<s>
In	O
machine	O
learning	O
,	O
the	O
radial	B-Algorithm
basis	I-Algorithm
function	I-Algorithm
kernel	I-Algorithm
,	O
or	O
RBF	B-Algorithm
kernel	I-Algorithm
,	O
is	O
a	O
popular	O
kernel	O
function	O
used	O
in	O
various	O
kernelized	B-Algorithm
learning	O
algorithms	O
.	O
</s>
<s>
In	O
particular	O
,	O
it	O
is	O
commonly	O
used	O
in	O
support	B-Algorithm
vector	I-Algorithm
machine	I-Algorithm
classification	B-General_Concept
.	O
</s>
<s>
Since	O
the	O
value	O
of	O
the	O
RBF	B-Algorithm
kernel	I-Algorithm
decreases	O
with	O
distance	O
and	O
ranges	O
between	O
zero	O
(	O
in	O
the	O
limit	O
)	O
and	O
one	O
(	O
when	O
)	O
,	O
it	O
has	O
a	O
ready	O
interpretation	O
as	O
a	O
similarity	O
measure	O
.	O
</s>
<s>
Because	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
and	O
other	O
models	O
employing	O
the	O
kernel	O
trick	O
do	O
not	O
scale	O
well	O
to	O
large	O
numbers	O
of	O
training	O
samples	O
or	O
large	O
numbers	O
of	O
features	O
in	O
the	O
input	O
space	O
,	O
several	O
approximations	O
to	O
the	O
RBF	B-Algorithm
kernel	I-Algorithm
(	O
and	O
similar	O
kernels	O
)	O
have	O
been	O
introduced	O
.	O
</s>
<s>
where	O
is	O
the	O
implicit	O
mapping	O
embedded	O
in	O
the	O
RBF	B-Algorithm
kernel	I-Algorithm
.	O
</s>
<s>
One	O
way	O
to	O
construct	O
such	O
a	O
z	O
is	O
to	O
randomly	O
sample	O
from	O
the	O
Fourier	B-Algorithm
transformation	I-Algorithm
of	O
the	O
kernelwhere	O
are	O
independent	O
samples	O
from	O
the	O
normal	O
distribution	O
.	O
</s>
<s>
Another	O
approach	O
uses	O
the	O
Nyström	B-Algorithm
method	I-Algorithm
to	O
approximate	O
the	O
eigendecomposition	O
of	O
the	O
Gram	B-Algorithm
matrix	I-Algorithm
K	O
,	O
using	O
only	O
a	O
random	O
sample	O
of	O
the	O
training	O
set	O
.	O
</s>
