Biology Reference
In-Depth Information
CB:
m
max
x
x
i
(13.9a)
i
=1
i
=1
a
ij
f
ir
x
i
i
=1
>
i
=1
a
ij
f
iξ
x
i
subject to
i
=1
,
∀r,ξ
∈{
1
,...,k
}
, r
=
ξ,j
∈
S
r
(13.9b)
f
ir
x
i
f
iξ
x
i
x
i
∈{
0
,
1
},
∀i ∈{
1
,...,m}
(13.9c)
α
-CB:
m
max
x
x
i
(13.10a)
i
=1
i
=1
i
=1
a
ij
f
ir
x
i
i
=1
a
ij
f
iξ
x
i
i
=1
subject to
>α
j
+
,
∀r,ξ ∈{
1
,...,k}, r
=
ξ,j ∈ S
r
(13.10b)
f
ir
x
i
f
iξ
x
i
x
i
∈{
0
,
1
}
,
∀
i
∈{
1
,...,m
}
(13.10c)
β
-CB:
m
max
x
x
i
(13.11a)
i
=1
i
=1
i
=1
a
ij
f
ir
x
i
i
=1
a
ij
f
iξ
x
i
i
=1
subject to
>β
j
,
∀r,ξ ∈{
1
,...,k}, r
=
ξ,j ∈ S
r
f
ir
x
i
f
iξ
x
i
(13.11b)
x
i
∈{
0
,
1
},
∀i ∈{
1
,...,m}
(13.11c)
The goal in the CB problem is to find the largest set of features that can be
used to construct a consistent biclustering
∗
.The
α
-CB and
β
-CB problems are
similar to the original CB problem but the aim is to select features that can be
used to construct
α
-consistent and
β
-consistent biclusterings, respectively.
In (13.9),
x
i
,i
=1
,...m
are the decision variables.
x
i
=1if
i
-th feature
is selected, and
x
i
=0otherwise.
f
ik
=1if feature
i
belongs to class
k
,and
f
ik
=0otherwise. The objective is to maximize the number of features selected
and (13.9b) ensures that the biclustering is consistent with respect to the selected
features.
∗
Note that the number of selected features is the most commonly used objective function.
Other
objectives such as maximizing the weighted sum of selected features can also be considered.
Search WWH ::
Custom Search