Multi-objective Classiﬁcation and Feature Selection of Covid-19 Proteins

Sequences using NSGA-II and MAP-Elites

Vijay Sambhe

1 a

, Shanmukha Rajesh

1 b

, Enrique Naredo

1,2 c

, Douglas Mota Dias

1,2,3 d

Meghana Kshirsagar

1,2 e

and Conor Ryan

1,2 f

University of Limerick, Limerick, Ireland

Lero – Science Foundation Ireland Research Centre for Software, Ireland

UERJ – Rio de Janeiro State University, Brazil

Keywords:

DNA Sequences, MAP-Elites, k-mer, NSGA-II, Feature Selection, Genetic Algorithms.

Abstract:

The advent of the Covid-19 pandemic has resulted in a global crisis making the health systems vulnerable,

challenging the research community to ﬁnd novel approaches to facilitate early detection of infections. This

open-up a window of opportunity to exploit machine learning and artiﬁcial intelligence techniques to address

some of the issues related to this disease. In this work, we address the classiﬁcation of ten SARS-CoV-2

protein sequences related to Covid-19 using k-mer frequency as features and considering two objectives; clas-

siﬁcation performance and feature selection. The ﬁrst set of experiments considered the objectives one at the

time, four techniques were used for the feature selection and twelve well known machine learning methods,

where three are neural network based for the classiﬁcation. The second set of experiments considered a multi-

objective approach where we tested a well known multi-objective approach Non-dominated Sorting Genetic

Algorithm II (NSGA-II), and the Multi-dimensional Archive of Phenotypic Elites (MAP-Elites), which con-

siders quality+diversity containers to guide the search through elite solutions. The experimental results shows

that ResNet and PCA is the best combination using single objectives. Whereas, for the mulit-classiﬁcation,

NSGA-II outperforms ME with two out of three classiﬁers, while ME gets competitive results bringing more

diverse set of solutions.

1 INTRODUCTION

Covid-19 has become a major concern for the whole

world. Currently, there is a heavy workload on patho-

logical laboratories and many cases tested there have

been instances of false-negative test results (Wets-

man, 2020; Abc7news, 2020). On the other hand,

even with false-positive test results, a patient can face

the wrong medication.

In the current pandemic situation of Covid-19,

health care systems are experiencing extremely high

demand for testing of Corona infections. At the same

time, health care systems struggle not to ignore the

testing of other traditional infections.

The biotechnology ﬁeld can beneﬁt immensely

from computer science methods such as machine

https://orcid.org/0000-0003-3057-8172

https://orcid.org/0000-0002-2477-3089

https://orcid.org/0000-0001-9818-911X

https://orcid.org/0000-0002-1783-6352

https://orcid.org/0000-0002-8182-2465

https://orcid.org/0000-0002-7002-5815

learning, deep neural networks, evolutionary comput-

ing, and data mining. In a very recent development, a

team at MIT (Massachusetts Institute of Technology)

Artiﬁcial Intelligence agency took a novel approach

to predicting peptides to provide a high population

of coverage for a Covid-19 spike protein-based vac-

cine which is in multiple clinical trials (Rachel, 2020;

Hamley, 2020).

Artiﬁcial intelligence techniques can aid in diag-

nostics to treatments offering support to healthcare

(Bohr and Memarzadeh, 2020). One method of in-

fection detection is offered through the pattern recog-

nition of genetic sequences of the viral and bacterial

infectious organisms.

In this research work, we address the problem of

feature reduction and multi-classiﬁcation of protein

sequences of “Severe acute respiratory syndrome-

related coronavirus”, commonly named as SARS-

CoV-2 (Gorbalenya et al., 2020). We conducted pri-

marily two sets of experiments: single and multi-

objective optimization approaches. In the single-

objective approach, we used four techniques for the

feature selection, and from their results, we per-

Sambhe, V., Rajesh, S., Naredo, E., Dias, D., Kshirsagar, M. and Ryan, C.

Multi-objective Classiﬁcation and Feature Selection of Covid-19 Proteins Sequences using NSGA-II and MAP-Elites.

DOI: 10.5220/0010388512411248

In Proceedings of the 13th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2021) - Volume 2, pages 1241-1248

ISBN: 978-989-758-484-8

1241

formed the classiﬁcation using 12 methods, where 9

are well-known traditional machine learning methods

and the last three are neural network-based methods.

In the multi-objective optimization, we addressed

both the feature selection and the classiﬁcation prob-

lem at the same time, using Non-dominated Sorting

Genetic Algorithm II (NSGA-II) (Deb et al., 2002),

and Map-Elites (ME) (Mouret and Clune, 2015) ap-

plying just three of the best classiﬁers found in the

previous process. On one hand, NSGA-II is a well

known multi-objective evolutionary algorithm, where

the standard implementation rewards solutions closer

to the target. On the other hand, ME is a state-of-the-

art method that guides the search by considering both

quality and diversity.

In the literature, we can ﬁnd several works us-

ing conventional methods to address deoxyribonu-

cleic acid (DNA) sequences, to our best of our knowl-

edge, this is the ﬁrst work to apply ME on this prob-

lem domain.

The experimental results show that the protein se-

quences classiﬁcation can be addressed using a multi-

objective approach obtaining a set of solutions con-

sidering both objectives; classiﬁcation performance

and feature selection in the Pareto front. On the other

hand, ME reaches similar classiﬁcation performance

and bringing more diverse solutions, and deserves a

deeper study to apply this approach to solve similar

problem domains.

In this paper, Section 2 describes the related work,

Information on SARS-CoV-2 sequences, NSGA-II,

and Map-Elites Algorithm. Section 3 is dedicated to

the experimental setup, then Section 4 presents and

discusses the experimental results. Finally, Section 5

gives the conclusions and future work.

2 BACKGROUND

The Coronavirus disease (Covid-19) is mainly trans-

mitted to human beings through droplets, coughs,

sneezes, or exhales from infected persons. The

SARS-CoV-2 is composed of various proteins and the

tissue samples collected from a person infected with

the Covid-19 virus contain the samples of these same

proteins.

In its replicating mechanism in a human host cell,

these various structural and non-structural proteins

are produced again and composed together to form

a whole new viral entity. The study of virology of

the Covid-19 virus gives a better understanding of the

structure of the virus and the proteins it contains.

In biological terms, DNA computing is a compli-

cated task that relies heavily on biochemical reactions

of DNA molecules leading it many times to imper-

fect computations. To make this molecular compu-

tation reliable, more efforts are focused on designing

a better DNA sequencing methods. Authors in (Kim

et al., 2002) formulated the DNA sequence design by

using a multi-objective evolutionary algorithm (EA)

constrained in nature into the DNA sequence design

system.

In another study, (Randhawa et al., 2020) used

a supervised machine learning-based approach for a

real-time prediction of Covid19 virus for its taxon-

omy predictions providing the hypothesis of the bat

origin theory. They used several traditional machine

learning techniques to tackle that task; Linear Dis-

criminant, Linear SVM, Quadratic SVM, Fine KNN,

Subspace Discriminant, Subspace KNN, and Accu-

racy.

More recently in (Alkady et al., 2020), used hu-

man protein sequences of COVID-19 to predict the

country origin of the sample and considered three

stages including data preprocessing, data labeling,

and classiﬁcation. In the classiﬁcation stage, the

authors applied several machine learning methods,

such as Linear Regression (LR), K-Nearest Neighbor

(KNN), and Support Vector Machine (SVM) classi-

ﬁers.

The Covid-19 disease virus has structural and

non-structural components made up of proteins. It

is already well known that coronavirus disease-2019

(COVID-19) is caused by the SARS-CoV-2 virus

(Romano et al., 2020).

The SARS-CoV-2 virus has one of the largest

known ribonucleic acid (RNA) genomes. A com-

mon measurement used to describe the length of a

DNA or RNA molecule is kb, which stands for ’kilo-

base pairs’, where a base pair corresponds to approx-

imately 3.4

A (340 pm) of length along the strand,

and to roughly 618 or 643 daltons for DNA and RNA

respectively(Alberts et al., 2018). This virus is ap-

proximately 30 kb in length and is a positive sense

single-stranded genomic RNA (Khailany et al., 2020;

Malik, 2020).

Some viruses encode RNA genome to store their

genetic information (Cm.jefferson.edu, ). As the

SARS-CoV-2 virus infects humans, the replicating

mechanism of the virus involves the replication of

the same proteins and later forming of the whole vi-

ral entity. Our aim is that the correct classiﬁcation of

the viral protein sequences could help towards the di-

agnostic assessment and detection of vaccination ap-

proaches.

A genome sequence is described in terms of four

basic nucleotides; A, T, G, and C, which denote chem-

ical bases adenine, thymine, guanine, and cytosine

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

1242

respectively. An amino acid is speciﬁed by a triplet

of these bases and a protein is composed of one

or more chains of amino acids (Cm.jefferson.edu, ;

Genome.gov, ). Furthermore, the protein sequences

encode regions in terms of the bases, in this work we

use this speciﬁc information to address the classiﬁca-

tion of SARS-CoV-2 virus samples.

The term of k-mer is primarily used within the

context of computational genomics and sequence

analysis, in which k-mers are composed of nu-

cleotides (i.e. A, T, G, and C), and they are subse-

quences of length k contained within a biological se-

quence (Compeau et al., 2011).

Given a sequence of length k, the term k-

mer refers to all possible combinations of the sub-

sequences in that sequence. More generally, a se-

quence of length m will have m − k + 1 k-mers and n

total possible k-mers, where n is the number of possi-

ble monomers, four in the case of DNA corresponding

to the base nucleotides.

The use of k-mer is widely used in many of the

applications related to DNA sequences; for instance,

a study from (Solis-Reyes et al., 2018) used k-mer

based and deep neural networks for sub-typing of

HIV-1 genome having higher accuracy against a com-

plex dataset.

In a research paper by (Kaehler, 2017), the au-

thors used a metagenomic data with DNA sequences

from bacterial communities. The raw sequence data

was transformed using k-mers and a numeric summa-

rization vector. To address the high dimensionality,

some feature selection methods were used to reduce

the number of dimensions.

On the other hand, there is some evidence of using

evolutionary algorithms to address DNA sequences.

For instance, in (Chen et al., 1999) authors used ge-

netic algorithms to manipulate bit strings using point-

wise mutation and crossover.

Furthermore, a study by (Quinonez et al., 2019)

addressed the problem of feature selection using the

Map-Elites algorithm in a classiﬁcation problem us-

ing Bayes Classiﬁer becoming a good choice to use

in this research work.

NSGA-II resemble the process of natural selection

by selecting the ﬁttest individuals and reproduction

in order to produce offspring of the next generation

(Davis, 1991). In general, we can deﬁne an individual

composed by a tuple of the form I = (P, G,S), where

P stands for the phenotype, G for the genotype, and S

for the score.

The observable properties of the individual I are

known as the phenotype P, i.e. protein sequences. For

a classiﬁcation problem, the features selected from

the protein sequences are used to make a decision to

what class label they belong, then that solution is eval-

uated trough a function, which will we refer as to the

ﬁtness function because it assigns a quality score to

P, named as ﬁtness score S.

In the evolutionary process individuals I with

higher S have more chances to recombine their G with

other individuals or just to mutate some position in G,

creating in this way increasingly better solutions until

ideally an optimal or near-optimal one appears.

The Multi-dimensional Archive of Phenotypic

Elites also known as Map-Elites (ME) (Mouret and

Clune, 2015) is an algorithm that illuminates the con-

tainers of quality and diversity where the solutions are

stored. ME creates a map of high-performing solu-

tions (elites) searching the higher-dimensional feature

space and mapping them in a low dimensional feature

space deﬁned by the user and keeping a diverse set of

high-performing solutions.

Implementing ME requires deﬁning the feature

space of interest, for instance, by classiﬁcation perfor-

mance and feature selection. These dimensions can

be discretized and their granularity is manually or au-

tomatically speciﬁed. ME search for the highest per-

forming solution for each cell in the already deﬁned

search space.

The overall process of ME is similar to any

population-based algorithm, starting with a random

population. ME concurrently map the genotypical

and phenotypical storing the information into contain-

ers of the same size, this way the mapping process is

easily performed.

The general process starts choosing a cell or set

of cells in the container to perform genetic operations

and create new solutions that are placed in the con-

tainer if there is not any other solution inside. Best

solutions replace the old solutions and the cell is il-

luminated with the new quality score. These elite so-

lutions are replaced iteratively by new and better so-

lutions, maintaining the diversity of solutions which

helps to avoid getting into regions of local optima.

3 EXPERIMENTAL SETUP

In this section, we give a detailed explanation of the

whole process to address the multi-classiﬁcation of

Covid protein sequences.

The samples from SARS-CoV-2 were manually

collected from the viral protein dataset was down-

loaded from the virus repositories from (NCBI, 2020)

and the search parameters were: (i) Virus: SARS-

CoV-2, (ii) Texid: 2697049, (iii) Host: Homo (hu-

mans), (iv) Taxid:9605, (v) Data type: Protein coding

region, (vi) File format: FASTA.

Multi-objective Classiﬁcation and Feature Selection of Covid-19 Proteins Sequences using NSGA-II and MAP-Elites

1243

In this research, we worked with 10 classes of pro-

teins from a downloaded dataset with 78,555 samples

and the length of the protein sequences ranged from

6 to 3,822 nucleotides. In this work, we selected 10

protein sequences from the coding region; Envelope

protein, Membrane glycoprotein, Nucleocapsid phos-

phoprotein, orf10, orf3, orf6, orf7a, orf7b, orf8, and

Spike glycoprotein.

At the time of this research, there had been mini-

mal mutation with the SARS-CoV-2 virus in humans,

hence the samples from across the globe were quite

identical. The raw dataset contained 72,605 dupli-

cated samples from a total of 78,555, and after re-

moval, we got only 5,950 unique samples.

The next step in pre-processing the dataset was to

balance the classes. Three protein classes had less

than 300 samples and the other three more than 700

samples. We used a resampling method to increase

the lower represented classes and a downsampling

method for the over-represented classes. The thresh-

old to balance the entire dataset was 500, where just

the class envelope contains 9 more samples, result-

ing in a total of 5,009 samples in the pre-processed

dataset.

Following the conventional approach used in

bioinformatics, we used sub-sequences of length k

contained within the dataset samples (Kaehler, 2017;

Randhawa et al., 2020).

In this work, we empirically selected k = 6 to

use all the sub-sequences of length 6. The number

of k-mers contained in the samples is variable, and

a typical sample could contain more than 12,000 k-

mers. The information used from the k-mers is the

frequency found in each sample.

To avoid any bias from the k-mers frequency, we

used the normalization technique called Term Fre-

quency Inverse Document Frequency (TF-IDF) ap-

plied to each k-mer. TF-IDF is a well-known tech-

nique in Natural Language Processing (NLP), useful

for scoring words (Prawira, 2020). Here, TF-IDF is

used to evaluate how relevant a k-mer is to a collec-

tion of protein sub-sequences in each sample. This

is done by multiplying the frequency a k-mer appears

in a sub-sequence and the inverse sub-sequence fre-

quency of the k-mer across a set of sub-sequences.

The protein classiﬁcation problem then is ad-

dressed using the resulting frequency vector as a fea-

ture vector with a domain in [0, 1] to relate each sam-

ple to one of the ten protein classes. In the following

sections, we explain two different sets of experiments

to address the classiﬁcation and feature selection. The

ﬁrst set of experiments addresses each task separately

as a single-objective optimization problem. On the

other hand, the second set of experiments addresses

both at the same time as a multi-objective optimiza-

tion problem.

In this set of experiments, the classiﬁcation of

SARS-CoV-2 protein sequences is addressed as a

single-objective optimization problem. The goal is to

test twelve well known classiﬁer methods with four

feature selection strategies each and using a stratiﬁed

5-fold cross-validation. From now on we refer to the

features as the vector of k-mer frequency from each

sample, where in some cases they can contain more

than 12,000 features.

The feature selection strategies used are: (i) PCA,

(ii) 75th-Perc, (iii) α-Best, and (iv) β-Best. The ﬁrst

strategy for feature selection used is the principal

component analysis (PCA). We extracted 9 principal

components so that it covered 95% variance of the

data. The second strategy used is selecting the fea-

tures according to a percentile of the highest scores,

where we selected the 75th percentile (75th-Perc) us-

ing the Chi-squared distribution. For this technique,

the number of features obtained was 91.

The third and fourth strategies select the best

features from two measures; ANOVA and the Chi-

squared distribution. Using the third one, we selected

α as 1,000 highest scores (α-Best), using the analysis

of variance (ANOVA) and the F-test to verify the vari-

ance between the means of α features signiﬁcantly

different, for this technique. Using the fourth one, we

selected β as 1,000 highest scores (β-Best), using the

Chi-squared distribution for this technique.

Table 1 shows the list of twelve classiﬁer methods

used in our experiments, where the ﬁrst nine are well

known traditional machine learning methods and the

last three methods are neural network-based.

For the CNN method, we used 1D convolution

layer (Conv1D), rectiﬁed linear unit (activation layer),

Max Pooling 1D, and ﬁnally a fully connected layer,

using 50 epochs for training with the loss function

‘categorical crossentropy’ and the optimizer ‘adam’.

To apply Conv1D, we had to transform the input data

by expanding the shape of the array by inserting a new

axis.

Whereas, the ResNet, the residual block con-

sists of a stacking of convolutional (Conv1D), batch

normalization, rectiﬁed linear (ReLU) activation,

Conv1D, and again batch normalization layers.

For the multi-objective optimization, we used two

methods: (i) NSGA-II, and (ii) MAP-Elites. From

the ﬁrst set of experiments, we select three of the ma-

chine learning methods as classiﬁers: MNB, SGD,

and RF. The dataset for these experiments was di-

vided into 75% for training (3,756) and 25% for test-

ing (1,253). The features used in this set of experi-

ments are the same used for the single-objective ex-

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

1244

Table 1: List of the methods used as classiﬁers in the ex-

periments. Short stands for the abbreviation for the method

used.

Short Description

MNB Naive Bayes for multinomial models

SGD Stochastic Gradient Descent

RF Random Forest

KNN k-nearest neighbors

GNB Gaussian Naive Bayes

LR Logistic Regression classiﬁer

LSV Linear Support Vector classiﬁer

SVM-p SVM with polynomial kernel function

SVM-r SVM with Radial Basis Functions

NN Neural Network

CNN Convolutional Neural Network

ResNet Residual Neural Network

periments. We design the ﬁrst experiment to compare

NSGA-II vs MAP-Elites using 200 features randomly

chosen, then we performed a second experiment to

analyse the performance of MAP-Elites considering

the entire features set (>12,000).

Table 2: Parameters used to run NSGA-II and MAP-Elites.

Parameter Value

Runs 30

Generations 100

Population 100

Selection Tournament, (size 3)

Crossover One point, 0.9

Mutation 0.1

Table 2 shows the main parameters used to run exper-

iments with NSGA-II and MAP-Elites. A binary rep-

resentation was used on the comparison from both al-

gorithms to perform the feature selection. In the sec-

ond ME experiment, we used a discrete representation

composed of integers in the range of the total number

of dimensions of the dataset. We extended this exper-

iment further by changing two parameters with popu-

lation size as 1,000 and generations as 1,000. But we

used only the MNB classiﬁer.

The function used to reward the best classiﬁers on

all the experiments is based on the accuracy perfor-

mance, given by

Accuracy =

T P + T N

T P + T N + FP + FN

(1)

In all the experiments we used open-source tools,

such as Python3, scikit-learn, NumPy, SciPy, and

matplotlib. For the multi-objective experiments, we

used mainly DEAP (Fortin et al., 2012), and QDpy

(Cazenille, 2018) with modiﬁcation to implement the

cross over rate and mutation rate for the integration

with DEAP.

4 RESULTS

This section presents the experimental results from

the single and multi-objective approaches to address

the classiﬁcation and feature selection of protein se-

quences of SARS-CoV-2.

4.1 Single-objective

In this set of experiments, we addressed ﬁrst the fea-

ture selection and then the classiﬁcation problem. The

classiﬁer methods used are listed in Table 1 and the

techniques used for feature selection are (i) PCA, (ii)

75th-Perc, (iii) α-Best, and (iv) β-Best. ResNet is the

overall best classiﬁer from all the single objective set

of experiments, particularly using PCA as the feature

selection technique. RF is the best classiﬁer when us-

ing 75th−Perc, CNN is the best combined with α-

Best, and MNB with β-Best.

Table 3 shows a summary of the experimental re-

sults for accuracy performance. The table shows an

averaged performance using a stratiﬁed 5-fold cross-

validation for each combination.

The experimental results show a high performance

from all traditional machine learning methods tested.

The ﬁrst three methods shown in the ﬁrst section

of Table 3 are used for the multi-objective experi-

ments. The neural network-based methods perform

quite well, particularly the CNN and ResNet choices.

Table 3: Summary of the single objective classiﬁcation ac-

curacy performance for the four feature selection techniques

in the columns and nine well known machine learning meth-

ods in the ﬁrst section of the rows and three neural networks

based at the ﬁnal section, best performance are bold.

Classiﬁer PCA 75th-Perc α-Best β-Best

MNB 0.9569 0.9860 0.9928 0.9998

SGD 0.9792 0.9898 0.9968 0.9984

RF 0.9984 0.9934 0.9976 0.9988

KNN 0.9986 0.9916 0.9974 0.9986

GNB 0.9858 0.9639 0.9914 0.9914

LR 0.9940 0.9908 0.9938 0.9976

LSV 0.9620 0.9914 0.9896 0.9980

SVM-p 0.9930 0.7624 0.6412 0.8491

SVM-r 0.9936 0.9840 0.9828 0.9914

NN 0.9978 0.9926 0.9952 0.9990

CNN 0.9750 0.9926 0.9980 0.9990

ResNet 0.9990 0.9978 0.9990 0.9932

Multi-objective Classiﬁcation and Feature Selection of Covid-19 Proteins Sequences using NSGA-II and MAP-Elites

1245

4.2 Multi-objective

In the second set of experiments, we selected just

three of the best classiﬁers from the ﬁrst set of exper-

iments, and we addressed both feature selection and

the classiﬁcation problem using a multi-objective ap-

proach. As an optimizer, we used two different al-

gorithms; (i) NSGA-II, and (ii) the quality-diversity

algorithm named as MAP-Elites (ME).

Table 4 summarizes the experimental results, and

the columns show the three traditional classiﬁers se-

lected from the single objective experiments. The

upper section of the table shows the averaged per-

formance results from the experiments using 200

features randomly selected for NSGA-II and ME.

Whereas, in the lower section of the table, the third

row shows the averaged performance results from the

experiments using all the features only for ME, with

100 individuals in the population (ME2-100), and the

fourth row shows the results using a similar conﬁg-

uration, but increasing the population size to 1,000

individuals (ME2-1000).

This comparison gives evidence that NSGA-II fo-

cuses on selecting a reduced number of features,

meanwhile ME focus more on ﬁnding more diverse

solutions with a higher number of features.

Furthermore, Figure 2 shows the quality and di-

versity containers from a typical run of ME, where

each row shows both containers from each classiﬁer

used: MNB, SGD, and RF. The results of this experi-

ment considers 200 randomly chosen features.

(a) ME2-MNB-100 (b) ME2-MNB-1000

Figure 1: Plots showing the Pareto front of a typical run

from ME using all features; the postﬁx stands for the num-

ber of individuals used.

The experimental results using the multi-objective ap-

proach, using either NSGA-II or ME, showed that ad-

dressing the selection feature and the accuracy at the

(a) Quality-MNB (b) Diversity-MNB

(e) Quality-RF (f) Diversity-RF

Figure 2: Illumination of the quality and diversity contain-

ers of ME from a typical run using 200 features randomly

chosen.

same time is better than the combination of the tradi-

tional machine learning methods and the feature se-

lection techniques using a single-objective approach,

but not better than the speciﬁc combination of MNB

classiﬁer and β-Best feature selection technique.

This experiment shows that by increasing the

number of individuals in the population, ME searches

the space more uniformly and bring more diversity in

the solutions, reaching more than 95% of accuracy,

while selecting a low number of features.

In Figure 3, we can observe four sub-ﬁgures show-

ing in the columns the quality and diversity contain-

ers for ME and in the rows the plots for the classiﬁer

used; the last row shows the plots for the choice of

using 1,000 individuals. In this experiment, we used

all the features available and the experimental results

show that the combination of ME and MNB get better

results as expected, and another beneﬁt is the reduc-

tion of features selected to get this performance.

ICAART 2021 - 13th International Conference on Agents and Artiﬁcial Intelligence

1246

Table 4: Multi-objective averaged classiﬁcation performance over 30 experimental runs for NSGA-II and MAP-Elites.

MNB SGD RF

Accuracy Features Accuracy Features Accuracy Features

NSGA-II 0.9801 ± 0.0000 37 ± 12 0.9815 ± 0.0004 48 ± 16 0.9815 ± 0.0004 25 ± 3

ME 0.9776 ± 0.0000 78 ± 6 0.9809 ± 0.0011 78 ± 4 0.9827 ± 0.0000 71 ± 4

ME-2 0.8305 ± 0.2000 70 ± 44 0.8952 ± 0.1300 72 ± 41 0.9403 ± 0.0802 68 ± 33

(a) Q-MNB, Ind:100 (b) D-MNB, Ind:100

(e) Q-RF, Ind:100 (f) D-RF, Ind:100

(g) Q-MNB, Ind:1000 (h) D-MNB, Ind:1000

Figure 3: Illumination of the quality and diversity contain-

ers of ME from a typical run using all features. The ﬁrst

three rows show the classiﬁer with 100 individuals, and the

fourth row shows the containers of the MNB classiﬁer using

1,000 individuals.

5 CONCLUSIONS

In this research work, we addressed the problem of

multi-classiﬁcation and feature selection of protein

sequences of SARS-CoV-2 using single and multi-

objective approaches using the protein sequences as

coding regions. The pre-processing consisted of re-

moving duplicates and balancing the dataset. The

features used consisted of the normalized k-mer fre-

quency. In the ﬁrst set of conventional experiments,

we used a single-objective approach addressing ﬁrst

the feature selection and then the classiﬁcation prob-

lem. For the feature selection, we used four tech-

niques for the feature selection and twelve well-

known machine learning classiﬁer methods, nine tra-

ditional ones, and three neural network-based.

In the second set of experiments, we selected just

three of the best classiﬁers from the ﬁrst set of exper-

iments and we addressed both feature selection and

the classiﬁcation problem using a multi-objective ap-

proach. As an optimiser, we used two different algo-

rithms; (i) NSGA-II, and (ii) a quality-diversity algo-

rithm named as MAP-Elites. Furthermore, we imple-

mented the mutation and crossover rate on the QDpy

library to integrate it with DEAP.

The experimental results show that a combination

of conventional methods can be used to perform sep-

arately the feature selection ﬁrst and then the clas-

siﬁcation, having good results. Furthermore, the re-

sults show that this problem can be successfully ad-

dressed as a multi-classiﬁcation optimization problem

using a traditional evolutionary algorithm or a quality-

diversity algorithm, such as MAP-Elites.

NSGA-II shows that consistently selects fewer

features and getting a good classiﬁcation perfor-

mance. On the other hand, MAP-Elites clearly shows

that explores better the search space and ﬁnds a wider

Pareto front, while getting competitive results. This

research shows that dimension reduction and multi-

classiﬁcation can be applied on long RNA-based viral

genomic sequences and such a mechanism can be use

for diagnostic purposes.

There are several different directions to follow

from this research line, for instance, using protein se-

Multi-objective Classiﬁcation and Feature Selection of Covid-19 Proteins Sequences using NSGA-II and MAP-Elites

1247

quences from other diseases and train models to iden-

tify correctly the samples with SARS-CoV-2. An-

other research line is to use genetic programming or

grammatical evolution to evolve classiﬁers and MAP-

Elites to keep a trade off between quality and diversity

in the solutions and compare the evolutionary meth-

ods against state-of-the-art machine learning, such as;

(i) gradient boosting, and (ii) least absolute shrinkage

and selection operator (LASSO).

ACKNOWLEDGEMENTS

This work was conducted with the ﬁnancial sup-

port of the Science Foundation Ireland (SFI) Centre

for Research Training in Artiﬁcial Intelligence un-

der Grant No. 18/CRT/6223, by the research Grant

No. 16/IA/4605, and by Lero, the Irish Software

Engineering Research Centre (www.lero.ie). The

fourth author is partially ﬁnanced by the Coordenac¸

de Aperfeic¸oamento de Pessoal de N

ıvel Superior -

Brasil (CAPES) - Finance Code 001.

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