<s>
The	O
multi-surface	B-Algorithm
method	I-Algorithm
(	O
MSM	O
)	O
is	O
a	O
form	O
of	O
decision	O
making	O
using	O
the	O
concept	O
of	O
piecewise-linear	O
separability	O
of	O
datasets	O
to	O
categorize	O
data	O
.	O
</s>
<s>
The	O
method	O
may	O
be	O
formulated	O
as	O
a	O
feedforward	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
with	O
weights	O
that	O
are	O
trained	O
via	O
linear	B-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
Comparisons	O
between	O
neural	O
networks	O
trained	O
with	O
the	O
MSM	O
versus	O
backpropagation	B-Algorithm
show	O
MSM	O
is	O
better	O
able	O
to	O
classify	O
data	O
.	O
</s>
<s>
The	O
decision	O
problem	O
associated	O
linear	B-Algorithm
program	I-Algorithm
for	O
the	O
MSM	O
is	O
NP-Complete	O
.	O
</s>
<s>
If	O
the	O
intersection	O
of	O
convex	O
hulls	O
of	O
the	O
two	O
sets	O
is	O
the	O
empty	O
set	O
,	O
then	O
it	O
is	O
possible	O
to	O
use	O
a	O
single	O
linear	B-Algorithm
program	I-Algorithm
to	O
obtain	O
a	O
linear	O
discriminant	O
of	O
the	O
form	O
,	O
.	O
</s>
<s>
Usually	O
,	O
in	O
real	O
applications	O
,	O
the	O
sets	O
 '	O
convex	O
hulls	O
do	O
intersect	O
,	O
and	O
a	O
(	O
often	O
non-convex	O
)	O
piecewise-linear	O
discriminant	O
can	O
be	O
used	O
,	O
through	O
the	O
use	O
of	O
several	O
linear	B-Algorithm
programs	I-Algorithm
.	O
</s>
