<s>
Sammon	B-Algorithm
mapping	I-Algorithm
or	O
Sammon	B-Algorithm
projection	I-Algorithm
is	O
an	O
algorithm	O
that	O
maps	B-Algorithm
a	O
high-dimensional	O
space	O
to	O
a	O
space	O
of	O
lower	O
dimensionality	O
(	O
see	O
multidimensional	O
scaling	O
)	O
by	O
trying	O
to	O
preserve	O
the	O
structure	O
of	O
inter-point	O
distances	O
in	O
high-dimensional	O
space	O
in	O
the	O
lower-dimension	O
projection	O
.	O
</s>
<s>
It	O
is	O
particularly	O
suited	O
for	O
use	O
in	O
exploratory	B-General_Concept
data	I-General_Concept
analysis	I-General_Concept
.	O
</s>
<s>
It	O
is	O
considered	O
a	O
non-linear	O
approach	O
as	O
the	O
mapping	O
cannot	O
be	O
represented	O
as	O
a	O
linear	O
combination	O
of	O
the	O
original	O
variables	O
as	O
possible	O
in	O
techniques	O
such	O
as	O
principal	B-Application
component	I-Application
analysis	I-Application
,	O
which	O
also	O
makes	O
it	O
more	O
difficult	O
to	O
use	O
for	O
classification	O
applications	O
.	O
</s>
<s>
Sammon	B-Algorithm
's	I-Algorithm
mapping	I-Algorithm
aims	O
to	O
minimize	O
the	O
following	O
error	O
function	O
,	O
which	O
is	O
often	O
referred	O
to	O
as	O
Sammon	B-Algorithm
's	I-Algorithm
stress	I-Algorithm
or	O
Sammon	O
's	O
error	O
:	O
</s>
<s>
The	O
minimization	O
can	O
be	O
performed	O
either	O
by	O
gradient	B-Algorithm
descent	I-Algorithm
,	O
as	O
proposed	O
initially	O
,	O
or	O
by	O
other	O
means	O
,	O
usually	O
involving	O
iterative	O
methods	O
.	O
</s>
<s>
Many	O
implementations	O
prefer	O
to	O
use	O
the	O
first	O
Principal	B-Application
Components	I-Application
as	O
a	O
starting	O
configuration	O
.	O
</s>
<s>
The	O
Sammon	B-Algorithm
mapping	I-Algorithm
has	O
been	O
one	O
of	O
the	O
most	O
successful	O
nonlinear	O
metric	O
multidimensional	O
scaling	O
methods	O
since	O
its	O
advent	O
in	O
1969	O
,	O
but	O
effort	O
has	O
been	O
focused	O
on	O
algorithm	O
improvement	O
rather	O
than	O
on	O
the	O
form	O
of	O
the	O
stress	O
function	O
.	O
</s>
<s>
and	O
right	O
Bregman	B-Algorithm
divergence	I-Algorithm
.	O
</s>
