Information Technology Reference
In-Depth Information
σ
f
i
(
T
x
j
)
≤
σ
max
(7.8)
H
0
:
μ
f
i
(
T
x
j
)=
μ
f
i
(
T
−
T
x
j
)
(7.9)
In Equation 7.9,
H
0
should be rejected with a confidence equal to or greater
than
γ
min
, in favor of the hypothesis that the means
μ
f
i
(
T
x
j
)and
μ
f
i
(
T −T
x
j
)are
statistically different. To reject
H
0
with confidence
γ
min
,the
Z
value, calculated
using Equation 7.10, must be in the rejection region illustrated in Figure 7.2. The
critical
Z
values
Z
1
and
Z
2
depend on the
γ
min
value as shown in Table 7.1:
Z
=
μ
f
i
(
T
x
j
)
−
μ
f
i
(
T
−
T
x
j
)
(7.10)
σ
f
i
(
T
x
j
)
√
(
|T
x
|
)
f
i
, returned by the algorithm, relates a feature
f
i
with a cate-
gory
x
j
, where the values of
f
i
have a statistically different behavior in images
of category
x
j
. This property indicates that
f
i
is an interesting feature to dis-
tinguish the images of category
x
j
from the remaining images. The StARMiner
algorithm also gives information about the feature behavior in the mined rules.
A rule mined by StARMiner, on its complete form is:
Arule
x
j
→
x
j
→
f
i
,
μ
f
i
(
T
x
j
),
μ
f
i
(
T
−
T
x
j
),
σ
f
i
(
T
x
j
),
σ
f
i
(
T
−
T
x
j
)
where,
μ
f
i
(
T
x
)and
σ
f
i
(
T
x
) are, respectively, the mean and the standard devia-
tion of
f
i
values in the images from category
x
j
;
μ
f
i
(
T
x
j
)and
σ
f
i
(
T
T
x
j
)are,
respectively, the mean and the standard deviation of
f
i
values in the images that
are not from category
x
j
. Algorithm 1 presents a description of StARMiner.
To perform StARMiner, the dataset under analysis is scanned twice. The first
scan calculates the mean of each feature (lines 1 to 6). The second dataset scan
−
Fig. 7.2.
Illustration of the rejection regions of a hypothesis test
Table 7.1.
Critic
Z
values
γ
min
0.9
0.95 0.99
Z
1
-1.64 -1.96 -2.58
Z
2
1.64 1.96 2.58
