<s>
Given	O
a	O
population	O
whose	O
members	O
each	O
belong	O
to	O
one	O
of	O
a	O
number	O
of	O
different	O
sets	O
or	O
classes	O
,	O
a	O
classification	B-General_Concept
rule	I-General_Concept
or	O
classifier	B-General_Concept
is	O
a	O
procedure	O
by	O
which	O
the	O
elements	O
of	O
the	O
population	O
set	O
are	O
each	O
predicted	O
to	O
belong	O
to	O
one	O
of	O
the	O
classes	O
.	O
</s>
<s>
A	O
perfect	O
classification	B-General_Concept
is	O
one	O
for	O
which	O
every	O
element	O
in	O
the	O
population	O
is	O
assigned	O
to	O
the	O
class	O
it	O
really	O
belongs	O
to	O
.	O
</s>
<s>
An	O
imperfect	O
classification	B-General_Concept
is	O
one	O
in	O
which	O
some	O
errors	O
appear	O
,	O
and	O
then	O
statistical	O
analysis	O
must	O
be	O
applied	O
to	O
analyse	O
the	O
classification	B-General_Concept
.	O
</s>
<s>
A	O
special	O
kind	O
of	O
classification	B-General_Concept
rule	I-General_Concept
is	O
binary	B-General_Concept
classification	I-General_Concept
,	O
for	O
problems	O
in	O
which	O
there	O
are	O
only	O
two	O
classes	O
.	O
</s>
<s>
Given	O
a	O
data	O
set	O
consisting	O
of	O
pairs	O
x	O
and	O
y	O
,	O
where	O
x	O
denotes	O
an	O
element	O
of	O
the	O
population	O
and	O
y	O
the	O
class	O
it	O
belongs	O
to	O
,	O
a	O
classification	B-General_Concept
rule	I-General_Concept
h(x )	O
is	O
a	O
function	O
that	O
assigns	O
each	O
element	O
x	O
to	O
a	O
predicted	O
class	O
A	O
binary	B-General_Concept
classification	I-General_Concept
is	O
such	O
that	O
the	O
label	O
y	O
can	O
take	O
only	O
one	O
of	O
two	O
values	O
.	O
</s>
<s>
In	O
a	O
binary	B-General_Concept
classification	I-General_Concept
,	O
the	O
elements	O
that	O
are	O
not	O
correctly	O
classified	O
are	O
named	O
false	O
positives	O
and	O
false	O
negatives	O
.	O
</s>
<s>
Some	O
classification	B-General_Concept
rules	I-General_Concept
are	O
static	O
functions	O
.	O
</s>
<s>
A	O
computer	B-General_Concept
classifier	I-General_Concept
can	O
be	O
able	O
to	O
learn	O
or	O
can	O
implement	O
static	O
classification	B-General_Concept
rules	I-General_Concept
.	O
</s>
<s>
For	O
a	O
training	O
data-set	O
,	O
the	O
true	O
labels	O
yj	O
are	O
unknown	O
,	O
but	O
it	O
is	O
a	O
prime	O
target	O
for	O
the	O
classification	B-General_Concept
procedure	O
that	O
the	O
approximation	O
as	O
well	O
as	O
possible	O
,	O
where	O
the	O
quality	O
of	O
this	O
approximation	O
needs	O
to	O
be	O
judged	O
on	O
the	O
basis	O
of	O
the	O
statistical	O
or	O
probabilistic	O
properties	O
of	O
the	O
overall	O
population	O
from	O
which	O
future	O
observations	O
will	O
be	O
drawn	O
.	O
</s>
<s>
Given	O
a	O
classification	B-General_Concept
rule	I-General_Concept
,	O
a	O
classification	B-General_Concept
test	I-General_Concept
is	O
the	O
result	O
of	O
applying	O
the	O
rule	O
to	O
a	O
finite	O
sample	O
of	O
the	O
initial	O
data	O
set	O
.	O
</s>
<s>
Classification	B-General_Concept
can	O
be	O
thought	O
of	O
as	O
two	O
separate	O
problems	O
–	O
binary	B-General_Concept
classification	I-General_Concept
and	O
multiclass	B-General_Concept
classification	I-General_Concept
.	O
</s>
<s>
In	O
binary	B-General_Concept
classification	I-General_Concept
,	O
a	O
better	O
understood	O
task	O
,	O
only	O
two	O
classes	O
are	O
involved	O
,	O
whereas	O
multiclass	B-General_Concept
classification	I-General_Concept
involves	O
assigning	O
an	O
object	O
to	O
one	O
of	O
several	O
classes	O
.	O
</s>
<s>
Since	O
many	O
classification	B-General_Concept
methods	O
have	O
been	O
developed	O
specifically	O
for	O
binary	B-General_Concept
classification	I-General_Concept
,	O
multiclass	B-General_Concept
classification	I-General_Concept
often	O
requires	O
the	O
combined	O
use	O
of	O
multiple	O
binary	B-General_Concept
classifiers	I-General_Concept
.	O
</s>
<s>
An	O
important	O
point	O
is	O
that	O
in	O
many	O
practical	O
binary	B-General_Concept
classification	I-General_Concept
problems	O
,	O
the	O
two	O
groups	O
are	O
not	O
symmetric	O
–	O
rather	O
than	O
overall	O
accuracy	O
,	O
the	O
relative	O
proportion	O
of	O
different	O
types	O
of	O
errors	O
is	O
of	O
interest	O
.	O
</s>
<s>
In	O
multiclass	B-General_Concept
classifications	I-General_Concept
,	O
the	O
classes	O
may	O
be	O
considered	O
symmetrically	O
(	O
all	O
errors	O
are	O
equivalent	O
)	O
,	O
or	O
asymmetrically	O
,	O
which	O
is	O
considerably	O
more	O
complicated	O
.	O
</s>
<s>
Binary	B-General_Concept
classification	I-General_Concept
methods	O
include	O
probit	B-Architecture
regression	I-Architecture
and	O
logistic	O
regression	O
.	O
</s>
<s>
Multiclass	B-General_Concept
classification	I-General_Concept
methods	O
include	O
multinomial	B-General_Concept
probit	I-General_Concept
and	O
multinomial	O
logit	O
.	O
</s>
<s>
When	O
the	O
classification	B-General_Concept
function	O
is	O
not	O
perfect	O
,	O
false	O
results	O
will	O
appear	O
.	O
</s>
<s>
Using	O
the	O
dot	O
locations	O
,	O
we	O
can	O
build	O
a	O
confusion	B-General_Concept
matrix	I-General_Concept
to	O
express	O
the	O
values	O
.	O
</s>
<s>
False	O
positive	O
is	O
commonly	O
denoted	O
as	O
the	O
top	O
right	O
(	O
Condition	O
negative	O
X	O
test	O
outcome	O
positive	O
)	O
unit	O
in	O
a	O
Confusion	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
False	O
negative	O
is	O
commonly	O
denoted	O
as	O
the	O
bottom	O
left	O
(	O
Condition	O
positive	O
X	O
test	O
outcome	O
negative	O
)	O
unit	O
in	O
a	O
Confusion	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
True	O
positive	O
is	O
commonly	O
denoted	O
as	O
the	O
top	O
left	O
(	O
Condition	O
positive	O
X	O
test	O
outcome	O
positive	O
)	O
unit	O
in	O
a	O
Confusion	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
True	O
negative	O
is	O
commonly	O
denoted	O
as	O
the	O
bottom	O
right	O
(	O
Condition	O
negative	O
X	O
test	O
outcome	O
negative	O
)	O
unit	O
in	O
a	O
Confusion	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
In	O
training	O
a	O
classifier	B-General_Concept
,	O
one	O
may	O
wish	O
to	O
measure	O
its	O
performance	O
using	O
the	O
well-accepted	O
metrics	O
of	O
sensitivity	O
and	O
specificity	O
.	O
</s>
<s>
It	O
may	O
be	O
instructive	O
to	O
compare	O
the	O
classifier	B-General_Concept
to	O
a	O
random	O
classifier	B-General_Concept
that	O
flips	O
a	O
coin	O
based	O
on	O
the	O
prevalence	O
of	O
a	O
disease	O
.	O
</s>
<s>
Suppose	O
then	O
that	O
we	O
have	O
a	O
random	O
classifier	B-General_Concept
that	O
guesses	O
that	O
the	O
patient	O
has	O
the	O
disease	O
with	O
that	O
same	O
probability	O
and	O
guesses	O
that	O
he	O
does	O
not	O
with	O
the	O
same	O
probability	O
.	O
</s>
<s>
The	O
probability	O
of	O
a	O
true	O
positive	O
is	O
the	O
probability	O
that	O
the	O
patient	O
has	O
the	O
disease	O
times	O
the	O
probability	O
that	O
the	O
random	O
classifier	B-General_Concept
guesses	O
this	O
correctly	O
,	O
or	O
.	O
</s>
<s>
From	O
the	O
definitions	O
above	O
,	O
the	O
sensitivity	O
of	O
this	O
classifier	B-General_Concept
is	O
.	O
</s>
<s>
So	O
,	O
while	O
the	O
measure	O
itself	O
is	O
independent	O
of	O
disease	O
prevalence	O
,	O
the	O
performance	O
of	O
this	O
random	O
classifier	B-General_Concept
depends	O
on	O
disease	O
prevalence	O
.	O
</s>
<s>
The	O
classifier	B-General_Concept
may	O
have	O
performance	O
that	O
is	O
like	O
this	O
random	O
classifier	B-General_Concept
,	O
but	O
with	O
a	O
better-weighted	O
coin	O
(	O
higher	O
sensitivity	O
and	O
specificity	O
)	O
.	O
</s>
<s>
An	O
alternative	O
measure	O
of	O
performance	O
is	O
the	O
Matthews	B-General_Concept
correlation	I-General_Concept
coefficient	I-General_Concept
,	O
for	O
which	O
any	O
random	O
classifier	B-General_Concept
will	O
get	O
an	O
average	O
score	O
of	O
0	O
.	O
</s>
<s>
The	O
extension	O
of	O
this	O
concept	O
to	O
non-binary	O
classifications	O
yields	O
the	O
confusion	B-General_Concept
matrix	I-General_Concept
.	O
</s>
