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Table 2.
AUC and std.errors obtained from the single- and multi-view systems at a
case
level with the one-sided
p
-values and 95% confidence intervals for the differences
CASE
AUC
±
std.err
p
-value Confidence interval
max
MV-CAD-Causal 0.833
±
0
.
013
Method
-
-
MV-CAD-LR
0.835
±
0
.
013
41%
(
−
0
.
007
,
0
.
005)
MV-CAD-NB
0.826
±
0
.
014
21%
(
−
0
.
004
,
0
.
010)
SV-CAD
0.797
±
0
.
014
1.1%
(0
.
003
,
0
.
040)
train
MV-CAD-Causal 0.847
±
0
.
013
-
-
0.835
±
0
.
014
(0
.
002
,
0
.
026)
MV-CAD-LR
1.3%
0.833
±
0
.
014
(0
.
005
,
0
.
022)
MV-CAD-NB
0.1%
SV-CAD
0.797
±
0
.
014
0.1%
(0
.
009
,
0
.
043)
The results show that
MV-CAD-Causal
significantly outperforms
SV-CAD
at
both breast and case level. With respect to the two multi-view benchmark
methods, our causal model is superior at a breast level and a case level us-
ing training as a combining scheme (
CaseNet
). As expected the case results
for
MV-CAD-Causal
using the maximum (MAX) out of two breast probabilities
has less satisfactory performance than using training in the causal independence
model. This shows that combining all available information in a proper way is
beneficial for accurate case classification.
Although
MV-CAD-NB
and
MV-CAD-LR
are overall less accurate than the last
two stages of the multi-view causal model, it is clear that all three
MV-CAD
models achieve superior performance with respect to
SV-CAD
. This result follows
naturally from the explicit representation of multi-view dependences at a region
and view level of the multi-view model and it clearly indicates the importance
of incorporating multi-view information in the development of CAD systems.
To get more insight into the areas of improvement at a case level we plotted
ROC curves for all systems. For all the plots we observed the same tendency
of an increased true positive rate at low false positive rates (
<
0
.
5)-a result
ultimately desired at the screening practice where the number of normal cases
is considerably larger than the cancerous ones; Figure 8 presents the ROC plot
for the best performing models.
Evaluation of the multi-view model fitness.
To have a closer look at the
quality of classification for the three multi-view models, we compute the av-
erage log-likelihood (
ALL
) of the probabilities for different
units
-link, region,
MLO/CC view, breast and case-by:
N
ALL
(
Cl
)=
1
N
−
ln
P
(
Cl
i
|E
i
)
,
(3)
i
=1
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