<s>
In	O
machine	O
learning	O
,	O
a	O
margin	B-General_Concept
classifier	I-General_Concept
is	O
a	O
classifier	B-General_Concept
which	O
is	O
able	O
to	O
give	O
an	O
associated	O
distance	O
from	O
the	O
decision	O
boundary	O
for	O
each	O
example	O
.	O
</s>
<s>
For	O
instance	O
,	O
if	O
a	O
linear	B-General_Concept
classifier	I-General_Concept
(	O
e.g.	O
</s>
<s>
perceptron	B-Algorithm
or	O
linear	B-General_Concept
discriminant	I-General_Concept
analysis	I-General_Concept
)	O
is	O
used	O
,	O
the	O
distance	O
(	O
typically	O
euclidean	O
distance	O
,	O
though	O
others	O
may	O
be	O
used	O
)	O
of	O
an	O
example	O
from	O
the	O
separating	O
hyperplane	O
is	O
the	O
margin	B-Algorithm
of	O
that	O
example	O
.	O
</s>
<s>
The	O
notion	O
of	O
margin	B-Algorithm
is	O
important	O
in	O
several	O
machine	O
learning	O
classification	O
algorithms	O
,	O
as	O
it	O
can	O
be	O
used	O
to	O
bound	O
the	O
generalization	B-Algorithm
error	I-Algorithm
of	O
the	O
classifier	B-General_Concept
.	O
</s>
<s>
Of	O
particular	O
prominence	O
is	O
the	O
generalization	B-Algorithm
error	I-Algorithm
bound	O
on	O
boosting	B-Algorithm
algorithms	O
and	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
.	O
</s>
<s>
See	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
and	O
maximum-margin	O
hyperplane	O
for	O
details	O
.	O
</s>
<s>
The	O
margin	B-Algorithm
for	O
an	O
iterative	O
boosting	B-Algorithm
algorithm	O
given	O
a	O
set	O
of	O
examples	O
with	O
two	O
classes	O
can	O
be	O
defined	O
as	O
follows	O
.	O
</s>
<s>
The	O
classifier	B-General_Concept
is	O
given	O
an	O
example	O
pair	O
where	O
is	O
a	O
domain	O
space	O
and	O
is	O
the	O
label	O
of	O
the	O
example	O
.	O
</s>
<s>
The	O
iterative	O
boosting	B-Algorithm
algorithm	O
then	O
selects	O
a	O
classifier	B-General_Concept
at	O
each	O
iteration	O
where	O
is	O
a	O
space	O
of	O
possible	O
classifiers	B-General_Concept
that	O
predict	O
real	O
values	O
.	O
</s>
<s>
This	O
hypothesis	O
is	O
then	O
weighted	O
by	O
as	O
selected	O
by	O
the	O
boosting	B-Algorithm
algorithm	O
.	O
</s>
<s>
By	O
this	O
definition	O
,	O
the	O
margin	B-Algorithm
is	O
positive	O
if	O
the	O
example	O
is	O
labeled	O
correctly	O
and	O
negative	O
if	O
the	O
example	O
is	O
labeled	O
incorrectly	O
.	O
</s>
<s>
This	O
definition	O
may	O
be	O
modified	O
and	O
is	O
not	O
the	O
only	O
way	O
to	O
define	O
margin	B-Algorithm
for	O
boosting	B-Algorithm
algorithms	O
.	O
</s>
<s>
Many	O
classifiers	B-General_Concept
can	O
give	O
an	O
associated	O
margin	B-Algorithm
for	O
each	O
example	O
.	O
</s>
<s>
However	O
,	O
only	O
some	O
classifiers	B-General_Concept
utilize	O
information	O
of	O
the	O
margin	B-Algorithm
while	O
learning	O
from	O
a	O
data	O
set	O
.	O
</s>
<s>
Many	O
boosting	B-Algorithm
algorithms	O
rely	O
on	O
the	O
notion	O
of	O
a	O
margin	B-Algorithm
to	O
give	O
weights	O
to	O
examples	O
.	O
</s>
<s>
If	O
a	O
convex	O
loss	O
is	O
utilized	O
(	O
as	O
in	O
AdaBoost	B-Algorithm
,	O
LogitBoost	B-Algorithm
,	O
and	O
all	O
members	O
of	O
the	O
AnyBoost	O
family	O
of	O
algorithms	O
)	O
then	O
an	O
example	O
with	O
higher	O
margin	B-Algorithm
will	O
receive	O
less	O
(	O
or	O
equal	O
)	O
weight	O
than	O
an	O
example	O
with	O
lower	O
margin	B-Algorithm
.	O
</s>
<s>
This	O
leads	O
the	O
boosting	B-Algorithm
algorithm	O
to	O
focus	O
weight	O
on	O
low	O
margin	B-Algorithm
examples	O
.	O
</s>
<s>
BrownBoost	B-Algorithm
)	O
,	O
the	O
margin	B-Algorithm
still	O
dictates	O
the	O
weighting	O
of	O
an	O
example	O
,	O
though	O
the	O
weighting	O
is	O
non-monotone	O
with	O
respect	O
to	O
margin	B-Algorithm
.	O
</s>
<s>
There	O
exists	O
boosting	B-Algorithm
algorithms	O
that	O
probably	O
maximize	O
the	O
minimum	O
margin	B-Algorithm
(	O
e.g.	O
</s>
<s>
Support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
probably	O
maximize	O
the	O
margin	B-Algorithm
of	O
the	O
separating	O
hyperplane	O
.	O
</s>
<s>
Support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
that	O
are	O
trained	O
using	O
noisy	O
data	O
(	O
there	O
exists	O
no	O
perfect	O
separation	O
of	O
the	O
data	O
in	O
the	O
given	O
space	O
)	O
maximize	O
the	O
soft	O
margin	B-Algorithm
.	O
</s>
<s>
More	O
discussion	O
of	O
this	O
can	O
be	O
found	O
in	O
the	O
support	B-Algorithm
vector	I-Algorithm
machine	I-Algorithm
article	O
.	O
</s>
<s>
The	O
voted-perceptron	O
algorithm	O
is	O
a	O
margin	B-Algorithm
maximizing	O
algorithm	O
based	O
on	O
an	O
iterative	O
application	O
of	O
the	O
classic	O
perceptron	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
One	O
theoretical	O
motivation	O
behind	O
margin	B-General_Concept
classifiers	I-General_Concept
is	O
that	O
their	O
generalization	B-Algorithm
error	I-Algorithm
may	O
be	O
bound	O
by	O
parameters	O
of	O
the	O
algorithm	O
and	O
a	O
margin	B-Algorithm
term	O
.	O
</s>
<s>
An	O
example	O
of	O
such	O
a	O
bound	O
is	O
for	O
the	O
AdaBoost	B-Algorithm
algorithm	O
.	O
</s>
<s>
Assume	O
the	O
VC-dimension	O
of	O
the	O
underlying	O
base	O
classifier	B-General_Concept
is	O
and	O
.	O
</s>
