Databases Reference
In-Depth Information
More generally, a bicluster is interesting if the rows change in a synchronized way with
respect to the columns and vice versa. Mathematically, a
bicluster with coherent
values
(also known as
a pattern-based cluster
) is a submatrix
I
J
such that for
any
i
2
I
and
j
2
J
,
e
ij
D
c
C
i
C
j
, where
j
are the adjustment for row
i
and column
j
, respectively. For example, Figure 11.7 shows a bicluster with coherent
values.
It can be shown that
I
J
is a bicluster with coherent values if and only if for
any
i
1
,
i
2
2
I
and
j
1
,
j
2
2
J
, then
e
i
1
j
1
e
i
2
j
1
D
e
i
1
j
2
e
i
2
j
2
. Moreover, instead of using
addition, we can define a bicluster with coherent values using multiplication, that
i
and
is,
e
ij
D
c
i
j
. Clearly, biclusters with constant values on rows or columns are
special cases of biclusters with coherent values.
In some applications, we may only be interested in the up- or down-regulated
changes across genes or conditions without constraining the exact values. A
biclus-
ter with coherent evolutions on rows
is a submatrix
I
J
such that for any
i
1
,
i
2
2
I
and
j
1
,
j
2
2
J
,
e
i
2
j
1
e
i
2
j
2
/ 0. For example, Figure 11.8 shows a biclus-
ter with coherent evolutions on rows. Symmetrically, we can define biclusters with
coherent evolutions on columns.
.
e
i
1
j
1
e
i
1
j
2
/.
Next, we study how to mine biclusters.
10
10
10
10
10
20
20
20
20
20
50
50
50
50
50
0
0
0
0
0
Figure11.6
Bicluster with constant values on rows.
10
50
30
70
20
20
60
40
80
30
50
90
70
110
60
0
40
20
60
10
Figure11.7
Bicluster with coherent values.
10
50
30
70
20
20
100
50
1000
30
50
100
90
120
80
0
80
20
100
10
Figure11.8
Bicluster with coherent evolutions on rows.
