<s>
A	O
receiver	B-Algorithm
operating	I-Algorithm
characteristic	I-Algorithm
curve	I-Algorithm
,	O
or	O
ROC	B-Algorithm
curve	I-Algorithm
,	O
is	O
a	O
graphical	B-Application
plot	I-Application
that	O
illustrates	O
the	O
diagnostic	O
ability	O
of	O
a	O
binary	B-General_Concept
classifier	I-General_Concept
system	O
as	O
its	O
discrimination	O
threshold	O
is	O
varied	O
.	O
</s>
<s>
The	O
method	O
was	O
originally	O
developed	O
for	O
operators	O
of	O
military	O
radar	B-Application
receivers	O
starting	O
in	O
1941	O
,	O
which	O
led	O
to	O
its	O
name	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	O
.	O
</s>
<s>
The	O
true-positive	O
rate	O
is	O
also	O
known	O
as	O
sensitivity	O
,	O
recall	O
or	O
probability	B-General_Concept
of	I-General_Concept
detection	I-General_Concept
.	O
</s>
<s>
The	O
false-positive	O
rate	O
is	O
also	O
known	O
as	O
probability	O
of	O
false	B-Error_Name
alarm	I-Error_Name
and	O
can	O
be	O
calculated	O
as	O
(	O
1	O
−	O
specificity	O
)	O
.	O
</s>
<s>
The	O
ROC	O
can	O
also	O
be	O
thought	O
of	O
as	O
a	O
plot	O
of	O
the	O
power	B-General_Concept
as	O
a	O
function	O
of	O
the	O
Type	O
I	O
Error	O
of	O
the	O
decision	O
rule	O
(	O
when	O
the	O
performance	O
is	O
calculated	O
from	O
just	O
a	O
sample	O
of	O
the	O
population	O
,	O
it	O
can	O
be	O
thought	O
of	O
as	O
estimators	O
of	O
these	O
quantities	O
)	O
.	O
</s>
<s>
The	O
ROC	B-Algorithm
curve	I-Algorithm
is	O
thus	O
the	O
sensitivity	O
or	O
recall	O
as	O
a	O
function	O
of	O
fall-out	B-General_Concept
.	O
</s>
<s>
In	O
general	O
,	O
if	O
the	O
probability	O
distributions	O
for	O
both	O
detection	O
and	O
false	B-Error_Name
alarm	I-Error_Name
are	O
known	O
,	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
can	O
be	O
generated	O
by	O
plotting	O
the	O
cumulative	O
distribution	O
function	O
(	O
area	O
under	O
the	O
probability	O
distribution	O
from	O
to	O
the	O
discrimination	O
threshold	O
)	O
of	O
the	O
detection	O
probability	O
in	O
the	O
y-axis	O
versus	O
the	O
cumulative	O
distribution	O
function	O
of	O
the	O
false-alarm	O
probability	O
on	O
the	O
x-axis	O
.	O
</s>
<s>
ROC	B-Algorithm
analysis	I-Algorithm
provides	O
tools	O
to	O
select	O
possibly	O
optimal	O
models	O
and	O
to	O
discard	O
suboptimal	O
ones	O
independently	O
from	O
(	O
and	O
prior	O
to	O
specifying	O
)	O
the	O
cost	O
context	O
or	O
the	O
class	O
distribution	O
.	O
</s>
<s>
ROC	B-Algorithm
analysis	I-Algorithm
is	O
related	O
in	O
a	O
direct	O
and	O
natural	O
way	O
to	O
cost/benefit	O
analysis	O
of	O
diagnostic	O
decision	O
making	O
.	O
</s>
<s>
The	O
ROC	B-Algorithm
curve	I-Algorithm
was	O
first	O
developed	O
by	O
electrical	O
engineers	O
and	O
radar	B-Application
engineers	O
during	O
World	O
War	O
II	O
for	O
detecting	O
enemy	O
objects	O
in	O
battlefields	O
and	O
was	O
soon	O
introduced	O
to	O
psychology	O
to	O
account	O
for	O
perceptual	O
detection	O
of	O
stimuli	O
.	O
</s>
<s>
ROC	B-Algorithm
analysis	I-Algorithm
since	O
then	O
has	O
been	O
used	O
in	O
medicine	O
,	O
radiology	O
,	O
biometrics	O
,	O
forecasting	O
of	O
natural	O
hazards	O
,	O
meteorology	O
,	O
model	O
performance	O
assessment	O
,	O
and	O
other	O
areas	O
for	O
many	O
decades	O
and	O
is	O
increasingly	O
used	O
in	O
machine	O
learning	O
and	O
data	B-Application
mining	I-Application
research	O
.	O
</s>
<s>
A	O
classification	O
model	O
(	O
classifier	B-General_Concept
or	O
diagnosis	O
)	O
is	O
a	O
mapping	B-Algorithm
of	O
instances	O
between	O
certain	O
classes/groups	O
.	O
</s>
<s>
Because	O
the	O
classifier	B-General_Concept
or	O
diagnosis	O
result	O
can	O
be	O
an	O
arbitrary	O
real	O
value	O
(	O
continuous	O
output	O
)	O
,	O
the	O
classifier	B-General_Concept
boundary	O
between	O
classes	O
must	O
be	O
determined	O
by	O
a	O
threshold	O
value	O
(	O
for	O
instance	O
,	O
to	O
determine	O
whether	O
a	O
person	O
has	O
hypertension	O
based	O
on	O
a	O
blood	O
pressure	O
measure	O
)	O
.	O
</s>
<s>
Consider	O
a	O
two-class	O
prediction	O
problem	O
(	O
binary	B-General_Concept
classification	I-General_Concept
)	O
,	O
in	O
which	O
the	O
outcomes	O
are	O
labeled	O
either	O
as	O
positive	O
(	O
p	O
)	O
or	O
negative	O
(	O
n	O
)	O
.	O
</s>
<s>
There	O
are	O
four	O
possible	O
outcomes	O
from	O
a	O
binary	B-General_Concept
classifier	I-General_Concept
.	O
</s>
<s>
The	O
four	O
outcomes	O
can	O
be	O
formulated	O
in	O
a	O
2×2	O
contingency	B-Application
table	I-Application
or	O
confusion	B-General_Concept
matrix	I-General_Concept
,	O
as	O
follows	O
:	O
</s>
<s>
The	O
contingency	B-Application
table	I-Application
can	O
derive	O
several	O
evaluation	O
"	O
metrics	O
"	O
(	O
see	O
infobox	O
)	O
.	O
</s>
<s>
To	O
draw	O
a	O
ROC	B-Algorithm
curve	I-Algorithm
,	O
only	O
the	O
true	O
positive	O
rate	O
(	O
TPR	O
)	O
and	O
false	B-General_Concept
positive	I-General_Concept
rate	I-General_Concept
(	O
FPR	O
)	O
are	O
needed	O
(	O
as	O
functions	O
of	O
some	O
classifier	B-General_Concept
parameter	O
)	O
.	O
</s>
<s>
Each	O
prediction	O
result	O
or	O
instance	O
of	O
a	O
confusion	B-General_Concept
matrix	I-General_Concept
represents	O
one	O
point	O
in	O
the	O
ROC	O
space	O
.	O
</s>
<s>
As	O
the	O
size	O
of	O
the	O
sample	O
increases	O
,	O
a	O
random	O
classifier	B-General_Concept
's	O
ROC	O
point	O
tends	O
towards	O
the	O
diagonal	O
line	O
.	O
</s>
<s>
The	O
result	O
of	O
method	O
A	O
clearly	O
shows	O
the	O
best	O
predictive	O
power	B-General_Concept
among	O
A	O
,	O
B	O
,	O
and	O
C	O
.	O
The	O
result	O
of	O
B	O
lies	O
on	O
the	O
random	O
guess	O
line	O
(	O
the	O
diagonal	O
line	O
)	O
,	O
and	O
it	O
can	O
be	O
seen	O
in	O
the	O
table	O
that	O
the	O
accuracy	O
of	O
B	O
is	O
50%	O
.	O
</s>
<s>
This	O
mirrored	O
method	O
simply	O
reverses	O
the	O
predictions	O
of	O
whatever	O
method	O
or	O
test	O
produced	O
the	O
C	O
contingency	B-Application
table	I-Application
.	O
</s>
<s>
Although	O
the	O
original	O
C	O
method	O
has	O
negative	O
predictive	O
power	B-General_Concept
,	O
simply	O
reversing	O
its	O
decisions	O
leads	O
to	O
a	O
new	O
predictive	O
method	O
C′	O
which	O
has	O
positive	O
predictive	O
power	B-General_Concept
.	O
</s>
<s>
The	O
closer	O
a	O
result	O
from	O
a	O
contingency	B-Application
table	I-Application
is	O
to	O
the	O
upper	O
left	O
corner	O
,	O
the	O
better	O
it	O
predicts	O
,	O
but	O
the	O
distance	O
from	O
the	O
random	O
guess	O
line	O
in	O
either	O
direction	O
is	O
the	O
best	O
indicator	O
of	O
how	O
much	O
predictive	O
power	B-General_Concept
a	O
method	O
has	O
.	O
</s>
<s>
the	O
method	O
is	O
worse	O
than	O
a	O
random	O
guess	O
)	O
,	O
all	O
of	O
the	O
method	O
's	O
predictions	O
must	O
be	O
reversed	O
in	O
order	O
to	O
utilize	O
its	O
power	B-General_Concept
,	O
thereby	O
moving	O
the	O
result	O
above	O
the	O
random	O
guess	O
line	O
.	O
</s>
<s>
In	O
binary	B-General_Concept
classification	I-General_Concept
,	O
the	O
class	O
prediction	O
for	O
each	O
instance	O
is	O
often	O
made	O
based	O
on	O
a	O
continuous	O
random	O
variable	O
,	O
which	O
is	O
a	O
"	O
score	O
"	O
computed	O
for	O
the	O
instance	O
(	O
e.g.	O
</s>
<s>
Therefore	O
,	O
the	O
true	O
positive	O
rate	O
is	O
given	O
by	O
and	O
the	O
false	B-General_Concept
positive	I-General_Concept
rate	I-General_Concept
is	O
given	O
by	O
.	O
</s>
<s>
The	O
ROC	B-Algorithm
curve	I-Algorithm
plots	O
parametrically	O
versus	O
with	O
as	O
the	O
varying	O
parameter	O
.	O
</s>
<s>
The	O
experimenter	O
can	O
adjust	O
the	O
threshold	O
(	O
green	O
vertical	O
line	O
in	O
the	O
figure	O
)	O
,	O
which	O
will	O
in	O
turn	O
change	O
the	O
false	B-General_Concept
positive	I-General_Concept
rate	I-General_Concept
.	O
</s>
<s>
the	O
area	O
between	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
and	O
the	O
no-discrimination	O
line	O
multiplied	O
by	O
two	O
is	O
called	O
the	O
Gini	O
coefficient	O
.	O
</s>
<s>
the	O
area	O
under	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
,	O
or	O
"	O
AUC	O
"	O
(	O
"	O
area	O
under	O
curve	O
"	O
)	O
,	O
or	O
A	O
 '	O
(	O
pronounced	O
"	O
a-prime	O
"	O
)	O
,	O
or	O
"	O
c-statistic	O
"	O
(	O
"	O
concordance	O
statistic	O
"	O
)	O
.	O
</s>
<s>
the	O
sensitivity	B-Algorithm
index	I-Algorithm
d′	O
(	O
pronounced	O
"	O
d-prime	B-Algorithm
"	O
)	O
,	O
the	O
distance	O
between	O
the	O
mean	O
of	O
the	O
distribution	O
of	O
activity	O
in	O
the	O
system	O
under	O
noise-alone	O
conditions	O
and	O
its	O
distribution	O
under	O
signal-alone	O
conditions	O
,	O
divided	O
by	O
their	O
standard	B-General_Concept
deviation	I-General_Concept
,	O
under	O
the	O
assumption	O
that	O
both	O
these	O
distributions	O
are	O
normal	O
with	O
the	O
same	O
standard	B-General_Concept
deviation	I-General_Concept
.	O
</s>
<s>
However	O
,	O
any	O
attempt	O
to	O
summarize	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
into	O
a	O
single	O
number	O
loses	O
information	O
about	O
the	O
pattern	O
of	O
tradeoffs	O
of	O
the	O
particular	O
discriminator	O
algorithm	O
.	O
</s>
<s>
When	O
using	O
normalized	O
units	O
,	O
the	O
area	O
under	O
the	O
curve	O
(	O
often	O
referred	O
to	O
as	O
simply	O
the	O
AUC	O
)	O
is	O
equal	O
to	O
the	O
probability	O
that	O
a	O
classifier	B-General_Concept
will	O
rank	O
a	O
randomly	O
chosen	O
positive	O
instance	O
higher	O
than	O
a	O
randomly	O
chosen	O
negative	O
one	O
(	O
assuming	O
'	O
positive	O
 '	O
ranks	O
higher	O
than	O
'	O
negative	O
 '	O
)	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
when	O
given	O
one	O
randomly	O
selected	O
positive	O
instance	O
and	O
one	O
randomly	O
selected	O
negative	O
instance	O
,	O
AUC	O
is	O
the	O
probability	O
that	O
the	O
classifier	B-General_Concept
will	O
be	O
able	O
to	O
tell	O
which	O
one	O
is	O
which	O
.	O
</s>
<s>
It	O
can	O
be	O
shown	O
that	O
the	O
AUC	O
is	O
closely	O
related	O
to	O
the	O
Mann	B-General_Concept
–	I-General_Concept
Whitney	I-General_Concept
U	I-General_Concept
,	O
which	O
tests	O
whether	O
positives	O
are	O
ranked	O
higher	O
than	O
negatives	O
.	O
</s>
<s>
It	O
is	O
also	O
equivalent	O
to	O
the	O
Wilcoxon	B-General_Concept
test	I-General_Concept
of	I-General_Concept
ranks	I-General_Concept
.	O
</s>
<s>
For	O
a	O
predictor	O
,	O
an	O
unbiased	O
estimator	O
of	O
its	O
AUC	O
can	O
be	O
expressed	O
by	O
the	O
following	O
Wilcoxon-Mann-Whitney	B-General_Concept
statistic	O
:	O
</s>
<s>
Another	O
problem	O
with	O
ROC	O
AUC	O
is	O
that	O
reducing	O
the	O
ROC	B-Algorithm
Curve	I-Algorithm
to	O
a	O
single	O
number	O
ignores	O
the	O
fact	O
that	O
it	O
is	O
about	O
the	O
tradeoffs	O
between	O
the	O
different	O
systems	O
or	O
performance	O
points	O
plotted	O
and	O
not	O
the	O
performance	O
of	O
an	O
individual	O
system	O
,	O
as	O
well	O
as	O
ignoring	O
the	O
possibility	O
of	O
concavity	O
repair	O
,	O
so	O
that	O
related	O
alternative	O
measures	O
such	O
as	O
Informedness	B-General_Concept
or	O
DeltaP	O
are	O
recommended	O
.	O
</s>
<s>
These	O
measures	O
are	O
essentially	O
equivalent	O
to	O
the	O
Gini	O
for	O
a	O
single	O
prediction	O
point	O
with	O
DeltaP	O
 '	O
=	O
Informedness	B-General_Concept
=	O
2AUC-1	O
,	O
whilst	O
DeltaP	O
=	O
Markedness	O
represents	O
the	O
dual	O
(	O
viz	O
.	O
</s>
<s>
predicting	O
the	O
prediction	O
from	O
the	O
real	O
class	O
)	O
and	O
their	O
geometric	O
mean	O
is	O
the	O
Matthews	B-General_Concept
correlation	I-General_Concept
coefficient	I-General_Concept
.	O
</s>
<s>
Whereas	O
ROC	O
AUC	O
varies	O
between	O
0	O
and	O
1	O
—	O
with	O
an	O
uninformative	O
classifier	B-General_Concept
yielding	O
0.5	O
—	O
the	O
alternative	O
measures	O
known	O
as	O
Informedness	B-General_Concept
,	O
Certainty	O
and	O
Gini	O
Coefficient	O
(	O
in	O
the	O
single	O
parameterization	O
or	O
single	O
system	O
case	O
)	O
all	O
have	O
the	O
advantage	O
that	O
0	O
represents	O
chance	O
performance	O
whilst	O
1	O
represents	O
perfect	O
performance	O
,	O
and	O
−1	O
represents	O
the	O
"	O
perverse	O
"	O
case	O
of	O
full	O
informedness	B-General_Concept
always	O
giving	O
the	O
wrong	O
response	O
.	O
</s>
<s>
Bringing	O
chance	O
performance	O
to	O
0	O
allows	O
these	O
alternative	O
scales	O
to	O
be	O
interpreted	O
as	O
Kappa	B-General_Concept
statistics	I-General_Concept
.	O
</s>
<s>
Informedness	B-General_Concept
has	O
been	O
shown	O
to	O
have	O
desirable	O
characteristics	O
for	O
Machine	O
Learning	O
versus	O
other	O
common	O
definitions	O
of	O
Kappa	O
such	O
as	O
Cohen	B-General_Concept
Kappa	I-General_Concept
and	O
Fleiss	O
Kappa	O
.	O
</s>
<s>
Sometimes	O
it	O
can	O
be	O
more	O
useful	O
to	O
look	O
at	O
a	O
specific	O
region	O
of	O
the	O
ROC	B-Algorithm
Curve	I-Algorithm
rather	O
than	O
at	O
the	O
whole	O
curve	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
compute	O
partial	B-General_Concept
AUC	I-General_Concept
.	O
</s>
<s>
For	O
example	O
,	O
one	O
could	O
focus	O
on	O
the	O
region	O
of	O
the	O
curve	O
with	O
low	O
false	B-General_Concept
positive	I-General_Concept
rate	I-General_Concept
,	O
which	O
is	O
often	O
of	O
prime	O
interest	O
for	O
population	O
screening	O
tests	O
.	O
</s>
<s>
The	O
Total	B-General_Concept
Operating	I-General_Concept
Characteristic	I-General_Concept
(	O
TOC	O
)	O
also	O
characterizes	O
diagnostic	O
ability	O
while	O
revealing	O
more	O
information	O
than	O
the	O
ROC	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
TOC	O
shows	O
the	O
total	O
information	O
in	O
the	O
contingency	B-Application
table	I-Application
for	O
each	O
threshold	O
.	O
</s>
<s>
the	O
size	O
of	O
every	O
entry	O
in	O
the	O
contingency	B-Application
table	I-Application
for	O
each	O
threshold	O
.	O
</s>
<s>
These	O
figures	O
are	O
the	O
TOC	O
and	O
ROC	B-Algorithm
curves	I-Algorithm
using	O
the	O
same	O
data	O
and	O
thresholds	O
.	O
</s>
<s>
Additionally	O
,	O
the	O
TOC	O
curve	O
shows	O
that	O
the	O
number	O
of	O
false	B-Error_Name
alarms	I-Error_Name
is	O
4	O
and	O
the	O
number	O
of	O
correct	O
rejections	O
is	O
16	O
.	O
</s>
<s>
At	O
any	O
given	O
point	O
in	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
,	O
it	O
is	O
possible	O
to	O
glean	O
values	O
for	O
the	O
ratios	O
of	O
and	O
.	O
</s>
<s>
However	O
,	O
these	O
two	O
values	O
are	O
insufficient	O
to	O
construct	O
all	O
entries	O
of	O
the	O
underlying	O
two-by-two	O
contingency	B-Application
table	I-Application
.	O
</s>
<s>
An	O
alternative	O
to	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
is	O
the	O
detection	B-Error_Name
error	I-Error_Name
tradeoff	I-Error_Name
(	O
DET	O
)	O
graph	O
,	O
which	O
plots	O
the	O
false	O
negative	O
rate	O
(	O
missed	O
detections	O
)	O
vs.	O
the	O
false	B-General_Concept
positive	I-General_Concept
rate	I-General_Concept
(	O
false	B-Error_Name
alarms	I-Error_Name
)	O
on	O
non-linearly	O
transformed	O
x	O
-	O
and	O
y-axes	O
.	O
</s>
<s>
The	O
DET	O
plot	O
is	O
used	O
extensively	O
in	O
the	O
automatic	B-Application
speaker	I-Application
recognition	I-Application
community	O
,	O
where	O
the	O
name	O
DET	O
was	O
first	O
used	O
.	O
</s>
<s>
If	O
a	O
standard	O
score	O
is	O
applied	O
to	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
,	O
the	O
curve	O
will	O
be	O
transformed	O
into	O
a	O
straight	O
line	O
.	O
</s>
<s>
This	O
z-score	O
is	O
based	O
on	O
a	O
normal	O
distribution	O
with	O
a	O
mean	O
of	O
zero	O
and	O
a	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
one	O
.	O
</s>
<s>
The	O
linearity	O
of	O
the	O
zROC	O
curve	O
depends	O
on	O
the	O
standard	B-General_Concept
deviations	I-General_Concept
of	O
the	O
target	O
and	O
lure	O
strength	O
distributions	O
.	O
</s>
<s>
If	O
the	O
standard	B-General_Concept
deviations	I-General_Concept
are	O
equal	O
,	O
the	O
slope	O
will	O
be	O
1.0	O
.	O
</s>
<s>
If	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
target	O
strength	O
distribution	O
is	O
larger	O
than	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
lure	O
strength	O
distribution	O
,	O
then	O
the	O
slope	O
will	O
be	O
smaller	O
than	O
1.0	O
.	O
</s>
<s>
Another	O
variable	O
used	O
isd	O
 '	O
(	O
d	B-Algorithm
prime	I-Algorithm
)	O
(	O
discussed	O
above	O
in	O
"	O
Other	O
measures	O
"	O
)	O
,	O
which	O
can	O
easily	O
be	O
expressed	O
in	O
terms	O
of	O
z-values	O
.	O
</s>
<s>
The	O
z-score	O
of	O
an	O
ROC	B-Algorithm
curve	I-Algorithm
is	O
always	O
linear	O
,	O
as	O
assumed	O
,	O
except	O
in	O
special	O
situations	O
.	O
</s>
<s>
Instead	O
of	O
the	O
subject	O
simply	O
answering	O
yes	O
or	O
no	O
to	O
a	O
specific	O
input	O
,	O
the	O
subject	O
gives	O
the	O
input	O
a	O
feeling	O
of	O
familiarity	O
,	O
which	O
operates	O
like	O
the	O
original	O
ROC	B-Algorithm
curve	I-Algorithm
.	O
</s>
<s>
The	O
ROC	B-Algorithm
curve	I-Algorithm
was	O
first	O
used	O
during	O
World	O
War	O
II	O
for	O
the	O
analysis	O
of	O
radar	B-Application
signals	I-Application
before	O
it	O
was	O
employed	O
in	O
signal	O
detection	O
theory	O
.	O
</s>
<s>
Following	O
the	O
attack	B-Application
on	I-Application
Pearl	I-Application
Harbor	I-Application
in	O
1941	O
,	O
the	O
United	O
States	O
army	O
began	O
new	O
research	O
to	O
increase	O
the	O
prediction	O
of	O
correctly	O
detected	O
Japanese	O
aircraft	O
from	O
their	O
radar	B-Application
signals	I-Application
.	O
</s>
<s>
For	O
these	O
purposes	O
they	O
measured	O
the	O
ability	O
of	O
a	O
radar	B-Application
receiver	O
operator	O
to	O
make	O
these	O
important	O
distinctions	O
,	O
which	O
was	O
called	O
the	O
Receiver	B-Algorithm
Operating	I-Algorithm
Characteristic	I-Algorithm
.	O
</s>
<s>
In	O
the	O
1950s	O
,	O
ROC	B-Algorithm
curves	I-Algorithm
were	O
employed	O
in	O
psychophysics	O
to	O
assess	O
human	O
(	O
and	O
occasionally	O
non-human	O
animal	O
)	O
detection	O
of	O
weak	O
signals	O
.	O
</s>
<s>
In	O
medicine	O
,	O
ROC	B-Algorithm
analysis	I-Algorithm
has	O
been	O
extensively	O
used	O
in	O
the	O
evaluation	O
of	O
diagnostic	O
tests	O
.	O
</s>
<s>
ROC	B-Algorithm
curves	I-Algorithm
are	O
also	O
used	O
extensively	O
in	O
epidemiology	O
and	O
medical	O
research	O
and	O
are	O
frequently	O
mentioned	O
in	O
conjunction	O
with	O
evidence-based	O
medicine	O
.	O
</s>
<s>
In	O
radiology	O
,	O
ROC	B-Algorithm
analysis	I-Algorithm
is	O
a	O
common	O
technique	O
to	O
evaluate	O
new	O
radiology	O
techniques	O
.	O
</s>
<s>
In	O
the	O
social	O
sciences	O
,	O
ROC	B-Algorithm
analysis	I-Algorithm
is	O
often	O
called	O
the	O
ROC	O
Accuracy	O
Ratio	O
,	O
a	O
common	O
technique	O
for	O
judging	O
the	O
accuracy	O
of	O
default	O
probability	O
models	O
.	O
</s>
<s>
ROC	B-Algorithm
curves	I-Algorithm
are	O
widely	O
used	O
in	O
laboratory	O
medicine	O
to	O
assess	O
the	O
diagnostic	O
accuracy	O
of	O
a	O
test	O
,	O
to	O
choose	O
the	O
optimal	O
cut-off	O
of	O
a	O
test	O
and	O
to	O
compare	O
diagnostic	O
accuracy	O
of	O
several	O
tests	O
.	O
</s>
<s>
ROC	B-Algorithm
curves	I-Algorithm
also	O
proved	O
useful	O
for	O
the	O
evaluation	O
of	O
machine	O
learning	O
techniques	O
.	O
</s>
<s>
The	O
first	O
application	O
of	O
ROC	O
in	O
machine	O
learning	O
was	O
by	O
Spackman	O
who	O
demonstrated	O
the	O
value	O
of	O
ROC	B-Algorithm
curves	I-Algorithm
in	O
comparing	O
and	O
evaluating	O
different	O
classification	O
algorithms	O
.	O
</s>
<s>
ROC	B-Algorithm
curves	I-Algorithm
are	O
also	O
used	O
in	O
verification	O
of	O
forecasts	O
in	O
meteorology	O
.	O
</s>
<s>
The	O
extension	O
of	O
ROC	B-Algorithm
curves	I-Algorithm
for	O
classification	O
problems	O
with	O
more	O
than	O
two	O
classes	O
is	O
cumbersome	O
.	O
</s>
<s>
Every	O
possible	O
decision	O
rule	O
that	O
one	O
might	O
use	O
for	O
a	O
classifier	B-General_Concept
for	O
classes	O
can	O
be	O
described	O
in	O
terms	O
of	O
its	O
true	O
positive	O
rates	O
.	O
</s>
<s>
With	O
this	O
definition	O
,	O
the	O
VUS	O
is	O
the	O
probability	O
that	O
the	O
classifier	B-General_Concept
will	O
be	O
able	O
to	O
correctly	O
label	O
all	O
examples	O
when	O
it	O
is	O
given	O
a	O
set	O
that	O
has	O
one	O
randomly	O
selected	O
example	O
from	O
each	O
class	O
.	O
</s>
<s>
The	O
implementation	O
of	O
a	O
classifier	B-General_Concept
that	O
knows	O
that	O
its	O
input	O
set	O
consists	O
of	O
one	O
example	O
from	O
each	O
class	O
might	O
first	O
compute	O
a	O
goodness-of-fit	O
score	O
for	O
each	O
of	O
the	O
possible	O
pairings	O
of	O
an	O
example	O
to	O
a	O
class	O
,	O
and	O
then	O
employ	O
the	O
Hungarian	B-Algorithm
algorithm	I-Algorithm
to	O
maximize	O
the	O
sum	O
of	O
the	O
selected	O
scores	O
over	O
all	O
possible	O
ways	O
to	O
assign	O
exactly	O
one	O
example	O
to	O
each	O
class	O
.	O
</s>
<s>
Given	O
the	O
success	O
of	O
ROC	B-Algorithm
curves	I-Algorithm
for	O
the	O
assessment	O
of	O
classification	O
models	O
,	O
the	O
extension	O
of	O
ROC	B-Algorithm
curves	I-Algorithm
for	O
other	O
supervised	O
tasks	O
has	O
also	O
been	O
investigated	O
.	O
</s>
<s>
In	O
the	O
latter	O
,	O
RROC	O
curves	O
become	O
extremely	O
similar	O
to	O
ROC	B-Algorithm
curves	I-Algorithm
for	O
classification	O
,	O
with	O
the	O
notions	O
of	O
asymmetry	O
,	O
dominance	O
and	O
convex	O
hull	O
.	O
</s>
