IEEE Computational Intelligence Magazine - May 2020 - 75

80 h to find an optimal solution. FLGP
significantly reduces the computational
cost. The testing time of FLGP and GPGLF on FEI_1 and FEI_2 are within
0.2 min. The testing time of GP-GLF
on VGDB is over 0.4 min, while FLGP
needs less than 0.1 min for testing. The
comparisons demonstrate that FLGP is
faster than the previous GP-GLF method in [13]. FLGP has a more flexible
program structure and a smaller function
set than GP-GLF, which improve
FLGP's search efficiency and reduce the
complexity of the evolved solutions.

B. Analysis on Example Solutions
of FLGP

1) An Example Solution on FEI_2
An example solution of FLGP on the
FEI_2 data set is visualized in Figure 8.
This example solution achieves 100%
classification accuracy on both the training and test sets. Two example images
from the two classes (smile and natural)
are used for visualization to show what
and how features are extracted. This solution detects a 50 × 50 region using
Region_S and a 38 × 46 rectangle region

90
60

0.6
GP-GLF
FLGP

(Minute)

(Hour)

the mean accuracy by over 13% on
VGDB and KTH, and by over 9% on
SCENE compared with the three CNNs.
Surprisingly, CNN-8 performs worse
than CNN-5 on six data sets except for
FEI_2 and SCENE, which indicates that
an increase in the depth of CNNs cannot
guarantee an increase in classification
accuracy. A more complex model may
require more training instances/samples in
order to obtain satisfactory results. Compared with the three methods with predefined model complexity, the flexible
representation allows FLGP to evolve
solutions of variable depths, which is
more flexible for solving different image
classification tasks.
The results indicate that the features
learned by FLGP are more effective
than those by the three CNNs with different architectures for image classification. Compared with the three CNNs,
FLGP uses a simpler program structure
and a set of functions and terminals, but
it achieves better performance on different types of data sets. This main reason is
that FLGP learns various numbers and
types of features, which is more flexible
than the three CNNs. FLGP can learn
not only global features but also local
features from automatically detected
regions. However, it may be difficult for
the three CNNs to learn effective local
features from the whole input image.

30
0

FEI_1

FEI_2

VGDB

GP-GLF
FLGP

0.4
0.2
0

FEI_1

Data Set
(a)

FEI_2

VGDB

Data Set
(b)

FIGURE 7 The training (a) and testing (b) time of FLGP and GP-GLF on the FEI_1, FEI_2 and
VGDB data sets (Note that the GP-GLF method has only been examined on binary classification
data sets).

276 Features

VI. Further Analysis

This section further compares FLGP
with GP-GLF on the computational cost.
Then it deeply analyzes the best solutions
evolved by FLGP to fully understand
why it achieves good performance.

L_SIFT

G_DIF

L_SIFT

G_DIF

A. FLGP versus GP-GLF on
Computational Cost

The comparisons of FLGP and GPGLF in training time and testing time
on each of the three data sets are shown
in Fig. 7. It is obvious that FLGP is
much faster than GP-GLF in both training and testing. FLGP uses less than 6 h
for training on each data set, while GPGLF uses more than 8 h on FEI_1 and
FEI_2 and more than 80 h on VGDB
for training. The VGDB data set is very
challenging so that GP-GLF uses over

FeaCon3 (L_SIFT (Region_S (Image, 112, 11, 50)),
L_SIFT (Region_R (Image, 130, 64, 38, 46)), G_DIF (Image))
FIGURE 8 An example of best-of-the-run solution evolved by the proposed FLGP approach on
the FEI_2 data set and two example images are used as the inputs of the example solution to
show the process of feature extraction.

MAY 2020 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE

IEEE Computational Intelligence Magazine - May 2020

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - May 2020