<s>
The	O
winnow	B-Algorithm
algorithm	I-Algorithm
is	O
a	O
technique	O
from	O
machine	O
learning	O
for	O
learning	O
a	O
linear	B-General_Concept
classifier	I-General_Concept
from	O
labeled	O
examples	O
.	O
</s>
<s>
It	O
is	O
very	O
similar	O
to	O
the	O
perceptron	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
However	O
,	O
the	O
perceptron	B-Algorithm
algorithm	I-Algorithm
uses	O
an	O
additive	O
weight-update	O
scheme	O
,	O
while	O
Winnow	B-Algorithm
uses	O
a	O
multiplicative	B-Algorithm
scheme	I-Algorithm
that	O
allows	O
it	O
to	O
perform	O
much	O
better	O
when	O
many	O
dimensions	O
are	O
irrelevant	O
(	O
hence	O
its	O
name	O
winnow	B-Algorithm
)	O
.	O
</s>
<s>
During	O
training	O
,	O
Winnow	B-Algorithm
is	O
shown	O
a	O
sequence	O
of	O
positive	O
and	O
negative	O
examples	O
.	O
</s>
<s>
The	O
algorithm	O
can	O
also	O
be	O
used	O
in	O
the	O
online	B-Algorithm
learning	I-Algorithm
setting	O
,	O
where	O
the	O
learning	O
and	O
the	O
classification	O
phase	O
are	O
not	O
clearly	O
separated	O
.	O
</s>
<s>
The	O
basic	O
algorithm	O
,	O
Winnow1	B-Algorithm
,	O
is	O
as	O
follows	O
.	O
</s>
<s>
The	O
instance	O
space	O
is	O
,	O
that	O
is	O
,	O
each	O
instance	O
is	O
described	O
as	O
a	O
set	O
of	O
Boolean-valued	O
features	B-Algorithm
.	O
</s>
<s>
When	O
the	O
learner	O
is	O
given	O
an	O
example	O
,	O
it	O
applies	O
the	O
typical	O
prediction	O
rule	O
for	O
linear	B-General_Concept
classifiers	I-General_Concept
:	O
</s>
<s>
Balanced	O
Winnow	B-Algorithm
maintains	O
two	O
sets	O
of	O
weights	O
,	O
and	O
thus	O
two	O
hyperplanes	O
.	O
</s>
<s>
This	O
can	O
then	O
be	O
generalized	O
for	O
multi-label	B-Algorithm
classification	I-Algorithm
.	O
</s>
<s>
In	O
certain	O
circumstances	O
,	O
it	O
can	O
be	O
shown	O
that	O
the	O
number	O
of	O
mistakes	O
Winnow	B-Algorithm
makes	O
as	O
it	O
learns	O
has	O
an	O
upper	O
bound	O
that	O
is	O
independent	O
of	O
the	O
number	O
of	O
instances	O
with	O
which	O
it	O
is	O
presented	O
.	O
</s>
<s>
If	O
the	O
Winnow1	B-Algorithm
algorithm	O
uses	O
and	O
on	O
a	O
target	O
function	O
that	O
is	O
a	O
-literal	O
monotone	O
disjunction	O
given	O
by	O
,	O
then	O
for	O
any	O
sequence	O
of	O
instances	O
the	O
total	O
number	O
of	O
mistakes	O
is	O
bounded	O
by	O
:	O
</s>
