<s>
The	O
Partial	B-General_Concept
Area	I-General_Concept
Under	I-General_Concept
the	I-General_Concept
ROC	I-General_Concept
Curve	I-General_Concept
(	O
pAUC	O
)	O
is	O
a	O
metric	O
for	O
the	O
performance	O
of	O
binary	O
classifier	O
.	O
</s>
<s>
It	O
is	O
computed	O
based	O
on	O
the	O
receiver	B-Algorithm
operating	I-Algorithm
characteristic	I-Algorithm
(	O
ROC	O
)	O
curve	O
that	O
illustrates	O
the	O
diagnostic	O
ability	O
of	O
a	O
given	O
binary	O
classifier	O
system	O
as	O
its	O
discrimination	O
threshold	O
is	O
varied	O
.	O
</s>
<s>
The	O
ROC	B-Algorithm
curve	I-Algorithm
is	O
created	O
by	O
plotting	O
the	O
true	O
positive	O
rate	O
(	O
TPR	O
)	O
against	O
the	O
false	B-General_Concept
positive	I-General_Concept
rate	I-General_Concept
(	O
FPR	O
)	O
at	O
various	O
threshold	O
settings.The	O
area	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
(	O
AUC	O
)	O
is	O
often	O
used	O
to	O
summarize	O
in	O
a	O
single	O
number	O
the	O
diagnostic	O
ability	O
of	O
the	O
classifier	O
.	O
</s>
<s>
The	O
AUC	O
is	O
simply	O
defined	O
as	O
the	O
area	O
of	O
the	O
ROC	O
space	O
that	O
lies	O
below	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
To	O
overcome	O
this	O
limitation	O
of	O
AUC	O
,	O
it	O
was	O
proposed	O
to	O
compute	O
the	O
area	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
in	O
the	O
area	O
of	O
the	O
ROC	O
space	O
that	O
corresponds	O
to	O
interesting	O
(	O
i.e.	O
,	O
practically	O
viable	O
or	O
acceptable	O
)	O
values	O
of	O
FPR	O
and	O
TPR	O
.	O
</s>
<s>
the	O
classifiers’	O
ROC	B-Algorithm
curves	I-Algorithm
cross	O
each	O
other	O
.	O
</s>
<s>
These	O
performance	O
metrics	O
are	O
commonly	O
known	O
as	O
“	O
partial	O
AUC	O
”	O
(	O
pAUC	O
)	O
:	O
the	O
pAUC	O
is	O
the	O
area	O
of	O
the	O
selected	O
region	O
of	O
the	O
ROC	O
space	O
that	O
lies	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
The	O
idea	O
of	O
the	O
partial	O
AUC	O
was	O
originally	O
proposed	O
with	O
the	O
goal	O
of	O
restricting	O
the	O
evaluation	O
of	O
given	O
ROC	B-Algorithm
curves	I-Algorithm
in	O
the	O
range	O
of	O
false	B-General_Concept
positive	I-General_Concept
rates	I-General_Concept
that	O
are	O
considered	O
interesting	O
for	O
diagnostic	O
purposes	O
.	O
</s>
<s>
Thus	O
,	O
the	O
partial	O
AUC	O
was	O
computed	O
as	O
the	O
area	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
in	O
the	O
vertical	O
band	O
of	O
the	O
ROC	O
space	O
where	O
FPR	O
is	O
in	O
the	O
range	O
[	O
,	O
]	O
.	O
</s>
<s>
when	O
comparing	O
two	O
classifiers	O
via	O
the	O
associated	O
ROC	B-Algorithm
curves	I-Algorithm
,	O
a	O
relatively	O
small	O
change	O
in	O
selecting	O
the	O
RoI	O
may	O
lead	O
to	O
different	O
conclusions	O
:	O
in	O
the	O
example	O
above	O
,	O
considering	O
the	O
band	O
where	O
leads	O
to	O
conclude	O
that	O
is	O
better	O
,	O
while	O
considering	O
the	O
band	O
where	O
leads	O
to	O
conclude	O
that	O
is	O
better	O
.	O
</s>
<s>
Another	O
type	O
of	O
partial	O
AUC	O
is	O
obtained	O
by	O
constraining	O
the	O
true	O
positive	O
rate	O
,	O
rather	O
than	O
the	O
false	B-General_Concept
positive	I-General_Concept
rate	I-General_Concept
.	O
</s>
<s>
That	O
is	O
,	O
the	O
partial	O
AUC	O
is	O
the	O
area	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
and	O
above	O
the	O
horizontal	O
line	O
.	O
</s>
<s>
by	O
limiting	O
the	O
false	B-General_Concept
positive	I-General_Concept
rate	I-General_Concept
,	O
a	O
limit	O
on	O
the	O
false	B-General_Concept
positive	I-General_Concept
rate	I-General_Concept
is	O
also	O
implicitly	O
set	O
;	O
</s>
<s>
when	O
comparing	O
two	O
classifiers	O
via	O
the	O
associated	O
ROC	B-Algorithm
curves	I-Algorithm
,	O
a	O
relatively	O
small	O
change	O
in	O
selecting	O
the	O
RoI	O
may	O
lead	O
to	O
different	O
conclusions	O
:	O
this	O
happens	O
when	O
is	O
close	O
to	O
the	O
point	O
where	O
the	O
given	O
ROC	B-Algorithm
curves	I-Algorithm
cross	O
each	O
other	O
.	O
</s>
<s>
The	O
two-way	O
pAUC	O
is	O
the	O
area	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
that	O
belongs	O
to	O
such	O
rectangle	O
.	O
</s>
<s>
As	O
with	O
the	O
pAUC	O
described	O
above	O
,	O
when	O
comparing	O
two	O
classifiers	O
via	O
the	O
associated	O
ROC	B-Algorithm
curves	I-Algorithm
,	O
a	O
relatively	O
small	O
change	O
in	O
selecting	O
the	O
RoI	O
may	O
lead	O
to	O
different	O
conclusions	O
.	O
</s>
<s>
RRA	O
=	O
1	O
indicates	O
perfect	O
accuracy	O
,	O
while	O
RRA	O
=	O
0	O
indicates	O
that	O
the	O
area	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
belonging	O
to	O
the	O
RoI	O
is	O
null	O
;	O
thus	O
accuracy	O
is	O
no	O
better	O
than	O
random	O
classification	O
's	O
.	O
</s>
<s>
One	O
of	O
the	O
most	O
popular	O
is	O
the	O
Phi	B-General_Concept
coefficient	I-General_Concept
(	O
also	O
known	O
as	O
the	O
Matthews	B-General_Concept
Correlation	I-General_Concept
Coefficient	I-General_Concept
)	O
.	O
</s>
<s>
The	O
pAUC	O
is	O
the	O
area	O
above	O
the	O
ellipse	O
and	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
It	O
is	O
common	O
practice	O
to	O
select	O
as	O
the	O
best	O
classification	O
the	O
point	O
of	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
with	O
the	O
highest	O
value	O
of	O
Youden	O
’s	O
J	O
=	O
TPR−FPR	O
.	O
</s>
<s>
Software	O
libraries	O
to	O
compute	O
pAUC	O
and	O
RRA	O
are	O
available	O
for	O
Python	B-Language
and	O
R	B-Language
.	O
</s>
