<s>
Elastic	B-Algorithm
maps	I-Algorithm
provide	O
a	O
tool	O
for	O
nonlinear	B-Algorithm
dimensionality	I-Algorithm
reduction	I-Algorithm
.	O
</s>
<s>
The	O
elastic	O
coefficients	O
of	O
this	O
system	O
allow	O
the	O
switch	O
from	O
completely	O
unstructured	O
k-means	B-Algorithm
clustering	I-Algorithm
(	O
zero	O
elasticity	O
)	O
to	O
the	O
estimators	O
located	O
closely	O
to	O
linear	O
PCA	B-Application
manifolds	I-Application
(	O
for	O
high	O
bending	O
and	O
low	O
stretching	O
modules	O
)	O
.	O
</s>
<s>
Elastic	B-Algorithm
map	I-Algorithm
is	O
represented	O
by	O
a	O
set	O
of	O
nodes	O
in	O
the	O
same	O
space	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
apply	O
weighting	O
factors	O
to	O
the	O
terms	O
of	O
this	O
sum	O
,	O
for	O
example	O
to	O
reflect	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
probability	O
density	O
function	O
of	O
any	O
subset	O
of	O
data	O
points	O
.	O
</s>
<s>
The	O
position	O
of	O
the	O
nodes	O
is	O
determined	O
by	O
the	O
mechanical	O
equilibrium	O
of	O
the	O
elastic	B-Algorithm
map	I-Algorithm
,	O
i.e.	O
</s>
<s>
Therefore	O
,	O
similar	O
to	O
principal	B-Application
component	I-Application
analysis	I-Application
or	O
k-means	B-Algorithm
,	O
a	O
splitting	O
method	O
is	O
used	O
:	O
</s>
<s>
This	O
expectation-maximization	B-Algorithm
algorithm	I-Algorithm
guarantees	O
a	O
local	O
minimum	O
of	O
.	O
</s>
<s>
The	O
method	O
of	O
elastic	B-Algorithm
maps	I-Algorithm
has	O
been	O
systematically	O
tested	O
and	O
compared	O
with	O
several	O
machine	O
learning	O
methods	O
on	O
the	O
applied	O
problem	O
of	O
identification	O
of	O
the	O
flow	O
regime	O
of	O
a	O
gas-liquid	O
flow	O
in	O
a	O
pipe	O
.	O
</s>
<s>
The	O
method	O
of	O
elastic	B-Algorithm
maps	I-Algorithm
provided	O
a	O
2D	O
map	O
,	O
where	O
the	O
area	O
of	O
each	O
regime	O
is	O
represented	O
.	O
</s>
<s>
Here	O
,	O
ANN	O
stands	O
for	O
the	O
backpropagation	B-Algorithm
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
,	O
SVM	B-Algorithm
stands	O
for	O
the	O
support	B-Algorithm
vector	I-Algorithm
machine	I-Algorithm
,	O
SOM	O
for	O
the	O
self-organizing	B-Algorithm
maps	I-Algorithm
.	O
</s>
<s>
In	O
this	O
technology	O
,	O
elastic	B-Algorithm
maps	I-Algorithm
are	O
used	O
in	O
combination	O
with	O
Principal	B-Application
Component	I-Application
Analysis	I-Application
(	O
PCA	O
)	O
,	O
Independent	B-Algorithm
Component	I-Algorithm
Analysis	I-Algorithm
(	O
ICA	O
)	O
and	O
backpropagation	B-Algorithm
ANN	O
.	O
</s>
<s>
The	O
textbook	O
provides	O
a	O
systematic	O
comparison	O
of	O
elastic	B-Algorithm
maps	I-Algorithm
and	O
self-organizing	B-Algorithm
maps	I-Algorithm
(	O
SOMs	O
)	O
in	O
applications	O
to	O
economic	O
and	O
financial	O
decision-making	O
.	O
</s>
