<s>
Multiple	B-Algorithm
kernel	I-Algorithm
learning	I-Algorithm
refers	O
to	O
a	O
set	O
of	O
machine	O
learning	O
methods	O
that	O
use	O
a	O
predefined	O
set	O
of	O
kernels	B-Algorithm
and	O
learn	O
an	O
optimal	O
linear	O
or	O
non-linear	O
combination	O
of	O
kernels	B-Algorithm
as	O
part	O
of	O
the	O
algorithm	O
.	O
</s>
<s>
Reasons	O
to	O
use	O
multiple	B-Algorithm
kernel	I-Algorithm
learning	I-Algorithm
include	O
a	O
)	O
the	O
ability	O
to	O
select	O
for	O
an	O
optimal	O
kernel	O
and	O
parameters	O
from	O
a	O
larger	O
set	O
of	O
kernels	B-Algorithm
,	O
reducing	O
bias	O
due	O
to	O
kernel	O
selection	O
while	O
allowing	O
for	O
more	O
automated	O
machine	O
learning	O
methods	O
,	O
and	O
b	O
)	O
combining	O
data	O
from	O
different	O
sources	O
(	O
e.g.	O
</s>
<s>
sound	O
and	O
images	O
from	O
a	O
video	O
)	O
that	O
have	O
different	O
notions	O
of	O
similarity	O
and	O
thus	O
require	O
different	O
kernels	B-Algorithm
.	O
</s>
<s>
Instead	O
of	O
creating	O
a	O
new	O
kernel	O
,	O
multiple	O
kernel	O
algorithms	O
can	O
be	O
used	O
to	O
combine	O
kernels	B-Algorithm
already	O
established	O
for	O
each	O
individual	O
data	O
source	O
.	O
</s>
<s>
Multiple	B-Algorithm
kernel	I-Algorithm
learning	I-Algorithm
approaches	O
have	O
been	O
used	O
in	O
many	O
applications	O
,	O
such	O
as	O
event	O
recognition	O
in	O
video	O
,	O
object	O
recognition	O
in	O
images	O
,	O
and	O
biomedical	O
data	O
fusion	O
.	O
</s>
<s>
Multiple	B-Algorithm
kernel	I-Algorithm
learning	I-Algorithm
algorithms	O
have	O
been	O
developed	O
for	O
supervised	O
,	O
semi-supervised	O
,	O
as	O
well	O
as	O
unsupervised	B-General_Concept
learning	I-General_Concept
.	O
</s>
<s>
Most	O
work	O
has	O
been	O
done	O
on	O
the	O
supervised	O
learning	O
case	O
with	O
linear	O
combinations	O
of	O
kernels	B-Algorithm
,	O
however	O
,	O
many	O
algorithms	O
have	O
been	O
developed	O
.	O
</s>
<s>
The	O
basic	O
idea	O
behind	O
multiple	B-Algorithm
kernel	I-Algorithm
learning	I-Algorithm
algorithms	O
is	O
to	O
add	O
an	O
extra	O
parameter	O
to	O
the	O
minimization	O
problem	O
of	O
the	O
learning	O
algorithm	O
.	O
</s>
<s>
As	O
an	O
example	O
,	O
consider	O
the	O
case	O
of	O
supervised	O
learning	O
of	O
a	O
linear	O
combination	O
of	O
a	O
set	O
of	O
kernels	B-Algorithm
.	O
</s>
<s>
Because	O
the	O
kernels	B-Algorithm
are	O
additive	O
(	O
due	O
to	O
properties	O
of	O
reproducing	O
kernel	O
Hilbert	O
spaces	O
)	O
,	O
this	O
new	O
function	O
is	O
still	O
a	O
kernel	O
.	O
</s>
<s>
is	O
typically	O
the	O
square	O
loss	O
function	O
(	O
Tikhonov	O
regularization	O
)	O
or	O
the	O
hinge	O
loss	O
function	O
(	O
for	O
SVM	B-Algorithm
algorithms	O
)	O
,	O
and	O
is	O
usually	O
an	O
norm	O
or	O
some	O
combination	O
of	O
the	O
norms	O
(	O
i.e.	O
</s>
<s>
Adaptations	O
of	O
existing	O
techniques	O
such	O
as	O
the	O
Sequential	O
Minimal	O
Optimization	O
have	O
also	O
been	O
developed	O
for	O
multiple	O
kernel	O
SVM-based	O
methods	O
.	O
</s>
<s>
Fixed	O
rules	O
approaches	O
such	O
as	O
the	O
linear	O
combination	O
algorithm	O
described	O
above	O
use	O
rules	O
to	O
set	O
the	O
combination	O
of	O
the	O
kernels	B-Algorithm
.	O
</s>
<s>
These	O
do	O
not	O
require	O
parameterization	O
and	O
use	O
rules	O
like	O
summation	O
and	O
multiplication	O
to	O
combine	O
the	O
kernels	B-Algorithm
.	O
</s>
<s>
This	O
has	O
been	O
done	O
with	O
similarity	O
measures	O
and	O
structural	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
approaches	O
.	O
</s>
<s>
Structural	B-General_Concept
risk	I-General_Concept
minimization	I-General_Concept
approaches	O
that	O
have	O
been	O
used	O
include	O
linear	O
approaches	O
,	O
such	O
as	O
that	O
used	O
by	O
Lanckriet	O
et	O
al	O
.	O
</s>
<s>
We	O
can	O
define	O
the	O
implausibility	O
of	O
a	O
kernel	O
to	O
be	O
the	O
value	O
of	O
the	O
objective	O
function	O
after	O
solving	O
a	O
canonical	O
SVM	B-Algorithm
problem	O
.	O
</s>
<s>
with	O
nonnegative	O
weights	O
for	O
individual	O
kernels	B-Algorithm
and	O
using	O
non-linear	O
combinations	O
of	O
kernels	B-Algorithm
.	O
</s>
<s>
This	O
model	O
is	O
then	O
optimized	O
using	O
a	O
customized	O
multinomial	B-General_Concept
probit	I-General_Concept
approach	O
with	O
a	O
Gibbs	B-Algorithm
sampler	I-Algorithm
.	O
</s>
<s>
Boosting	O
approaches	O
add	O
new	O
kernels	B-Algorithm
iteratively	O
until	O
some	O
stopping	O
criteria	O
that	O
is	O
a	O
function	O
of	O
performance	O
is	O
reached	O
.	O
</s>
<s>
The	O
parameters	O
and	O
are	O
learned	O
by	O
gradient	B-Algorithm
descent	I-Algorithm
on	O
a	O
coordinate	O
basis	O
.	O
</s>
<s>
Semisupervised	O
learning	O
approaches	O
to	O
multiple	B-Algorithm
kernel	I-Algorithm
learning	I-Algorithm
are	O
similar	O
to	O
other	O
extensions	O
of	O
supervised	O
learning	O
approaches	O
.	O
</s>
<s>
The	O
combined	O
minimization	O
problem	O
is	O
optimized	O
using	O
a	O
modified	O
block	O
gradient	B-Algorithm
descent	I-Algorithm
algorithm	O
.	O
</s>
<s>
Unsupervised	B-General_Concept
multiple	B-Algorithm
kernel	I-Algorithm
learning	I-Algorithm
algorithms	O
have	O
also	O
been	O
proposed	O
by	O
Zhuang	O
et	O
al	O
.	O
</s>
<s>
:	O
A	O
scalable	O
C++	O
MKL	O
SVM	B-Algorithm
library	O
that	O
can	O
handle	O
a	O
million	O
kernels	B-Algorithm
.	O
</s>
<s>
:	O
Generalized	O
Multiple	B-Algorithm
Kernel	I-Algorithm
Learning	I-Algorithm
code	O
in	O
MATLAB	B-Language
,	O
does	O
and	O
regularization	O
for	O
supervised	O
learning	O
.	O
</s>
<s>
:	O
A	O
MATLAB	B-Language
code	O
based	O
on	O
the	O
SimpleMKL	O
algorithm	O
for	O
MKL	O
SVM	B-Algorithm
.	O
</s>
<s>
:	O
A	O
Python	O
framework	O
for	O
MKL	O
and	O
kernel	B-Algorithm
machines	I-Algorithm
scikit-compliant	O
with	O
different	O
algorithms	O
,	O
e.g.	O
</s>
