Biomedical Engineering Reference
In-Depth Information
Fig. 5.3
(
a
) Functional dependence of the number of spatial association rules from the minimum
support threshold. (
b
) Histogram and minimum points
Algorithm 1
Automated setting of
min
1:
find minsup
(i,Œ
1
;
2
,Œ
min
;
max
)
2:
if
i
MAX ITERS
then
3:
return
.
1
C
2
/=2
4:
end if
5:
no Rules
SPADA
..
1
C
2
/=2/
6:
if
no Rules
max
then
7:
min
find minsup
.i
C
1;Œ
1
;.
1
C
2
/=2,Œ
min
;
max
)
8:
else if
no Rules
min
then
9:
min
find
mins
u
p.i
C
1;Œ.
1
C
2
/=2;
2
,Œ
min
;
max
)
10:
else
11:
min
.
1
C
2
=2/
12:
end if
13:
return
min
of potential modules. For this reason, we follow the approach suggested in [
23
]:
users are asked to choose an interval Œ
min
;maxfor the number of association rules
they want to examine, and a value for
min
is then automatically derived. Indeed,
the number of association rules generated by SPADA depends on
min
according
to some function , which is monotonically decreasing (Fig.
5.3
a). Therefore, the
selection of an interval Œ
min
;maxfor the number of association rules corresponds
to the selection of an interval Œ
1
;
2
for the support, which includes the optimal
value
min
.
Contrary to [
23
], where a linear search of the optimal value is proposed, we ap-
ply a dichotomic search for efficiency reasons. The formulation of the algorithm is
recursive (see Algorithm
1
). Initially, the procedure
find minsup
is invoked on the
support interval Œ0;1 and SPADA is run with
min
D
0:5. If necessary,
find minsup
is recursively invoked on either Œ0;0:5 or Œ0:5;1. Since the convergence of the
algorithm cannot be proven, we stop the search when the number of recursive invo-
cations exceeds a maximum iteration threshold
MAX ITERS
. A reasonable setting
is
MAX ITERS
D
5, since after five iterations, the width of the interval Œ
1
;
2
is
relatively small (
1
2
5
).
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