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In order to calculate the likelihood term in the above ratio, we need to take the
inverse and determinant of the covariance matrices for the vector
V
2
in both cases.
For details of rest of BBC algorithm, we refer to [26].
cMonkey.
Reiss et al. [46] proposed an integrated biclustering algorithm (named
cMonkey) used in heterogeneous genome-wide data sets for the inference of global
regulatory networks. In this model, each bicluster is modeled via a Markov chain
process, in which the bicluster is iteratively optimized, and its state is updated
based upon conditional probability distributions computed using the cluster's pre-
vious state. Three major distinct data types are used (gene expression, upstream
sequences, and association networks), and accordingly
p
-values for three such
model components are computed: the expression component, the sequence com-
ponent, and the network component. Here we only reviewed the expression
component.
Given the expression data matrix
A
, the variance in the measured levels of feature
j
is
2
j
1
n
∑
n
i
=
1
2
, where
a
j
=
∑
n
i
=
1
a
ij
/
σ
=
(
a
ij
−
a
j
)
n
. The mean expression level of
a
jk
=
μ
(
r
)
feature
j
over the bicluster's samples
ik
as defined previously. As
defined in [46] the likelihood of an arbitrary measurement
a
ij
relative to this mean
expression level is
S
k
is
exp
2
2
−
(
a
ij
−
a
jk
)
+
ε
1
p
(
a
ij
)=
2
,
2
j
(
σ
+
ε
2
)
2
j
2
π
(
σ
+
ε
)
where
for an unknown systematic error in condition
j
, here assumed to be the
same for all
j
. The likelihood of the measurements of an arbitrary sample
i
among
the conditions in bicluster
k
is
p
ε
(
S
i
)=
∏
j
∈F
k
p
(
a
ij
)
, and similarly the likelihood of
a feature
j
's measurements is
p
.
Before the following iterative steps, the Markov chain process by which a bi-
cluster is optimized requires “seeding” of the bicluster to start the procedure. The
iterative steps include searching for motifs in bicluster, computing conditional prob-
ability that each sample/feature is a member of the bicluster, and performing moves
sampled from the conditional probability.
(
F
j
)=
∏
i
∈S
k
p
(
a
ij
)
6.3.6 Comparison of Biclustering Algorithms
Since the biclustering algorithms are designed based on different bases and used in
different data, and the requirements are different for different applications, there is
no standard rule to judge which biclusters produced are better. In [44], Prelic et al.
defined match score of two clusters
,S
i
of samples as
S
i
B
2
)=
|S
i
∩S
i
|
S
(
B
1
,
|S
i
∪S
i
|
,
