<s>
Correlation	B-Algorithm
clustering	I-Algorithm
provides	O
a	O
method	O
for	O
clustering	O
a	O
set	O
of	O
objects	O
into	O
the	O
optimum	O
number	O
of	O
clusters	O
without	O
specifying	O
that	O
number	O
in	O
advance	O
.	O
</s>
<s>
In	O
machine	O
learning	O
,	O
correlation	B-Algorithm
clustering	I-Algorithm
or	O
cluster	O
editing	O
operates	O
in	O
a	O
scenario	O
where	O
the	O
relationships	O
between	O
the	O
objects	O
are	O
known	O
instead	O
of	O
the	O
actual	O
representations	O
of	O
the	O
objects	O
.	O
</s>
<s>
Unlike	O
other	O
clustering	B-Algorithm
algorithms	I-Algorithm
this	O
does	O
not	O
require	O
choosing	B-Algorithm
the	I-Algorithm
number	I-Algorithm
of	I-Algorithm
clusters	I-Algorithm
in	O
advance	O
because	O
the	O
objective	O
,	O
to	O
minimize	O
the	O
sum	O
of	O
weights	O
of	O
the	O
cut	O
edges	O
,	O
is	O
independent	O
of	O
the	O
number	O
of	O
clusters	O
.	O
</s>
<s>
The	O
minimum	O
disagreement	O
correlation	B-Algorithm
clustering	I-Algorithm
problem	O
is	O
the	O
following	O
optimization	O
problem	O
:	O
</s>
<s>
Instead	O
of	O
formulating	O
the	O
correlation	B-Algorithm
clustering	I-Algorithm
problem	O
in	O
terms	O
of	O
non-negative	O
edge	O
weights	O
and	O
a	O
partition	O
of	O
the	O
edges	O
into	O
attractive	O
and	O
repulsive	O
edges	O
the	O
problem	O
is	O
also	O
formulated	O
in	O
terms	O
of	O
positive	O
and	O
negative	O
edge	O
costs	O
without	O
partitioning	O
the	O
set	O
of	O
edges	O
explicitly	O
.	O
</s>
<s>
discuss	O
the	O
NP-completeness	O
proof	O
and	O
also	O
present	O
both	O
a	O
constant	O
factor	O
approximation	B-Algorithm
algorithm	I-Algorithm
and	O
polynomial-time	B-Algorithm
approximation	I-Algorithm
scheme	I-Algorithm
to	O
find	O
the	O
clusters	O
in	O
this	O
setting	O
.	O
</s>
<s>
The	O
authors	O
show	O
that	O
the	O
above	O
algorithm	O
is	O
a	O
3-approximation	O
algorithm	O
for	O
correlation	B-Algorithm
clustering	I-Algorithm
.	O
</s>
<s>
The	O
best	O
polynomial-time	O
approximation	B-Algorithm
algorithm	I-Algorithm
known	O
at	O
the	O
moment	O
for	O
this	O
problem	O
achieves	O
a	O
~	O
2.06	O
approximation	O
by	O
rounding	O
a	O
linear	O
program	O
,	O
as	O
shown	O
by	O
Chawla	O
,	O
Makarychev	O
,	O
Schramm	O
,	O
and	O
Yaroslavtsev	O
.	O
</s>
<s>
Karpinski	O
and	O
Schudy	O
proved	O
existence	O
of	O
a	O
polynomial	B-Algorithm
time	I-Algorithm
approximation	I-Algorithm
scheme	I-Algorithm
(	O
PTAS	O
)	O
for	O
that	O
problem	O
on	O
complete	O
graphs	O
and	O
fixed	O
number	O
of	O
clusters	O
.	O
</s>
<s>
that	O
the	O
optimization	O
of	O
the	O
correlation	B-Algorithm
clustering	I-Algorithm
functional	O
is	O
closely	O
related	O
to	O
well	O
known	O
discrete	O
optimization	O
methods	O
.	O
</s>
<s>
In	O
their	O
work	O
they	O
proposed	O
a	O
probabilistic	O
analysis	O
of	O
the	O
underlying	O
implicit	O
model	O
that	O
allows	O
the	O
correlation	B-Algorithm
clustering	I-Algorithm
functional	O
to	O
estimate	O
the	O
underlying	O
number	O
of	O
clusters	O
.	O
</s>
<s>
Correlation	B-Algorithm
clustering	I-Algorithm
also	O
relates	O
to	O
a	O
different	O
task	O
,	O
where	O
correlations	O
among	O
attributes	O
of	O
feature	B-Algorithm
vectors	I-Algorithm
in	O
a	O
high-dimensional	O
space	O
are	O
assumed	O
to	O
exist	O
guiding	O
the	O
clustering	B-Algorithm
process	I-Algorithm
.	O
</s>
<s>
These	O
correlations	O
may	O
be	O
different	O
in	O
different	O
clusters	O
,	O
thus	O
a	O
global	O
decorrelation	B-Algorithm
cannot	O
reduce	O
this	O
to	O
traditional	O
(	O
uncorrelated	O
)	O
clustering	O
.	O
</s>
<s>
Different	O
methods	O
for	O
correlation	B-Algorithm
clustering	I-Algorithm
of	O
this	O
type	O
are	O
discussed	O
in	O
and	O
the	O
relationship	O
to	O
different	O
types	O
of	O
clustering	O
is	O
discussed	O
in	O
.	O
</s>
<s>
See	O
also	O
Clustering	B-Algorithm
high-dimensional	I-Algorithm
data	I-Algorithm
.	O
</s>
<s>
Correlation	B-Algorithm
clustering	I-Algorithm
(	O
according	O
to	O
this	O
definition	O
)	O
can	O
be	O
shown	O
to	O
be	O
closely	O
related	O
to	O
biclustering	B-Algorithm
.	O
</s>
<s>
As	O
in	O
biclustering	B-Algorithm
,	O
the	O
goal	O
is	O
to	O
identify	O
groups	O
of	O
objects	O
that	O
share	O
a	O
correlation	O
in	O
some	O
of	O
their	O
attributes	O
;	O
where	O
the	O
correlation	O
is	O
usually	O
typical	O
for	O
the	O
individual	O
clusters	O
.	O
</s>
