<s>
In	O
machine	O
learning	O
the	O
random	B-Algorithm
subspace	I-Algorithm
method	I-Algorithm
,	O
also	O
called	O
attribute	B-Algorithm
bagging	I-Algorithm
or	O
feature	O
bagging	B-Algorithm
,	O
is	O
an	O
ensemble	B-Algorithm
learning	I-Algorithm
method	O
that	O
attempts	O
to	O
reduce	O
the	O
correlation	O
between	O
estimators	O
in	O
an	O
ensemble	O
by	O
training	O
them	O
on	O
random	O
samples	O
of	O
features	B-Algorithm
instead	O
of	O
the	O
entire	O
feature	O
set	O
.	O
</s>
<s>
In	O
ensemble	B-Algorithm
learning	I-Algorithm
one	O
tries	O
to	O
combine	O
the	O
models	O
produced	O
by	O
several	O
learners	O
into	O
an	O
ensemble	O
that	O
performs	O
better	O
than	O
the	O
original	O
learners	O
.	O
</s>
<s>
One	O
way	O
of	O
combining	O
learners	O
is	O
bootstrap	B-Algorithm
aggregating	I-Algorithm
or	O
bagging	B-Algorithm
,	O
which	O
shows	O
each	O
learner	O
a	O
randomly	O
sampled	O
subset	O
of	O
the	O
training	O
points	O
so	O
that	O
the	O
learners	O
will	O
produce	O
different	O
models	O
that	O
can	O
be	O
sensibly	O
averaged	O
.	O
</s>
<s>
In	O
bagging	B-Algorithm
,	O
one	O
samples	O
training	O
points	O
with	O
replacement	O
from	O
the	O
full	O
training	O
set	O
.	O
</s>
<s>
The	O
random	B-Algorithm
subspace	I-Algorithm
method	I-Algorithm
is	O
similar	O
to	O
bagging	B-Algorithm
except	O
that	O
the	O
features	B-Algorithm
(	O
"	O
attributes	O
"	O
,	O
"	O
predictors	O
"	O
,	O
"	O
independent	O
variables	O
"	O
)	O
are	O
randomly	O
sampled	O
,	O
with	O
replacement	O
,	O
for	O
each	O
learner	O
.	O
</s>
<s>
Informally	O
,	O
this	O
causes	O
individual	O
learners	O
to	O
not	O
over-focus	O
on	O
features	B-Algorithm
that	O
appear	O
highly	O
predictive/descriptive	O
in	O
the	O
training	O
set	O
,	O
but	O
fail	O
to	O
be	O
as	O
predictive	O
for	O
points	O
outside	O
that	O
set	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
random	O
subspaces	O
are	O
an	O
attractive	O
choice	O
for	O
high-dimensional	O
problems	O
where	O
the	O
number	O
of	O
features	B-Algorithm
is	O
much	O
larger	O
than	O
the	O
number	O
of	O
training	O
points	O
,	O
such	O
as	O
learning	O
from	O
fMRI	O
data	O
or	O
gene	O
expression	O
data	O
.	O
</s>
<s>
The	O
random	B-Algorithm
subspace	I-Algorithm
method	I-Algorithm
has	O
been	O
used	O
for	O
decision	B-Algorithm
trees	I-Algorithm
;	O
when	O
combined	O
with	O
"	O
ordinary	O
"	O
bagging	B-Algorithm
of	O
decision	B-Algorithm
trees	I-Algorithm
,	O
the	O
resulting	O
models	O
are	O
called	O
random	B-Algorithm
forests	I-Algorithm
.	O
</s>
<s>
It	O
has	O
also	O
been	O
applied	O
to	O
linear	B-General_Concept
classifiers	I-General_Concept
,	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
,	O
nearest	B-General_Concept
neighbours	I-General_Concept
and	O
other	O
types	O
of	O
classifiers	O
.	O
</s>
<s>
This	O
method	O
is	O
also	O
applicable	O
to	O
one-class	B-General_Concept
classifiers	I-General_Concept
.	O
</s>
<s>
The	O
random	B-Algorithm
subspace	I-Algorithm
method	I-Algorithm
has	O
also	O
been	O
applied	O
to	O
portfolio	O
selection	O
problem	O
showing	O
its	O
superiority	O
to	O
the	O
conventional	O
resampled	O
portfolio	O
essentially	O
based	O
on	O
Bagging	B-Algorithm
.	O
</s>
<s>
An	O
ensemble	O
of	O
models	O
employing	O
the	O
random	B-Algorithm
subspace	I-Algorithm
method	I-Algorithm
can	O
be	O
constructed	O
using	O
the	O
following	O
algorithm	O
:	O
</s>
<s>
Let	O
the	O
number	O
of	O
training	O
points	O
be	O
N	O
and	O
the	O
number	O
of	O
features	B-Algorithm
in	O
the	O
training	O
data	O
be	O
D	O
.	O
</s>
<s>
For	O
each	O
individual	O
model	O
l	O
,	O
create	O
a	O
training	O
set	O
by	O
choosing	O
d	O
features	B-Algorithm
from	O
D	O
with	O
replacement	O
and	O
train	O
the	O
model	O
.	O
</s>
