COVID-19 Diagnosis Using Chaotic Logistic Map Based Modified Whale Optimization: A Robust Feature and Parameter Selection Approach

The infectious disease known as COVID-19 is attributed to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). First identified in Wuhan, the capital of China's Hubei province, in 2019, this novel disease rapidly propagated across the globe, culminating in the unprecedented COVID-19 pandemic of 2019-2020. The global dissemination of this virus has precipitated severe health threats and economic disruption worldwide. Common symptoms of the disease include fever, cough, shortness of breath, muscle aches, diarrhea, and sore throat [1].

Medical imaging techniques such as computed tomography (CT) and chest x-ray (CXR) are commonly used to detect lung disorders. Chest CT scans are superior to CXR because they are less influenced by other chest tissues and are better at identifying lung problems [2]. CT imaging also reveals the fundamental anatomical characteristics of COVID-19. Radiologists recommend chest CT scans as the primary lung clinical diagnosis technique since COVID-19 development may be effectively quantified using CT scans [3].

The aspects of CT scan digital images with the development of computer-assisted diagnostic (CAD) technologies have benefited physicians in making rapid diagnosis. Depending on the features displayed in the CAD techniques and medical imaging may be used to provide a diagnosis. To sort Infected and not Infected CT scanning images, these frameworks typically use feature extraction, selection, and classification. When the dataset dimensions of predictive modelling continue to increases, feature selection (FS) process is adopted [4]. Various feature selection models have been adopted for COVID-19 prediction tasks. But still, the existing models struggles to provide high results on datasets that includes complex feature relationships and high redundancy.

Many researchers have been inspired to examine the application of Artificial Intelligence (AI) models for identifying COVID-19 from different medical images and then categorize the patients [5]. AI is categorized into Machine Learning (ML) and Deep Learning (DL). ML techniques which have been widely utilized for many applications for medical imaging CAD attempts for rapid identification of COVID-19 at earlier stage.

For instances, an automated ML algorithm is developed for the detection of COVID-19 using CT and X-Ray images [6]. Initially, these images were pre-processed by normalization to enhance the quality of the image and removing of noise. Secondly, the images were segmented using fuzzy c-means clustering. Then, essential features were selected form the feature vector using principal component analysis (PCA). Finally, the ML algorithms like k-Nearest Neighbour (k-NN) Sparse Representative Classifier (SRC), Artificial Neural Network (ANN) and Support Vector Machine (SVM) were employed to make decisions for normal, pneumonia, COVID-19 positive patients. On the other hand, classifier’s performances are decided based on the predefined parameter alone. The regularization of hyper-parameters is very important for improving a network’s generalization while handling different sample size datasets. In order to select the appropriate features and hyper-parameter for COVID-19 prediction, a Chaotic Logistic Map based Modified Whale Optimization with Improved Neural Network (CLM-MWO-INN) is presented in this paper to enhance the classifier’s performances.

1.1 Contribution of this research

The major objective of this framework is to select the relevant features and hyperparameters for improving the classifier performance for COVID-19 detection. At first, the features are extracted from the collected CT images using GLCM and GLRM techniques. Then, CLM-MWO is applied to select the suitable features from the extracted features and hyper parameter tuning of NN for the best possible results. In this method, hyper parameter tuning and FS are executed concurrently, since the selection of a model’s features might impact the hyperparameters’ performance. Finally, the INN model is constructed to classify and detect the COVID-19 risk levels. As the COVID-19 cases increases, the proposed model automatically categorizes the diseases patients from CT scans potentially saving time for doctors and physicians.

3.1 Feature extraction

The technique of assessing picture texture involves feature extraction. The findings provide a clearer picture of how texture and object shape are determined. When the method has a larger input data set, it should be reduced in size to make it easier to handle. Feature extraction is the process of converting an input image into a standard set of features. The clustered pixels were turned into quantitative data by using the feature extraction method on CT images of the healthy and COVID-19 types. The features used in this study are primarily the GLCM for extracting statistical features and GLRM for extracting run length features [12], as well as their procedures.

3.1.1 GLCM technique

The GLCM is described as a statistical paradigm that considers the spatial relationship between pixels [13]. It is a $2 \mathrm{D}$ histogram that calculates the relevance of each pixel in an image divided by a certain distance $D$. Assume that $J(a, b)$ is an image of size $U \times V$ with $l$ gray levels, and that, $J\left(a_1, b_1\right)$ and $J\left(a_2, b_2\right)$ are two pixels with gray level intensities $x_1$ and $x_2$ respectively. Considering, $\Delta_a=a_2-a_1$ in the direction of $a$ and $\Delta_b=b_2-b_1$ in the direction of $b$, the intersecting line has the identical interval $\theta$ as $\arctan \left(\frac{\Delta_b}{\Delta_a}\right)$. The modified co-incident matrix $C O_{\theta, D}$ is depicted in Eq. (1):

$\operatorname{CO}_{\theta, D}\left(i_1, i_2\right)=\left(N u m\left\{\begin{array}{c}\left(\left(a, b_1\right),\left(a_2, b_2\right) \epsilon(U \times V) *\right. \\ (U \times V) \backslash Z)\end{array}\right\}\right) \backslash M$     (1)

In above Eq. (1), $U \times V$ defines the numerical values in the co-incident matrix whereas M represents the total number of pixels. This model defines Z as a resulted condition given in Eq. (2):

$D \sin (\theta), \Delta_{-} b=D \cos (\theta)$     (2)

In general, θ equals to 0.459013 degrees and D ranges from 1 to 5. In the study [14], the five distinct texture features like power, variance, contrast, and autocorrelation, are concisely presented based on the applicability of co-incident matrices.

3.1.2 GLRM technique

GLRM is referred to as a mathematical element network. It returns a percentage of the pixels’ intensity along the supplied guidance, referred to as Run length. The GLRM estimates the dimension of homogenous cycles for every level of gray. It is calculated for four different orientations, each of which has eleven texture indices derived from the matrices. The $(a, b)$ component of GLRLM connects homogeneous segments of b pixels with intensity a from an image which is termed as GLRLM. Considering, the above-mentioned GLRM matrix with 11 features is achieved. 44 features (11 features 4 directions) have been completed for all images [15]. Short Run Emphasis (SRE), Long Run Emphasis (LRE), Gray Level Non-uniformity (GLN), Run Length Non-uniformity (RLN), Run Percentage (RP), Low Gray Level Run Emphasis (LGRE), and High Gray Level Run Emphasis (HGRE) are utilized in this method to determine the categorization performance [14].

These features use pixel grey levels in sequence to distinguish textures with similar SRE and LRE values but different grey level distributions. After that, using Histogram features, GLCM, GRLM, and their combinations, create feature sets. Totally For each CT scan normal and COVID-19 picture independently, twenty-nine characteristics were retrieved. The data set obtained by both techniques of feature extraction procedure is too vast and hence, it is difficult to implement as input to the classifier. As a result, the FS technique, which is detailed in the next section, is used to reduce dimensionality.

3.2 Feature and parameter optimization

To achieve adequate classification accuracy, a FS strategy is used to reduce the number of retrieved characteristics by excluding irrelevant and redundant features [16]. In categorization problems, FS is a common and crucial strategy for gaining more precision and a quicker convergence. This section controls the selection of the best attributes from a dataset using optimization agents. To study and evaluate the effectiveness of the proposed optimizer, the Genetic Alogrithm (GA), Particle Swarm Optimization (PSO), and WOA-based FS algorithms are presented. This component handles the optimizer’s agents in order to efficiently choose features. Here, the historical context of GA, PSO, and WOA is discussed.

3.2.1 GA

The normal selection and natural selection theories communicated in genetic engineering begin with the Genetic Algorithm. The selection cycle is an interaction in which the number of components is reduced to a small subset, resulting in a high precision order. The genetic algorithm [17] is outlined in the steps below.

Algorithm: GA $\left(\boldsymbol{n}, \chi_f, \chi_p, \mu\right)$, where $n$ is the number of individuals in the population; $\chi_f$ is the total number of chosen features from each chromosome; $\chi_p$ is the cumulative number of accepted parameters from each chromosome; and $\mu$ is the mutation rate.

//Initialize generation $0: k:=0 ; P_k:=\mathrm{a}$ population of $\mathrm{n}$ individuals produced at random;

//Determine $P_k$:

Configure

Fitness $F(i)=\max _{\vartheta}\left(\operatorname{accuracy}\left(\theta_{k i}\right)-\alpha * \frac{\text { selected features }\left(\theta_{k i}\right)}{\text { Total number of features }(n)}\right)$     (3)

// $F(i)=$ fitness function; $\vartheta$ is the initial population, $\theta_{k i}$ represents the $i^{\text {th }}$ chromosome in population, accuracy $\left(\theta_{k i}\right)$ depicts the classification performance achieved by using chromosome $\theta_{k i}, \alpha$ is a weighting parameter

Do

{

/Create generation $k+1$;

1 (i) Copy: Select $\left(1-\chi_f\right) \times n$ members and replace them in $P_k+1$;

(ii) Copy: Choose $\left(1-\chi_p\right) \times n$ members and transfer them into $P_k+1$;

2 (i) Crossover: Identify $\chi_f \times n$ members of $\mathrm{P} \mathrm{k}$, couple them, generate offspring, and add the offspring into $P_k+1$;

(ii) Crossover: Acquire $\chi_p \times n$ members of $P_k$; couple them; produce offspring; and integrate the offspring into $P_k+1$.

3 (i) Reconstruct: Evaluate $\mu_f \times n$ members of $P_k+1$; shift an arbitrary bit in every feature. //Compute $P_k+1$;

(ii) Reconstruct: Determine $\mu_p \times n$ members of $P_k+1$; reverse a randomized bit in every parameter//Compute $P_k+1$:

Calculate fitness ( $i$ ) for every $i \in P_k$;

Increment: $k:=k+1$;

}

While the fitness of the fittest individual in $P_k$ is insufficient;

Return the fittest member of $P_k$;

3.2.2 PSO

PSO is not a well-established improvement approach based on herds of birds or, more likely, schools of fish. The flock of birds (swarm) has developed a cooperative strategy for obtaining food, with every bird in the flock changing their chase strategy in accordance to updated information [18]. The concept of PSO calculation is linked to developmental calculations and a plethora of fictitious life frameworks. The Birds fly through the multidimensional chase space invisibly. Throughout the journey, each particle moves at its own unique speed in relation to space. The entire population is renewed by refreshing each particle. The multiplicity game plan propels itself forward, aiming for the highest objective capacity esteem point, where the particles eventually congregate. The following are the methods for improving molecular swarms:

Step 1: Initialization $X_f$ and $X_p$ using swarm particles $\| X_f$ selected feature by particle, $X_p$ selected parameter by particle.

Step 2: Calculate fitness of each particle $F(i)$ using Eq. (3).

Step 3: Evaluate the particle fitness for selected feature.

If Fitness of $X_{f_i}>pbest_i$ \\ $X_{f i}$ is the current position of particle $i$ for feature $f$.

$pbest_i=X_{f i}$.

If fitness of $p$ best $t_i>$ gbest $_i$.

$gbest _i=pbest_i$.

Step 4: Evaluate the particle fitness for selected parameter.

If Fitness of $X_{p_i}>$ pbest $_i \backslash \backslash X_{p i}$ is the current parameter of particle $i$ for parameter $p$. pbest $_i=X_{p i}$.

If fitness of pbest $_i>$ gbest $_i$.

$gbest_i=pbest_i$.

Step 5: Update the velocity of particle $i$ for feature and parameter-At each cycle the rates of the multitude particles are determined by Eq. (4) and Eq. (5):

$F\left(V_{i d}^{t+1}\right)=W * V_{i d}^{t+1}+c_1 * r_{1 i} *\left(p_{f i}-x_{f i}^t\right)+c_2 * r_{2 i} *\left(g_{f i}-x_{f i}^t\right)$     (4)

$P\left(V_{i d}^{t+1}\right)=W * V_{i d}^{t+1}+c_1 * r_{1 i} *\left(p_{p i}-x_{p i}^t\right)+c_2 * r_{2 i} *\left(g_{p i}-x_{p i}^t\right)$     (5)

where, $t$ denotes the replication in the process;

$d$ denotes the dimension in the exploration space.

$W$ is inertia weight;

$c_1$ and $c_2$ are acceleration constants.

$r_1$ and $r_2$ are arbitrary range consistently dispersed in $[0,1]$.

$pbest_i$ defines the best position of the particle.

$gbest_i$ defines the best area recalled by the particle.

$p_{f i}$ and $p_{p i}$ represent the best position of particle in $p_{b e s t}$ for feature and parameter selection.

$g_{f i}$ and $g_{p i}$ represent the best area reassigned by particle in $g_{b e s t}$ for feature and parameter selection.

The PSO is created by taking into account the components of each particle. The weighting perspectives $c_1$ and $c_2$ protect the particles from colliding (people). After refreshing particle $I$, the speed $(v)$ and random number $(r)$ are verified and ensured in a way shown, to avoid a crash.

Step 6: Update the position of particle $i$ for feature and parameter updating using:

$x_{f i}^{t+1}=x_{f i}^t+V_{f i}^{t+1}$     (6)

$x_{p i}^{t+1}=x_{p i}^t+V_{p i}^{t+1}$     (7)

Step 7: Step 4. If stopping criterion is not met, continue Steps 2 and 3.

Step 8: Return $g_{\text {best}}$ and its fitness values.

This is a considerable computational benefit over GA when the population is considerably large. The activity of reducing actual numbers is used to calculate movement and position. The PSO alters its speed (accelerating) toward $p_{\text {best}}$ (Personal Best) and $g_{\text {best}}$ (Global Best) regions (neighbourhood interpretation of PSO) and accelerates toward $p_{\text {best}}$ and $g_{\text {best}}$ areas.

3.2.3 WOA

Recently, there has been a lot of buzz about WOA, which was proposed in the study [19]. WOA is a population-based meta-heuristic technique that simulates humpback whale hunting behavior. Humpback whales will dive twelve meters underwater and lead a spiral of bubbles raising to the surface after they have identified their meal. Encircling prey, spiral bubble-net feeding maneuver, and hunt for prey are the three primary stages of position information [19].

Exploitation phase

Throughout the exploitation process, humpback whales assess the available best location as the target prey (global optimum) and modify their locations toward the global optimum based on two systems like shrinking encircling (circling prey) and circular elevating location in spiral bubble-net feeding function. The module of the shrinking encircling operation for FS and parameter selection is represented as follows:

$D_f=\left|C \bullet X_f^*(t)-X_f(t)\right|$      (8)

$X_f(t+1)=X_f^*(t)-A \bullet D_f$     (9)

$D_p=\left|C \bullet X_p{ }^*(t)-X_p(t)\right|$      (10)

$X_p(t+1)=X_p^*(t)-A \bullet D_p$      (11)

From Eq. (8) to Eq. (11), $X_f$ is the position vector for selecting features and parameters, $X_f{ }^*$ and $X_p{ }^*$ indicate the optimal elucidation acquired for identifying features and parameters, which will be changed in every repetition if a finest solution is determined, $t$ denotes the present iteration, $D$ denotes distance between $X$ position of $i^{\text {th }}$ whale and $X^*$ best solution whale. $\mid$. $\mid$ is the relative valuation, and $\bullet$ is an elementto-element multiplication. Here, $\mathrm{A}$ and $\mathrm{C}$ are two constants that are computed using the formula:

$A=2 a \bullet r-a$      (12)

$C=2 \bullet r$     (13)

where, $r$ is an arbitrary integer between 0 and 1. Throughout the repetitions in both the exploration and exploitation stages, it drops-out linearly from 2 to 0 so that the shrinking encircling behavior may be realized. The statistical expression of the spiral upgrading position for feature and parameter is a spiral Eq. (14)-Eq. (17):

$F\left(D_f{ }^{\prime}\right)=\left|X_f{ }^*\right|(t)-X_f(t)-X_f(t)$      (14)

$X_f(t+1)=D_f{ }^{\prime} \bullet e^{b l} \bullet \cos (2 \cos \pi l)+X_f{ }^*(t)$      (15)

$P\left(D_p{ }^{\prime}\right)=\left|X_p{ }^*\right|(t)-X_p(t)$     (16)

$X_p(t+1)=D_p{ }^{\prime} \bullet e^{b l} \bullet \cos (2 \cos \pi l)+X_p^*(t)$     (17)

where, $D^{\prime}$ indicates the distance between the $i^{t h}$ whale and the best solution obtained so far, $l$ is a random value in the interval $[-1,1]$, and $b$ is a constant that defines the form of a logarithmic spiral. It is important to note that when whales grab prey, both the spiral-shaped course and the diminishing encirclement occur concurrently. To simulate this behavior, each mechanism is constructed with a $50 \%$ chance for each characteristic and parameter.

$X_f(\mathrm{t}+1)=\left\{\begin{array}{c}X_f{ }^*(t)-A \bullet D_f \text { if } r<0.5 \\ D_f{ }^{\prime} \bullet e^{b l} \bullet \cos (2 \cos \pi l)+X_f{ }^*(t) \text { if } p<0.5\end{array}\right.$      (18)

$X_p(\mathrm{t}+1)=\left\{\begin{array}{c}X_p^*(t)-A \bullet D_p \text { if } r<0.5 \\ D_p{ }^{\prime} \bullet e^{b l} \bullet \cos (2 \cos \pi l)+X_p{ }^*(t) \text { if } r<0.5\end{array}\right.$     (19)

where, $r$ is a random integer between 0 and 1.

Exploration phase

Here, a global query is constructed to facilitate the investigation of feature and parameter data. Its statistical structure is comparable to Eq. (20) to (23), with the distinction that an arbitrary search agent, rather than the best agent, is assigned to direct the search. To upgrade the location, the stochastic parameter $|A|$ with a range greater than 1 or less than 1 is used to identify between exploration (search for prey) or exploitation (shrinking encircling mechanism).

$D_f=\left|C \bullet X_{\text {rand }}-X_f\right|$     (20)

$X_f(\mathrm{t}+1)=X_{\text {rand }}-A \bullet D_f$     (21)

$D_p=\left|C \bullet X_{\text {rand }}-X_p\right|$     (22)

$X_p(t+1)=X_{\text {rand }}-A \bullet D_p$     (23)

where, $X_{\text {rand}}$ is a location vector selected randomly from the present generation. The WOA pseudo code is described in Algorithm. Note that WOA may seamlessly transition among the stages of exploration and exploitation based on a single parameter. Although WOA is comparable with certain conventional MAs, it still has disadvantages such as poor precision and abrupt convergence. Therefore, modified WOA is used in this work.

Algorithm for WOA

Step 1: Begin

Step 2: Determine the whale population for feature $X_f(i=1,2,3 \ldots, n)$ and parameter $X_p(i=1,2,3 \ldots, n)$.

Step 3: Comute the fitness of each search agent $F(i)$ using Eq. (3).

Step 4: Determine best search agent for feature $X_f{ }^*$ and parameter $X_p{ }^*$.

Step 5: While ( $t<$ maximum number of iterations).

Step 6: For each exploration agent, update $a, A, C, l$ and $r$.

Step 7: if $1(r<0.5)$.

Step 8: if $2(|A|<1)$.

Step 9: Improve the ranking of present search agent for a feature using Eq. (9).

Step 10: Improve the present search agent's position for parameter using Eq. (11).

Step 11: else if $2(|A| \geq 1)$.

Step 12: Choose a random search agent $\left(\mathrm{X}_{\text {rand }}\right)$.

Step 13: Enhance the location of current search agent for feature using Eq. (21).

Step 14: Determine the current search agent position for parameter using Eq. (23).

Step 15: end if 2.

Step 16: else if $1(r \geq 0.5)$.

Step 17: Explore the location of current search agent for feature using Eq. (15).

Step 18: Upgrade the location using current search agent for parameter using Eq. (17).

Step 19: end if 1.

Step 20: end for.

Step 21: Inspect and fix redundant genes to ensure the validity of each search agent.

Step 22: Place $X_f{ }^*$ and $X_p{ }^*$ if there is a preferable solution is determined.

Step 23: $t=t+1$.

Step 24: end while }.

Step 25: return to step 4 and step 5 .

For the classifier to categorize the numerous feature categories, FS will be converted into a more consistent and relevant sort of feedback. This research introduces the chaotic-based whale optimized characteristics for machine approaches to categorize COVID-19 and non-COVID 19 characteristics in CT images. Using a ML algorithm, the accuracy, precision, and recall of the suggested method are compared to those of the GA, PSO, and whale methods.

5.1 Dataset description

In order to prove the efficiency of the proposed model, two different CT images dataset have been collected which is illustrated below.

Dataset 1: SARS-CoV-2 CT scan dataset [21] have been collected from real patients in hospitals from Sao Paulo, Brazil. The aim of this dataset is to encourage the research and development of artificial intelligent methods which are able to identify if a person is infected by SARS-CoV-2 through the analysis of his/her CT scans. The total CT images obtained from the given dataset for the performance evaluation are listed in Table 1.

Table 1. Observed CT images for COVID-19

Table 2. Observed CT images for various lung diseases categories

Dataset 2: In this dataset, The CT images also opted for five diseases categories like atelectasis, infiltration, pneumonia along with COVID-19 and non-Covid. In this study, different open public portals are analyzed to collect the CT data for the experiment purposes. The lung atelectasis images are taken from [22], The Covid and Non-Covid (Normal) images are gathered from [23], the viral pneumonia is taken from the study [24] and infiltration is obtained from [25]. The total CT images obtained from the given dataset for the performance evaluation are listed in Table 2.

5.2 Performance measures parameters

The attributes collected from the datasets are used in the training and testing procedures. In this assessment, 60% of the data was utilized for training and the remaining 40% for testing. The performance evaluation metric evaluated for the various methods is discussed below.

• TP (True Positive)-The number of normal images is identified as normal.
• TN (True Negative)-The number of disease images identified as disease.
• FP (False Positive)-The number of normal images is identified as disease images.
• FN (False Negative)-The number of diseased images is identified as normal.

Accuracy: The proportion of correct predictions. It can be calculated using:

Accuracy $=\frac{(T P+T N)}{(T P+T N+F P+F N)}$    (28)

Precision: The proportion of anticipated positive models which truly are positive.

Precision $=\frac{T P}{T P+F P}$     (29)

Recall: Recall (hit rate/sensitivity) is a metric that indicates how well a classifier recognizes positive examples.

Recall $=\frac{T N}{T P+F N}$     (30)

F1 Score: It is the ‘Harmonic Mean’ of recall with accuracy.

F1_Score $=\frac{(2 \times \text { Precision } \times \text { Recall })}{(\text { Precision } \times \text { Recall })}$     (31)

In this work, the confusion matrix was employed to characterize the efficiency of the proposed algorithm on given dataset 1 and dataset 2. It facilitates for the modeling of algorithm execution. It also makes detecting discrepancies across classes much easier. The purpose of this technique is to evaluate the efficiency of CLM-MWO using the INN algorithm. The suggested model is contrast with MLP, Random Forest (RF) and Extreme Learning Machine (ELM). Different dataset was used to evaluate it, as stated in the Table 3 and Table 4.

The Figure 2 shows the parameters like Accuracy, Precision, Recall and F1-Score have been determined and that the suggested feature selection approach outperforms previous algorithms for dataset-I. For instance, the accuracy of CLM-MWO-INN is 13.71%, 10.11%, 6.61% and 3.08% higher than the existing SVM, MLP, RF and ELM classifiers. The suggested approach improves INN classification accuracy by incorporating feature optimization techniques.

The Figure 3 shows comparison values of accuracy, precision, recall and F1-Score for proposed and existing models using the dataset-II. In dataset-II, different categories of lung diseases have been considered for this research work to prove the proposed model’s efficiency. From the Figure 3, it has been observed that the accuracy of CLM-MWO-INN is 10%, 6.64%, 4.36% and 2.75% higher than the SVM, MLP, RF and ELM models correspondingly.

Table 3. Performance evaluation for dataset-I

Table 4. Performance evaluation for dataset-II

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Figure 2. Performance analysis for dataset-I

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Figure 3. Performance analysis for dataset-II