<s>
A	O
self-organizing	B-Algorithm
map	I-Algorithm
(	O
SOM	O
)	O
or	O
self-organizing	B-Algorithm
feature	I-Algorithm
map	I-Algorithm
(	O
SOFM	B-Algorithm
)	O
is	O
an	O
unsupervised	B-General_Concept
machine	I-General_Concept
learning	I-General_Concept
technique	O
used	O
to	O
produce	O
a	O
low-dimensional	B-Algorithm
(	O
typically	O
two-dimensional	O
)	O
representation	O
of	O
a	O
higher	O
dimensional	O
data	O
set	O
while	O
preserving	O
the	O
topological	B-Architecture
structure	I-Architecture
of	O
the	O
data	O
.	O
</s>
<s>
An	O
SOM	O
is	O
a	O
type	O
of	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
but	O
is	O
trained	O
using	O
competitive	B-Algorithm
learning	I-Algorithm
rather	O
than	O
the	O
error-correction	O
learning	O
(	O
e.g.	O
,	O
backpropagation	B-Algorithm
with	O
gradient	B-Algorithm
descent	I-Algorithm
)	O
used	O
by	O
other	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
.	O
</s>
<s>
The	O
SOM	O
was	O
introduced	O
by	O
the	O
Finnish	O
professor	O
Teuvo	O
Kohonen	B-Algorithm
in	O
the	O
1980s	O
and	O
therefore	O
is	O
sometimes	O
called	O
a	O
Kohonen	B-Algorithm
map	I-Algorithm
or	O
Kohonen	B-Algorithm
network	I-Algorithm
.	O
</s>
<s>
The	O
Kohonen	B-Algorithm
map	I-Algorithm
or	O
network	O
is	O
a	O
computationally	O
convenient	O
abstraction	O
building	O
on	O
biological	O
models	O
of	O
neural	O
systems	O
from	O
the	O
1970s	O
and	O
morphogenesis	O
models	O
dating	O
back	O
to	O
Alan	O
Turing	O
in	O
the	O
1950s	O
.	O
</s>
<s>
Self-organizing	B-Algorithm
maps	I-Algorithm
,	O
like	O
most	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
,	O
operate	O
in	O
two	O
modes	O
:	O
training	O
and	O
mapping	O
.	O
</s>
<s>
The	O
number	O
of	O
nodes	O
and	O
their	O
arrangement	O
are	O
specified	O
beforehand	O
based	O
on	O
the	O
larger	O
goals	O
of	O
the	O
analysis	O
and	O
exploration	B-General_Concept
of	I-General_Concept
the	I-General_Concept
data	I-General_Concept
.	O
</s>
<s>
While	O
nodes	O
in	O
the	O
map	O
space	O
stay	O
fixed	O
,	O
training	O
consists	O
in	O
moving	O
weight	O
vectors	O
toward	O
the	O
input	O
data	O
(	O
reducing	O
a	O
distance	O
metric	O
such	O
as	O
Euclidean	O
distance	O
)	O
without	O
spoiling	O
the	O
topology	B-Architecture
induced	O
from	O
the	O
map	O
space	O
.	O
</s>
<s>
The	O
goal	O
of	O
learning	O
in	O
the	O
self-organizing	B-Algorithm
map	I-Algorithm
is	O
to	O
cause	O
different	O
parts	O
of	O
the	O
network	O
to	O
respond	O
similarly	O
to	O
certain	O
input	O
patterns	O
.	O
</s>
<s>
The	O
weights	O
of	O
the	O
neurons	O
are	O
initialized	O
either	O
to	O
small	O
random	O
values	O
or	O
sampled	O
evenly	O
from	O
the	O
subspace	O
spanned	O
by	O
the	O
two	O
largest	O
principal	B-Application
component	I-Application
eigenvectors	O
.	O
</s>
<s>
The	O
training	O
utilizes	O
competitive	B-Algorithm
learning	I-Algorithm
.	O
</s>
<s>
where	O
s	O
is	O
the	O
step	O
index	O
,	O
t	O
is	O
an	O
index	O
into	O
the	O
training	O
sample	O
,	O
u	O
is	O
the	O
index	O
of	O
the	O
BMU	O
for	O
the	O
input	O
vector	O
D(t )	O
,	O
α(s )	O
is	O
a	O
monotonically	O
decreasing	O
learning	O
coefficient	O
;	O
θ(u, v, s )	O
is	O
the	O
neighborhood	O
function	O
which	O
gives	O
the	O
distance	O
between	O
the	O
neuron	O
u	O
and	O
the	O
neuron	O
v	O
in	O
step	O
s	O
.	O
Depending	O
on	O
the	O
implementations	O
,	O
t	O
can	O
scan	O
the	O
training	O
data	O
set	O
systematically	O
(	O
t	O
is	O
0	O
,	O
1	O
,	O
2	O
...	O
T	O
,	O
then	O
repeat	O
,	O
T	O
being	O
the	O
training	O
sample	O
's	O
size	O
)	O
,	O
be	O
randomly	O
drawn	O
from	O
the	O
data	O
set	O
(	O
bootstrap	B-Application
sampling	I-Application
)	O
,	O
or	O
implement	O
some	O
other	O
sampling	O
method	O
(	O
such	O
as	O
jackknifing	O
)	O
.	O
</s>
<s>
While	O
representing	O
input	O
data	O
as	O
vectors	O
has	O
been	O
emphasized	O
in	O
this	O
article	O
,	O
any	O
kind	O
of	O
object	O
which	O
can	O
be	O
represented	O
digitally	O
,	O
which	O
has	O
an	O
appropriate	O
distance	O
measure	O
associated	O
with	O
it	O
,	O
and	O
in	O
which	O
the	O
necessary	O
operations	O
for	O
training	O
are	O
possible	O
can	O
be	O
used	O
to	O
construct	O
a	O
self-organizing	B-Algorithm
map	I-Algorithm
.	O
</s>
<s>
This	O
includes	O
matrices	O
,	O
continuous	O
functions	O
or	O
even	O
other	O
self-organizing	B-Algorithm
maps	I-Algorithm
.	O
</s>
<s>
Selection	O
of	O
initial	O
weights	O
as	O
good	O
approximations	O
of	O
the	O
final	O
weights	O
is	O
a	O
well-known	O
problem	O
for	O
all	O
iterative	O
methods	O
of	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
,	O
including	O
self-organizing	B-Algorithm
maps	I-Algorithm
.	O
</s>
<s>
Kohonen	B-Algorithm
originally	O
proposed	O
random	O
initiation	O
of	O
weights	O
.	O
</s>
<s>
More	O
recently	O
,	O
principal	B-Application
component	I-Application
initialization	O
,	O
in	O
which	O
initial	O
map	O
weights	O
are	O
chosen	O
from	O
the	O
space	O
of	O
the	O
first	O
principal	B-Application
components	I-Application
,	O
has	O
become	O
popular	O
due	O
to	O
the	O
exact	O
reproducibility	O
of	O
the	O
results	O
.	O
</s>
<s>
A	O
careful	O
comparison	O
of	O
random	O
initialization	O
to	O
principal	B-Application
component	I-Application
initialization	O
for	O
a	O
one-dimensional	O
map	O
,	O
however	O
,	O
found	O
that	O
the	O
advantages	O
of	O
principal	B-Application
component	I-Application
initialization	O
are	O
not	O
universal	O
.	O
</s>
<s>
Principal	B-Application
component	I-Application
initialization	O
was	O
preferable	O
(	O
for	O
a	O
one-dimensional	O
map	O
)	O
when	O
the	O
principal	O
curve	O
approximating	O
the	O
dataset	O
could	O
be	O
univalently	O
and	O
linearly	O
projected	O
on	O
the	O
first	O
principal	B-Application
component	I-Application
(	O
quasilinear	O
sets	O
)	O
.	O
</s>
<s>
This	O
may	O
be	O
visualized	O
by	O
a	O
U-Matrix	B-Algorithm
(	O
Euclidean	O
distance	O
between	O
weight	O
vectors	O
of	O
neighboring	O
cells	O
)	O
of	O
the	O
SOM	O
.	O
</s>
<s>
SOM	O
may	O
be	O
considered	O
a	O
nonlinear	O
generalization	O
of	O
Principal	B-Application
components	I-Application
analysis	I-Application
(	O
PCA	O
)	O
.	O
</s>
<s>
It	O
has	O
been	O
shown	O
,	O
using	O
both	O
artificial	O
and	O
real	O
geophysical	O
data	O
,	O
that	O
SOM	O
has	O
many	O
advantages	O
over	O
the	O
conventional	O
feature	B-Algorithm
extraction	I-Algorithm
methods	O
such	O
as	O
Empirical	O
Orthogonal	O
Functions	O
(	O
EOF	O
)	O
or	O
PCA	O
.	O
</s>
<s>
For	O
example	O
,	O
Elastic	B-Algorithm
maps	I-Algorithm
use	O
the	O
mechanical	O
metaphor	O
of	O
elasticity	O
to	O
approximate	O
principal	O
manifolds	O
:	O
the	O
analogy	O
is	O
an	O
elastic	O
membrane	O
and	O
plate	O
.	O
</s>
<s>
Similarly	O
,	O
after	O
training	O
a	O
grid	O
of	O
neurons	O
for	O
250	O
iterations	O
with	O
a	O
learning	B-General_Concept
rate	I-General_Concept
of	O
0.1	O
on	O
Fisher	B-Language
's	I-Language
Iris	I-Language
,	O
the	O
map	O
can	O
already	O
detect	O
the	O
main	O
differences	O
between	O
species	O
.	O
</s>
<s>
The	O
generative	B-Algorithm
topographic	I-Algorithm
map	I-Algorithm
(	O
GTM	O
)	O
is	O
a	O
potential	O
alternative	O
to	O
SOMs	O
.	O
</s>
<s>
In	O
the	O
sense	O
that	O
a	O
GTM	O
explicitly	O
requires	O
a	O
smooth	O
and	O
continuous	O
mapping	O
from	O
the	O
input	O
space	O
to	O
the	O
map	O
space	O
,	O
it	O
is	O
topology	B-Architecture
preserving	O
.	O
</s>
<s>
The	O
time	B-Algorithm
adaptive	I-Algorithm
self-organizing	I-Algorithm
map	I-Algorithm
(	O
TASOM	O
)	O
network	O
is	O
an	O
extension	O
of	O
the	O
basic	O
SOM	O
.	O
</s>
<s>
The	O
TASOM	O
employs	O
adaptive	O
learning	B-General_Concept
rates	I-General_Concept
and	O
neighborhood	O
functions	O
.	O
</s>
<s>
The	O
growing	B-Algorithm
self-organizing	I-Algorithm
map	I-Algorithm
(	O
GSOM	B-Algorithm
)	O
is	O
a	O
growing	O
variant	O
of	O
the	O
self-organizing	B-Algorithm
map	I-Algorithm
.	O
</s>
<s>
The	O
GSOM	B-Algorithm
was	O
developed	O
to	O
address	O
the	O
issue	O
of	O
identifying	O
a	O
suitable	O
map	O
size	O
in	O
the	O
SOM	O
.	O
</s>
<s>
By	O
using	O
a	O
value	O
called	O
the	O
spread	O
factor	O
,	O
the	O
data	O
analyst	O
has	O
the	O
ability	O
to	O
control	O
the	O
growth	O
of	O
the	O
GSOM	B-Algorithm
.	O
</s>
<s>
The	O
elastic	B-Algorithm
maps	I-Algorithm
approach	O
borrows	O
from	O
the	O
spline	B-Algorithm
interpolation	I-Algorithm
the	O
idea	O
of	O
minimization	O
of	O
the	O
elastic	O
energy	O
.	O
</s>
<s>
In	O
learning	O
,	O
it	O
minimizes	O
the	O
sum	O
of	O
quadratic	O
bending	O
and	O
stretching	O
energy	O
with	O
the	O
least	B-Algorithm
squares	I-Algorithm
approximation	I-Algorithm
error	O
.	O
</s>
