Information Technology Reference
In-Depth Information
-
Accuracy (Non Error Rate NER
): the probability of doing a generic correct
classification.
TP
+
TN
TP
+
FP
+
TN
+
FN
NER
=
(7)
-
Sensitivity (True Positive Rate TPR)
: the probability to classify a person as
sick when this is true.
TP
TP
+
FN
TPR
=
(8)
-
Specificity(TrueNegativeRateTNR
): the probability of classifying a person
as healthy when this is true.
TN
TN
+
FP
TNR
=
(9)
-
Precision w.r.t. diseased people (
PREC
POS
)
: the probability that, having
assigned a sample to the class of diseased people, it actually belongs to that
class.
TP
TP
+
FP
PREC
POS
=
(10)
-
Precision w.r.t. healthy people (
PREC
NEG
)
: the probability that, having
assigned a sample to the class of healthy people, it actually belongs to that
class.
TN
TN
+
FN
PREC
NEG
=
(11)
To obtain indexes able to describe completely the performance of the algo-
rithms, the corresponding confidence intervals must be evaluated:
σ
√
n
≤ μ
x
≤
σ
√
n
X − t
2
X
+
t
2
(12)
where
X
is the estimated index value,
n
is the number of the degrees of freedom,
σ
is the standard deviation and
t
2
is the quantile of the t-Student distribution
corresponding to
n
−
1 and a probability of
α
.
10 Lung Cancer Diagnosis by an Electronic Nose: Results
The goal of the implemented genetic algorithm was to identify the best combi-
nation of feature subset and the considered feature projection and classification
algorithms. The obtained solution suggested that the best fitness function (pro-
portional to the classification accuracy and its variance) was reached keeping four
of the initial hundreds of features, projecting them into one dimension by means
of Linear Discriminant Analysis (LDA) and classifying the new feature samples
using a
k
-Nearest Neighbors rule, with
k
= 9. The achieved results, all validated
using leave-one-subject-out cross-validation, are shown in Table 1, where the
corresponding performance indexes and confidence intervals are provided. These
results confirmed a previous pilot study where we achieved an average accuracy
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