![](bg7.png)
3.2 Experimental Results
Based on the standard deviation of classification
accuracy in Table 3, results that produced by EPSO
were consistent on all data sets. Interestingly, all
runs have achieved 100% LOOCV accuracy with
less than 71 selected genes on the Leukemia and
SRBCT the data sets. Moreover, over 91%
classification accuracies have been obtained on the
Colon data set. This means that EPSO has efficiently
selected and produced a near-optimal gene subset
from high-dimensional data (gene expression data).
Figure 2 shows that the averages of fitness
values of EPSO increase dramatically after a few
generations on all the data sets. A high fitness value
is obtained by a combination between a high
classification rate and a small number (subset) of
selected genes. The condition of the proposed
particles’ speed that should always be positive real
numbers started in the initialization method, the new
rule for updating particle’s positions, and the
modified sigmoid function provoke the early
convergence of EPSO. In contrast, the averages of
fitness values of BPSO was no improvement until
the last generation due to
( ( ) 0) ( ( ) 1) 0.5.
dd
ii
Px t Px t== ==
Leukaemia Data Set
0.88
0.9
0.92
0.94
0.96
0.98
1
0 50 100 150 200 250 300 350 400 450 500
Generation
Fitness
EPSO
BPSO
SRBCT Data Set
0.88
0.9
0.92
0.94
0.96
0.98
1
0 50 100 150 200 250 300 350 400 450 500
Generation
Fitness
EPSO
BPSO
Colon Data Set
0.8
0.82
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
0 50 100 150 200 250 300 350 400 450 500
Generation
Fitness
EPSO
BPSO
Figure 2: The relation between the average of fitness
values (10 runs on average) and the number of generations
for EPSO and BPSO.
According to the Table 4, overall, it is
worthwhile to mention that the classification
accuracy of EPSO are superior to BPSO in terms of
the best, average, and standard deviation results on
all the data sets.. Moreover, EPSO also produces a
smaller number of genes compared to BPSO. The
running times of EPSO are lower than BPSO in all
the data sets. EPSO can reduce its running times
because of the following reasons:
EPSO selects the smaller number of genes
compared to BPSO;
The computation of SVM is fast because it uses
the small number of features (genes) that
selected by EPSO for classification process;
EPSO only uses the speed of a particle for
comparing with
3
()
d
rt, whereas BPSO practices
all elements of a particle’s velocity vector for the
comparison.
For an objective comparison, we compare our
work with previous related works that used PSO-
based methods in their proposed methods (Shen et
al., 2008; Chuang et al., 2008; Li et al., 2008). It is
shown in Table 5. For all the data sets, the averages
of classification accuracies of our work were higher
than the previous works. Our work also have
resulted the smaller averages of the number of
selected genes on the data sets compared to the
previous works. The latest previous work also came
up with the similar LOOCV results (100%) to ours
on the Leukemia and SRBCT data sets, but they
used many genes (more than 400 genes) to obtain
the same results (Chuang et al., 2008). Moreover,
they could not have statistically meaningful
conclusions because their experimental results were
obtained by only one independent run on each data
set, and not based on average results. The average
results are important since their proposed method is
a stochastic approach. Additionally, in their
approach, the global best particles’ position is reset
to zero position when its fitness values do not
change after three successive iterations.
Theoretically, their approach is almost impossible to
result a near-optimal gene subset from high-
dimensional spaces (high-dimension data) because
the global best particles’ position should make a new
exploration and exploitation for searching the near-
optimal solution after its position reset to zero.
Overall, our work has outperformed the previous
related works in terms of LOOCV accuracy and the
number of selected genes.
According to Fig. 3 and Tables 3-5, EPSO is
reliable for gene selection since it has produced the
near-optimal solution from gene expression data.
This is due to the proposed particles’ speed, the
introduced rule, and the modified sigmoid function
increase the probability
(1)0
d
i
xt+=
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