Information Technology Reference
In-Depth Information
a
ij
=
μ
,∀
i
∈S
k
,∀
j
∈F
k
,
is a constant number.
2. Bicluster with constant values on rows or columns. For a bicluster
B
k
=(
S
k
,F
k
)
with constant values on rows, the identity for it is
where
μ
a
ij
=
μ
+
α
i
,
or
a
ij
=
μ
×
α
i
,∀
i
∈S
k
,∀
j
∈F
k
,
where
α
i
is an adjustment number for row
i
. The first identity
is additive and the second one is multiplicative. Note in some data processing
steps, the two are equivalent, for example, if doing logarithmic transformation
on the second data matrix case. For the case of constant values on columns, the
identity is
μ
is a constant and
a
ij
=
μ
+
β
j
,
or
a
ij
=
μ
×
β
j
,∀
i
∈S
k
,∀
j
∈F
k
,
β
j
is an adjustment number for column
j
.
3. Bicluster with coherent values. For a bicluster
B
k
=(
S
k
,F
k
)
where
μ
is a constant and
with coherent val-
ues, there are two transferable expressions. The first one is additive,
=
μ
+
α
+
β
,∀
∈S
k
,∀
∈F
k
,
a
ij
i
j
i
j
and the second one is multiplicative,
a
ij
=
μ
×
α
i
×
β
j
,∀
i
∈S
k
,∀
j
∈F
k
.
The method to transform the second into the first is still doing logarithmic trans-
formation on the second data matrix.
4. Bicluster with coherent evolutions. In the above three cases, the data matrix
A
R
2
. But for some cases, the algorithms are finding relationships of data
on rows or columns without considering the real value. For example, in order-
preserving submatrix (OPSM) algorithm, a bicluster is a group of rows whose
values induce a linear order across a subset of columns. Thus, the value of
a
ij
is
not always required in this situation since here the relationships between entries
are considered. For other cases, the bicluster with coherent evolutions will be
discussed in the following algorithms.
∈
Although the biclusters are classified into these four classes, there are still other
forms if the output bicluster was considered to reflect some relationships between
the
rows
and
columns
within
this
bicluster.
For
example,
in
[7],
a
δ
-valid pattern of bicluster is defined to satisfy max
(
a
ij
)
−
min
(
a
ij
)
<
δ
,∀
j
∈F
k
for
row
i
.
Besides this, data initialization influences bicluster types, for example, row
normalizing a bicluster with constant values on rows (type 2) will result a bi-
cluster constant values (type 1). Similarly, column normalizing a bicluster with
constant
values
on
columns
(type
2)
will
result
a
bicluster
constant
values
(type 1).
