	O
fixed	O
by	O
the	O
practitioner	O
,	O
but	O
the	O
sizes	O
of	O
those	O
clusters	O
are	O
inferred	O
from	O
the	O
data	O
.	O
</s>
<s>
Variations	O
of	O
the	O
adjusted	O
Rand	B-General_Concept
Index	I-General_Concept
account	O
for	O
different	O
models	O
of	O
random	O
clusterings	O
.	O
</s>
<s>
Though	O
the	O
Rand	B-General_Concept
Index	I-General_Concept
may	O
only	O
yield	O
a	O
value	O
between	O
0	O
and	O
+1	O
,	O
the	O
adjusted	O
Rand	B-General_Concept
index	I-General_Concept
can	O
yield	O
negative	O
values	O
if	O
the	O
index	O
is	O
less	O
than	O
the	O
expected	O
index	O
.	O
</s>
