<s>
In	O
a	O
statistical-classification	B-General_Concept
problem	O
with	O
two	O
classes	O
,	O
a	O
decision	B-General_Concept
boundary	I-General_Concept
or	O
decision	B-General_Concept
surface	I-General_Concept
is	O
a	O
hypersurface	O
that	O
partitions	O
the	O
underlying	O
vector	O
space	O
into	O
two	O
sets	O
,	O
one	O
for	O
each	O
class	O
.	O
</s>
<s>
The	O
classifier	B-General_Concept
will	O
classify	O
all	O
the	O
points	O
on	O
one	O
side	O
of	O
the	O
decision	B-General_Concept
boundary	I-General_Concept
as	O
belonging	O
to	O
one	O
class	O
and	O
all	O
those	O
on	O
the	O
other	O
side	O
as	O
belonging	O
to	O
the	O
other	O
class	O
.	O
</s>
<s>
A	O
decision	B-General_Concept
boundary	I-General_Concept
is	O
the	O
region	O
of	O
a	O
problem	O
space	O
in	O
which	O
the	O
output	O
label	O
of	O
a	O
classifier	B-General_Concept
is	O
ambiguous	O
.	O
</s>
<s>
If	O
the	O
decision	B-General_Concept
surface	I-General_Concept
is	O
a	O
hyperplane	O
,	O
then	O
the	O
classification	O
problem	O
is	O
linear	O
,	O
and	O
the	O
classes	O
are	O
linearly	O
separable	O
.	O
</s>
<s>
Decision	B-General_Concept
boundaries	I-General_Concept
are	O
not	O
always	O
clear	O
cut	O
.	O
</s>
<s>
Decision	B-General_Concept
boundaries	I-General_Concept
can	O
be	O
approximations	O
of	O
optimal	O
stopping	O
boundaries	O
.	O
</s>
<s>
The	O
decision	B-General_Concept
boundary	I-General_Concept
is	O
the	O
set	O
of	O
points	O
of	O
that	O
hyperplane	O
that	O
pass	O
through	O
zero	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
angle	O
between	O
a	O
vector	O
and	O
points	O
in	O
a	O
set	O
must	O
be	O
zero	O
for	O
points	O
that	O
are	O
on	O
or	O
close	O
to	O
the	O
decision	B-General_Concept
boundary	I-General_Concept
.	O
</s>
<s>
Decision	B-General_Concept
boundary	I-General_Concept
instability	O
can	O
be	O
incorporated	O
with	O
generalization	O
error	O
as	O
a	O
standard	O
for	O
selecting	O
the	O
most	O
accurate	O
and	O
stable	O
classifier	B-General_Concept
.	O
</s>
<s>
In	O
the	O
case	O
of	O
backpropagation	B-Algorithm
based	O
artificial	B-Architecture
neural	I-Architecture
networks	I-Architecture
or	O
perceptrons	B-Algorithm
,	O
the	O
type	O
of	O
decision	B-General_Concept
boundary	I-General_Concept
that	O
the	O
network	O
can	O
learn	O
is	O
determined	O
by	O
the	O
number	O
of	O
hidden	O
layers	O
the	O
network	O
has	O
.	O
</s>
<s>
If	O
it	O
has	O
one	O
hidden	O
layer	O
,	O
then	O
it	O
can	O
learn	O
any	O
continuous	O
function	O
on	O
compact	O
subsets	O
of	O
Rn	O
as	O
shown	O
by	O
the	O
universal	B-Algorithm
approximation	I-Algorithm
theorem	I-Algorithm
,	O
thus	O
it	O
can	O
have	O
an	O
arbitrary	O
decision	B-General_Concept
boundary	I-General_Concept
.	O
</s>
<s>
In	O
particular	O
,	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
find	O
a	O
hyperplane	O
that	O
separates	O
the	O
feature	O
space	O
into	O
two	O
classes	O
with	O
the	O
maximum	O
margin	O
.	O
</s>
<s>
Neural	B-Architecture
networks	I-Architecture
try	O
to	O
learn	O
the	O
decision	B-General_Concept
boundary	I-General_Concept
which	O
minimizes	O
the	O
empirical	O
error	O
,	O
while	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
try	O
to	O
learn	O
the	O
decision	B-General_Concept
boundary	I-General_Concept
which	O
maximizes	O
the	O
empirical	O
margin	O
between	O
the	O
decision	B-General_Concept
boundary	I-General_Concept
and	O
data	O
points	O
.	O
</s>
