A Novel Framework with High Diagnostic Sensitivity for Lung Cancer Detection by Electronic Nose

. 2019 Dec 3;19(23):5333. doi: 10.3390/s19235333

Algorithm 1 Algorithm of margin and sensitivity based ordering ensemble pruning (MSEP)

Input:
training set $D_{T r}$ , pruning set $D_{P r}$ , sample (x, y), size of training set $N_{T r}$ , size of pruning set $N_{P r}$ , base classifier h, initial ensemble H, size of initial ensemble M, size of final pruned ensemble T, parameter $θ$
Output:
The final sub-ensemble S

1:
Initialize S = $ϕ$ , $K L$ is an empty mark list;
2:
$/ /$ Train base classifiers;
3:
for each $h_{j} \in H$ do
4:
Extract ( $x_{i}$ , $y_{i}$ ) ∈ $D_{T r}$ with replacement as $E_{T r}$ with size of 30% × $N_{T r}$ ;
5:
Train $h_{j}$ with $E_{T r}$ ;
6:
end for
7:
$/ /$ Pruning procedures;
8:
for each $h_{j} \in H$ do
9:
$M S M = 0$ ;
10:
for each $x_{i} \in D_{P r}$ do
11:
$m a r g i n (x_{i}) = \frac{\sum_{j = 1}^{M} (I (h_{j} (x_{i}) = y_{i}) - (I (h_{j} (x_{i}) \neq y_{i}))}{M}$ ; ▹ refer to Equation (2)
12:
if $h_{j} (x_{i}) = y_{i}$ && $m a r g i n (x_{i}) > θ$ then ▹ refer to Equation (10)
13:
$N F_{i}^{H} = \frac{\sum_{j = 1}^{M} I (h_{j} (x_{i}) \neq y_{i})}{M}$ ; ▹ refer to Equation (11)
14:
$M S M = M S M + e^{y_{i} \cdot N F_{i}^{H}} \cdot e^{- m a r g i n (x_{i})}$ ; ▹ refer to Equation (10)
15:
end if
16:
end for
17:
$M S M = \frac{M S M}{N_{P r}}$ ; ▹ refer to Equation (10)
18:
Append pair $(h_{j}, M S M)$ to $K L$ ;
19:
end for
20:
Rank $K L$ in decreasing order based on $M S M$ ;
21:
return the top-T classifiers in $K L$ as S;