IEEE Computational Intelligence Magazine - May 2023 - 41

TABLE I The results of SC, PD, and DD obtained by the
compared approaches.
APPROACH
AMPEMO
AMPEMO*
sEA
nEA
LSTM RNN
AMP-LM
AMPGAN v2
LSRMAMP
SC
54.25
46.65{
1{
1.63{
13.85{
13.25{
10.15{
12.83{
PD
1.14
1.14
0.09{
0.14{
0.91{
0.75{
0.72{
0.53{
DD
35.78
33.77{
4.11{
5.95{
28.46{
20.82{
24.67{
20.61{
FIGURE 9. The peptide sequence space is mapped into a twodimensional
space with 50 50 squares by the SOM method for a
visual understanding. The green squares contain at least one known
AMP in the dataset, while the white squares do not contain any known
AMPs. Figures 11 and 12 use this figure as an underlayer to evaluate
the performance of an obtained AMP set.
where D is the set ofknown AMPs in the dataset and dðxi; xjÞ
is the distance between two peptides defined in (2). A larger
value of DD suggests a better ability to discover new AMPs.
Some known AMPs similar in the dataset may result in misleading
DD results. Hence, they are removed by a clearing
method [37].
4) Self-Organizing Map (SOM) [67]
The SOM method can map the peptide sequence space into a
two-dimensional space to visually observe the performance of
a peptide set. An SOM network has 50 50 ¼ 2; 500 nodes
in this study. The training data comprise 10,000 randomly
generated peptides. Each node is represented as a square in the
two-dimensional space, that is, the two-dimensional space is
composed of 2,500 squares. Each square represents a subspace
ofthe peptide sequence space.
Before evaluating the performance ofthe obtained peptide
set, Figure 9 shows an underlayer according to the distribution
of the known AMPs in the dataset in the two-dimensional
space. Each of the known AMPs is associated with its closest
node. If a square is associated with at least one AMP, it is
green; otherwise, it is white. Figure 9 shows that more than
half of the squares (55%) are not associated with any known
AMP. Numerous potential AMPs are not known to human
experts in these squares. Moreover, because even a square is a
vast space, the green squares are likely to contain unknown
AMPs that are very different from known AMPs.
The performance ofan obtained AMP set is visually examined
based on the underlayer. Each obtained AMP is associated with its
closest node. Awhite square turns red ifit is associated with at least
one obtained AMP. A green node turns blue ifit is associated with
at least one obtained AMP, and a darker blue node means that the
obtained AMPs aremuch dissimilar tothe knownAMPsinthe
square. Therefore, more squares with red and darker blue markers
indicate that the obtained AMP set has higher diversity and is
much different from the known AMPs in the dataset. Figures 11
and 12 show the results of the SOM obtained by the compared
approaches, which will be discussed in the following subsections.
To give evidence for the visual result by the SOM in each
figure, ISOM is proposed to quantify the performance of an
obtained AMP set as follows:
ISOM ¼ nred þ
X
q2Qblue
max
xa2Xq
obtained;xb2Xq
known
(15)
where nred is the number ofred squares, Qblue is the set ofblue
squares, Xq
Xq
obtained is the set of obtained AMPs in square q,
known is the set ofknown AMPs (i.e., AMPs from the dataset)
in square q, and dð;Þ is the distance between peptides calculated
by (2). A larger value of ISOM implies that the obtained
AMPs have a higher diversity and are more dissimilar to the
known AMPs.
B. DesigningAMPs in Variable Lengths
This subsection discusses the results ofthe compared approaches
to designing AMPs with variable lengths. The length is in the
range of[7, 48]. Table I shows the mean values ofSC, PD, and
DD obtained by the compared approaches, where 'y' indicates
that the compared approach performs statistically significantly
worse than AMPEMO. Note that AMPEMO is the variant of
AMPEMO without the local search strategy. Table I shows that
AMPEMOoutperforms the compared approaches for every performance
indicator (except for the results of AMPEMO on
PD). This observation indicates that AMPEMO is powerful in
discovering various AMPs.
According to the results of PD, the local search strategy
does not affect the uniform distribution ofthe obtained AMPs.
However, according to the results ofSC, the strategy can help
the evolutionary algorithm explore more AMPs that are dissimilar
to each other. These AMPs are more dissimilar to the
known AMPs in the dataset, according to the DD results.
sEA achieved the worst values ofSC, PD, andDD. The population
ofsEA usually converges to one optimal peptide and thus
finds only one AMP in each run, which explains why the value
MAY 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 41
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