<s>
Neural	B-Algorithm
gas	I-Algorithm
is	O
an	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
,	O
inspired	O
by	O
the	O
self-organizing	B-Algorithm
map	I-Algorithm
and	O
introduced	O
in	O
1991	O
by	O
Thomas	O
Martinetz	O
and	O
Klaus	O
Schulten	O
.	O
</s>
<s>
The	O
neural	B-Algorithm
gas	I-Algorithm
is	O
a	O
simple	O
algorithm	O
for	O
finding	O
optimal	O
data	O
representations	O
based	O
on	O
feature	B-Algorithm
vectors	I-Algorithm
.	O
</s>
<s>
The	O
algorithm	O
was	O
coined	O
"	O
neural	B-Algorithm
gas	I-Algorithm
"	O
because	O
of	O
the	O
dynamics	O
of	O
the	O
feature	B-Algorithm
vectors	I-Algorithm
during	O
the	O
adaptation	O
process	O
,	O
which	O
distribute	O
themselves	O
like	O
a	O
gas	O
within	O
the	O
data	O
space	O
.	O
</s>
<s>
It	O
is	O
applied	O
where	O
data	B-General_Concept
compression	I-General_Concept
or	O
vector	B-Algorithm
quantization	I-Algorithm
is	O
an	O
issue	O
,	O
for	O
example	O
speech	B-Application
recognition	I-Application
,	O
image	B-Algorithm
processing	I-Algorithm
or	O
pattern	O
recognition	O
.	O
</s>
<s>
As	O
a	O
robustly	O
converging	O
alternative	O
to	O
the	O
k-means	B-Algorithm
clustering	I-Algorithm
it	O
is	O
also	O
used	O
for	O
cluster	B-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
Given	O
a	O
probability	O
distribution	O
of	O
data	O
vectors	O
and	O
a	O
finite	O
number	O
of	O
feature	B-Algorithm
vectors	I-Algorithm
.	O
</s>
<s>
Subsequently	O
,	O
the	O
distance	O
order	O
of	O
the	O
feature	B-Algorithm
vectors	I-Algorithm
to	O
the	O
given	O
data	O
vector	O
is	O
determined	O
.	O
</s>
<s>
Let	O
denote	O
the	O
index	O
of	O
the	O
closest	O
feature	B-Algorithm
vector	I-Algorithm
,	O
the	O
index	O
of	O
the	O
second	O
closest	O
feature	B-Algorithm
vector	I-Algorithm
,	O
and	O
the	O
index	O
of	O
the	O
feature	B-Algorithm
vector	I-Algorithm
most	O
distant	O
to	O
.	O
</s>
<s>
After	O
sufficiently	O
many	O
adaptation	O
steps	O
the	O
feature	B-Algorithm
vectors	I-Algorithm
cover	O
the	O
data	O
space	O
with	O
minimum	O
representation	O
error	O
.	O
</s>
<s>
The	O
adaptation	O
step	O
of	O
the	O
neural	B-Algorithm
gas	I-Algorithm
can	O
be	O
interpreted	O
as	O
gradient	B-Algorithm
descent	I-Algorithm
on	O
a	O
cost	O
function	O
.	O
</s>
<s>
By	O
adapting	O
not	O
only	O
the	O
closest	O
feature	B-Algorithm
vector	I-Algorithm
but	O
all	O
of	O
them	O
with	O
a	O
step	O
size	O
decreasing	O
with	O
increasing	O
distance	O
order	O
,	O
compared	O
to	O
(	O
online	O
)	O
k-means	B-Algorithm
clustering	I-Algorithm
a	O
much	O
more	O
robust	O
convergence	O
of	O
the	O
algorithm	O
can	O
be	O
achieved	O
.	O
</s>
<s>
The	O
neural	B-Algorithm
gas	I-Algorithm
model	O
does	O
not	O
delete	O
a	O
node	O
and	O
also	O
does	O
not	O
create	O
new	O
nodes	O
.	O
</s>
<s>
A	O
number	O
of	O
variants	O
of	O
the	O
neural	B-Algorithm
gas	I-Algorithm
algorithm	O
exists	O
in	O
the	O
literature	O
so	O
as	O
to	O
mitigate	O
some	O
of	O
its	O
shortcomings	O
.	O
</s>
<s>
More	O
notable	O
is	O
perhaps	O
Bernd	O
Fritzke	O
's	O
growing	O
neural	B-Algorithm
gas	I-Algorithm
,	O
but	O
also	O
one	O
should	O
mention	O
further	O
elaborations	O
such	O
as	O
the	O
Growing	O
When	O
Required	O
network	O
and	O
also	O
the	O
incremental	O
growing	O
neural	B-Algorithm
gas	I-Algorithm
.	O
</s>
<s>
A	O
performance-oriented	O
approach	O
that	O
avoids	O
the	O
risk	O
of	O
overfitting	O
is	O
the	O
Plastic	O
Neural	B-Algorithm
gas	I-Algorithm
model	O
.	O
</s>
<s>
Fritzke	O
describes	O
the	O
growing	O
neural	B-Algorithm
gas	I-Algorithm
(	O
GNG	O
)	O
as	O
an	O
incremental	O
network	O
model	O
that	O
learns	O
topological	O
relations	O
by	O
using	O
a	O
"	O
Hebb-like	O
learning	O
rule	O
"	O
,	O
only	O
,	O
unlike	O
the	O
neural	B-Algorithm
gas	I-Algorithm
,	O
it	O
has	O
no	O
parameters	O
that	O
change	O
over	O
time	O
and	O
it	O
is	O
capable	O
of	O
continuous	O
learning	O
,	O
i.e.	O
</s>
<s>
Another	O
neural	B-Algorithm
gas	I-Algorithm
variant	O
inspired	O
in	O
the	O
GNG	O
algorithm	O
is	O
the	O
incremental	O
growing	O
neural	B-Algorithm
gas	I-Algorithm
(	O
IGNG	O
)	O
.	O
</s>
<s>
The	O
"	O
Plastic	O
Neural	B-Algorithm
Gas	I-Algorithm
"	O
model	O
solves	O
this	O
problem	O
by	O
making	O
decisions	O
to	O
add	O
or	O
remove	O
nodes	O
using	O
an	O
unsupervised	O
version	O
of	O
cross-validation	O
,	O
which	O
controls	O
an	O
equivalent	O
notion	O
of	O
"	O
generalization	O
ability	O
"	O
for	O
the	O
unsupervised	O
setting	O
.	O
</s>
<s>
While	O
growing-only	O
methods	O
only	O
cater	O
for	O
the	O
incremental	B-Algorithm
learning	I-Algorithm
scenario	O
,	O
the	O
ability	O
to	O
grow	O
and	O
shrink	O
is	O
suited	O
to	O
the	O
more	O
general	O
streaming	B-Operating_System
data	I-Operating_System
problem	O
.	O
</s>
<s>
To	O
find	O
the	O
ranking	O
of	O
the	O
feature	B-Algorithm
vectors	I-Algorithm
,	O
the	O
neural	B-Algorithm
gas	I-Algorithm
algorithm	O
involves	O
sorting	O
,	O
which	O
is	O
a	O
procedure	O
that	O
does	O
not	O
lend	O
itself	O
easily	O
to	O
parallelization	O
or	O
implementation	O
in	O
analog	O
hardware	O
.	O
</s>
