<s>
Generative	B-Algorithm
topographic	I-Algorithm
map	I-Algorithm
(	O
GTM	O
)	O
is	O
a	O
machine	O
learning	O
method	O
that	O
is	O
a	O
probabilistic	O
counterpart	O
of	O
the	O
self-organizing	B-Algorithm
map	I-Algorithm
(	O
SOM	O
)	O
,	O
is	O
probably	O
convergent	O
and	O
does	O
not	O
require	O
a	O
shrinking	O
neighborhood	O
or	O
a	O
decreasing	O
step	O
size	O
.	O
</s>
<s>
The	O
parameters	O
of	O
the	O
low-dimensional	O
probability	O
distribution	O
,	O
the	O
smooth	O
map	O
and	O
the	O
noise	O
are	O
all	O
learned	O
from	O
the	O
training	O
data	O
using	O
the	O
expectation-maximization	B-Algorithm
(	O
EM	B-Algorithm
)	O
algorithm	O
.	O
</s>
<s>
The	O
approach	O
is	O
strongly	O
related	O
to	O
density	O
networks	O
which	O
use	O
importance	B-Algorithm
sampling	I-Algorithm
and	O
a	O
multi-layer	B-Algorithm
perceptron	I-Algorithm
to	O
form	O
a	O
non-linear	O
latent	O
variable	O
model	O
.	O
</s>
<s>
Then	O
the	O
model	O
's	O
likelihood	O
can	O
be	O
maximized	O
by	O
EM	B-Algorithm
.	O
</s>
<s>
The	O
suggested	O
approach	O
to	O
the	O
nonlinear	O
mapping	O
is	O
to	O
use	O
a	O
radial	B-Algorithm
basis	I-Algorithm
function	I-Algorithm
network	I-Algorithm
(	O
RBF	O
)	O
to	O
create	O
a	O
nonlinear	O
mapping	O
between	O
the	O
latent	O
space	O
and	O
the	O
data	O
space	O
.	O
</s>
<s>
RBF	B-Algorithm
network	I-Algorithm
then	O
form	O
a	O
feature	O
space	O
and	O
the	O
nonlinear	O
mapping	O
can	O
then	O
be	O
taken	O
as	O
a	O
linear	B-Architecture
transform	I-Architecture
of	O
this	O
feature	O
space	O
.	O
</s>
<s>
In	O
data	O
analysis	O
,	O
GTMs	O
are	O
like	O
a	O
nonlinear	O
version	O
of	O
principal	B-Application
components	I-Application
analysis	I-Application
,	O
which	O
allows	O
high-dimensional	O
data	O
to	O
be	O
modelled	O
as	O
resulting	O
from	O
Gaussian	O
noise	O
added	O
to	O
sources	O
in	O
lower-dimensional	O
latent	O
space	O
.	O
</s>
<s>
The	O
disadvantage	O
is	O
that	O
it	O
is	O
a	O
'	O
data-mining	B-Application
'	O
approach	O
,	O
i.e.	O
</s>
<s>
While	O
nodes	O
in	O
the	O
self-organizing	B-Algorithm
map	I-Algorithm
(	O
SOM	O
)	O
can	O
wander	O
around	O
at	O
will	O
,	O
GTM	O
nodes	O
are	O
constrained	O
by	O
the	O
allowable	O
transformations	O
and	O
their	O
probabilities	O
.	O
</s>
<s>
it	O
uses	O
a	O
sound	O
optimization	O
procedure	O
(	O
EM	B-Algorithm
algorithm	I-Algorithm
)	O
.	O
</s>
