<s>
In	O
machine	O
learning	O
,	O
the	O
hinge	B-Algorithm
loss	I-Algorithm
is	O
a	O
loss	O
function	O
used	O
for	O
training	O
classifiers	B-General_Concept
.	O
</s>
<s>
The	O
hinge	B-Algorithm
loss	I-Algorithm
is	O
used	O
for	O
"	O
maximum-margin	O
"	O
classification	O
,	O
most	O
notably	O
for	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
(	O
SVMs	B-Algorithm
)	O
.	O
</s>
<s>
Note	O
that	O
should	O
be	O
the	O
"	O
raw	O
"	O
output	O
of	O
the	O
classifier	B-General_Concept
's	O
decision	O
function	O
,	O
not	O
the	O
predicted	O
class	O
label	O
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
linear	O
SVMs	B-Algorithm
,	O
,	O
where	O
are	O
the	O
parameters	O
of	O
the	O
hyperplane	O
and	O
is	O
the	O
input	O
variable(s )	O
.	O
</s>
<s>
When	O
and	O
have	O
the	O
same	O
sign	O
(	O
meaning	O
predicts	O
the	O
right	O
class	O
)	O
and	O
,	O
the	O
hinge	B-Algorithm
loss	I-Algorithm
.	O
</s>
<s>
While	O
binary	O
SVMs	B-Algorithm
are	O
commonly	O
extended	O
to	O
multiclass	B-General_Concept
classification	I-General_Concept
in	O
a	O
one-vs.-all	O
or	O
one-vs.-one	O
fashion	O
,	O
</s>
<s>
it	O
is	O
also	O
possible	O
to	O
extend	O
the	O
hinge	B-Algorithm
loss	I-Algorithm
itself	O
for	O
such	O
an	O
end	O
.	O
</s>
<s>
Several	O
different	O
variations	O
of	O
multiclass	O
hinge	B-Algorithm
loss	I-Algorithm
have	O
been	O
proposed	O
.	O
</s>
<s>
In	O
structured	B-General_Concept
prediction	I-General_Concept
,	O
the	O
hinge	B-Algorithm
loss	I-Algorithm
can	O
be	O
further	O
extended	O
to	O
structured	O
output	O
spaces	O
.	O
</s>
<s>
Structured	B-Algorithm
SVMs	I-Algorithm
with	O
margin	O
rescaling	O
use	O
the	O
following	O
variant	O
,	O
where	O
denotes	O
the	O
SVM	B-Algorithm
's	O
parameters	O
,	O
the	O
SVM	B-Algorithm
's	O
predictions	O
,	O
the	O
joint	O
feature	O
function	O
,	O
and	O
the	O
Hamming	O
loss	O
:	O
</s>
<s>
The	O
hinge	B-Algorithm
loss	I-Algorithm
is	O
a	O
convex	O
function	O
,	O
so	O
many	O
of	O
the	O
usual	O
convex	O
optimizers	O
used	O
in	O
machine	O
learning	O
can	O
work	O
with	O
it	O
.	O
</s>
