<s>
Also	O
known	O
as	O
classification	O
or	O
statistical	B-General_Concept
classification	I-General_Concept
,	O
pattern	O
recognition	O
aims	O
at	O
building	O
a	O
classifier	B-General_Concept
that	O
can	O
determine	O
the	O
class	O
of	O
an	O
input	O
pattern	O
.	O
</s>
<s>
Nonetheless	O
,	O
in	O
real	O
world	O
applications	O
such	O
as	O
character	B-Application
recognition	I-Application
,	O
a	O
certain	O
amount	O
of	O
information	O
on	O
the	O
problem	O
is	O
usually	O
known	O
beforehand	O
.	O
</s>
<s>
However	O
,	O
in	O
this	O
most	O
general	O
form	O
,	O
determining	O
a	O
model	O
from	O
a	O
finite	O
set	O
of	O
samples	O
without	O
prior	O
knowledge	O
is	O
an	O
ill-posed	B-Algorithm
problem	I-Algorithm
,	O
in	O
the	O
sense	O
that	O
a	O
unique	O
model	O
may	O
not	O
exist	O
.	O
</s>
<s>
Many	O
classifiers	B-General_Concept
incorporate	O
the	O
general	O
smoothness	O
assumption	O
that	O
a	O
test	O
pattern	O
similar	O
to	O
one	O
of	O
the	O
training	O
samples	O
tends	O
to	O
be	O
assigned	O
to	O
the	O
same	O
class	O
.	O
</s>
<s>
A	O
very	O
common	O
type	O
of	O
prior	O
knowledge	O
in	O
pattern	O
recognition	O
is	O
the	O
invariance	O
of	O
the	O
class	O
(	O
or	O
the	O
output	O
of	O
the	O
classifier	B-General_Concept
)	O
to	O
a	O
transformation	B-Algorithm
of	O
the	O
input	O
pattern	O
.	O
</s>
<s>
This	O
type	O
of	O
knowledge	O
is	O
referred	O
to	O
as	O
transformation-invariance	O
.	O
</s>
<s>
translation	B-Algorithm
;	O
</s>
<s>
rotation	B-General_Concept
;	O
</s>
<s>
scaling	B-Algorithm
.	O
</s>
<s>
The	O
function	O
in	O
these	O
equations	O
can	O
be	O
either	O
the	O
decision	O
function	O
of	O
the	O
classifier	B-General_Concept
or	O
its	O
real-valued	O
output	O
.	O
</s>
<s>
Another	O
approach	O
is	O
to	O
consider	O
class-invariance	O
with	O
respect	O
to	O
a	O
"	O
domain	O
of	O
the	O
input	O
space	O
"	O
instead	O
of	O
a	O
transformation	B-Algorithm
.	O
</s>
<s>
A	O
typical	O
application	O
of	O
this	O
type	O
of	O
prior	O
knowledge	O
is	O
a	O
classifier	B-General_Concept
invariant	O
to	O
permutations	O
of	O
rows	O
of	O
the	O
matrix	O
inputs	O
.	O
</s>
<s>
Moreover	O
,	O
not	O
taking	O
into	O
account	O
the	O
poor	O
quality	O
of	O
some	O
data	O
or	O
a	O
large	O
imbalance	O
between	O
the	O
classes	O
can	O
mislead	O
the	O
decision	O
of	O
a	O
classifier	B-General_Concept
.	O
</s>
