Efficient prediction of drug–drug interaction using deep learning models

Abstract

A drug–drug interaction or drug synergy is extensively utilised for cancer treatment. However, prediction of drug–drug interaction is defined as an ill‐posed problem, because manual testing is only implementable on small group of drugs. Predicting the drug–drug interaction score has been a popular research topic recently. Recently many machine learning models have proposed in the literature to predict the drug–drug interaction score efficiently. However, these models suffer from the over‐fitting issue. Therefore, these models are not so‐effective for predicting the drug–drug interaction score. In this work, an integrated convolutional mixture density recurrent neural network is proposed and implemented. The proposed model integrates convolutional neural networks, recurrent neural networks and mixture density networks. Extensive comparative analysis reveals that the proposed model significantly outperforms the competitive models.

1 Introduction

Even though many tools are available to predict the cancer in human beings, but development of an anti‐cancer treatment is still a challenging issue [1]. Generally, cancer patients need an efficient combination of various drugs so called drug–drug interaction (DDI) [2]. A DDI means a variation in the effect of given drug on the human body when a drug is taken at the same time with another drug [3]. It may increase, delay, decrease or cause adverse effects of either drug. However, prediction of an efficient drug combination is still a challenging issue [4]. Recently, many researchers have designed various machine and deep learning models to overcome this issue [5]. However, each model has its own inherent issues. Therefore, in this paper, we have studied these models and try to find the limitation of these models. The main objective is to present future direction for efficient prediction of drugs. An efficient combination has a huge impact on cancer patients through the fusion of various drug–drug combinations [6]. The DDI combinations help cancer patients against cancer pathogens attacking the body [7] like viruses [8] and bacteria [9] in different ways [10]. The specific drug targets specific intrusive pathogens and provides resistance to the host from the specific antigen [11]. The knowledge of DDI prediction can be implemented for the diagnostics of cancer patients [12]. It is therefore of interest to develop improved methods for predicting DDI in an efficient manner [13]. Therefore, DDI prediction becomes a significant issue [14]. Researchers have devoted great efforts to DDI prediction models by using machine learning models in the past decade [15]. Ensembling based machine learning models can be efficiently used to predict the DDI prediction [16].

The main novelty of this paper is illustrated as:

• An integrated deep‐learning model is designed and implemented to predict the DDI in an efficient manner.

• The proposed model integrates convolutional neural networks (CNNs), recurrent neural networks (RNNs) and mixture density networks (MDNs).

• Extensive experiments are performed on benchmark datasets.

• Extensive experiments are performed on benchmark dataset by considering the proposed and competitive machine learning models.

The reminder of the paper is organised as follows. Section 2 presents comprehensive study of the competitive models. In Section 3, the proposed method along with mathematical preliminaries is defined. Section 4 provides the experimental results of the proposed model. Finally, conclusion is presented in Section 5.

2 Related work

This section discusses various machine learning and deep learning models which have been implemented so far to predict the DDI.

Liu et al. predicted DDI using memory network and transfer weight matrix. The problem of unattainable automation processes and vocabulary gap in feature extraction are addressed [17]. Xu et al. designed a novel bidirectional long‐short‐term memory (LSTM) network‐based model which integrates biomedical resource with lexical and entity position details jointly to predict DDI [18]. Fakhraei designed a prediction model by considering a bipartite graph of drug–target interactions augmented with drug–drug and target–target similarity metric by using a probabilistic soft logic (PSL). Probabilistic rules of PSL are utilised to evaluate the interactions with models based on triad and tetrad structures [19].

Yue et al. addressed the issues of selecting discriminative features and data imbalancing in DDI detection. To increase the accuracy of DDIs detection, a multi‐layer feature selection method and an over‐sampling model are utilised [20]. Deepika et al. proposed a semi‐supervised learning framework for DDI. In this, SVM, Node2vec and a PU learning algorithm are utilised. Meta‐classifier predicts DDI more significantly than base classifiers [21].

You et al. designed linear classifier and deep neural network based on least absolute shrinkage and selection operator. The main advantage of this model is to repurposing the drugs for cancer patients [22]. Lee and Chen used the unsupervised deep learning to predict the DDI. It detects the adverse drug reactions and repurposes the drugs for cancer suffering patients [23].

Zhang et al. proposed an ensemble approach with linear neighbourhood regularisation and sparse feature learning for DDI predictions. An iterative algorithm is utilised to solve the objective function of the proposed model [24]. Zhou et al. proposed position based deep multi‐task learning algorithm for DDIs extraction from biomedical texts. It also predicts interaction of two drugs and further differentiates between the interaction types using multi‐task learning [25].

3 Proposed model

3.1 Neural networks

Neural networks are well‐known human neuron based models. These models are extensively utilised in literature to classify or predict continuous values. Mathematically, it is defined as

$$\alpha =\mathcal{F}(\chi ;\psi )$$ (1)

here, $\chi$ and $\alpha$ define input and output layers of neural networks, respectively. $\mathcal{F}$ and $\psi$ show structure and weight of neural networks, respectively.

The training loss $(l)$ of neural networks generally computed in terms of mean squared errors is defined as

$$l=\frac{1}{N}\sum _{n=1}^N({\hat{\alpha }}_n-{\alpha }_n){}^2$$ (2)

here, N and $\hat{y}$ define input features and target feature, respectively.

In several circumstances, a neural network obtains efficient prediction results. However, for several circumstances such as high non‐Gaussian inverse problem, neural networks perform poorly [26]. Therefore, RNNs can be used to handle this issue.

3.2 Recurrent neural network

RNNs [27] have recently got a significant attention of researchers. The state transition of RNNs is defined as

$$i_l={\phi }_i({\psi }_i{x}_t+U_i{i}_{t-1}+b_i)$$ (3)

where $x_t$, $i_l$ and ${\phi }_i$ define input, hidden state and activation function, respectively. ${\psi }_i$, $U_i$ and $b_i$ represent hidden weight of input, hidden state and hidden bias, respectively. The outcome of a RNN is defined as

$${\alpha }_t={\phi }_{\alpha }({\psi }_{\alpha }{i}_l+b_{\alpha })$$ (4)

where ${\alpha }_t$ and ${\phi }_{\alpha }$ show the output layer and activation function, respectively. ${\psi }_{\alpha }$ and $b_{\alpha }$ demonstrate hidden weight for input and output bias, respectively.

However, RNNs suffer from long‐term dependency issue during model building.

3.3 Mixture density network

In conventional neural network, a gradient‐descent based scheme is used for the optimisation of loss function. Commonly, these type of models can behave appropriately for those problems that can be defined using deterministic function $f(\chi )$. In this, for the same input sequence there is only one output value. Still, there is a possibility that one input may have more than one possible values for some stochastic problems. Usually, these type of issues can be described as a conditional distribution $C(\alpha |\chi )$ than a deterministic function $\alpha =f(\chi )$. In this kind of case, conventional neural networks may not perform as desired.

This kind of issues can be handled by replacing the original loss function with the conditional function. The Gaussian distribution can be used for the regression process. The representation capacity of a model can be improved by using mixed Gaussian distributions.

MDNs have been proposed by many researchers [28]. The conditional probabilities of MDN contain both loss function and mixed Gaussian distribution as compared to conventional neural network. Hence, the negative log probability needs to be minimised by the optimisation process. Therefore, the loss function is defined as

$$C(\alpha |\chi )=\sum _{p=1}^P{\pi }_{p}C(\alpha |\chi ;{\varphi }_p)$$ (5)

here, ${\pi }_p$ is the assignment probability for each model, with ${\sum }_{k=1}^K{\pi }_p=1,(0<{\pi }_p<1)$, x is the input and ${\varphi }_p$ is the internal parameters of the base distribution. For Gaussian's, ${\varphi }_p=\{{\mu }_p,{\phi }_p\}$, ${\mu }_p$ is the means and ${\phi }_p$ is the variances.

The main output layer of RNN, i.e. (4) can be redefined as

$${\varphi }_t={\phi }_{\varphi }({\psi }_{\varphi }{i}_l+b_{\varphi })$$ (6)

here, ${\phi }_{\varphi }$ represents the activation function, ${\varphi }_t$ denotes the output of RNN and input of MDN, $b_{\varphi }$ acts as output bias and ${\psi }_{\varphi }$ denotes hidden weight for an input.

After the completion of training process, mixed Gaussian distributions and neural network are used to demonstrate the target distributions.

3.4 Proposed deep neural network

A novel deep neural network framework is devised by using the merits of aforesaid three neural networks. The designed network is known as convolutional mixture density RNN. The working of the proposed model is illustrated as follows. The features of high dimensional inputs are captured using 1D CNN. Afterwards, LSTM‐RNN model is used for modelling the time series data of state transitions. To improve the prediction accuracy, the output layer comprises mix Gaussian densities. Due to this composition, we believe that the proposed model is capable of explaining the high dimensional time series data. The proposed model is illustrated in Fig. 1. Algorithm 1(see Fig. 2) shows the steps to elaborate the learning process of the proposed model.

Fig. 1.

Convolutional mixture density RNN

Fig. 2.

Algorithm: proposed model

The proposed model is unique with respect to adoption of a sequential density estimation approach as compared to other competitive models.

4 Performance analysis

To evaluate the performance of the proposed model, an experimental platform is designed and implemented in MATLAB 2019a tool. The effect of DDI is referred as a target variable. The benchmark DDI [29] is considered for experimental results. A 20‐fold cross‐validation is considered to overcome over‐fitting problem associated with the competitive machine learning models. To achieve cross‐validation, initially training data is decomposed into 10 folds (i.e. subsets). Consider first‐fold for validation and utilise remaining 19‐subsets in cross‐validation training set. After obtaining the model, performance of remaining 9‐subsets are computed. To prevent over‐fitting, average of computed performance results are computed. Since we are considering every fold, therefore, the problem of over‐fitting is reduced. 20–90% ratio of dataset is considered to build and test the model. The acceptance error is set to be $\pm 0.15$ to compute the accuracy. For comparative analysis, nine well‐known predictions models are considered. These models are decision tree (DT) [30], random forest (RF) [31], L1 norm support vector machine (L1‐SVM) [32], L2 norm support vector machine (L2‐SVM) [33], artificial neural networks (ANNs) [34], k‐nearest neighbour (kNN) [35], CNN [36], long short term memory (LSTM) networks [37] and adaptive neuro‐fuzzy inference system (ANFIS) [38]. The parameters setting of the proposed and the competitive models are their default values as mentioned in their respective literature.

4.1 Drug‐synergy dataset

NCI‐ALMANAC [39] could be the largest‐to‐date phenotypic drug combination for high‐throughput screening. It includes around 290,000 synergy combinations from couples of 104 drugs, evaluated by Food and Drug administration (FDA), authenticated drugs over 60 cancer cell lines. Fig. 3 shows the typical layout of the proposed model and the used dataset. The drugs contain a wide selection of organic substance families, along with various inorganic molecules (arsenic trioxide, connected and cisplatin platinum‐organic substances). Certainly, just three clusters containing eight drugs are evaluated with a Tanimoto score, threshold of 0.8 (Everolimus and Sirolimus, Vincristine with Vinblastine and Doxorubicin‐Idarubicin‐Daunorubicin‐Epirubicin clusters), while the rest of the 96 drugs have minimum similarity between them [40].

Fig. 3.

Diagrammatic workflow of the proposed drug synergy prediction model

NCI‐ALMANAC have collected drug synergy data from three assessment institutes: NCI's Frederick National Lab for University of Pittsburgh (FG, 136,129 synergy scores), SRI International (FF, 146,147 synergy scores) and Cancer Study (screening middle rule 1A, 11,259 synergy scores). The synergy of drug couples is calculated in these assessment institutes contrary to the National Cancer Institute (NCI)‐60, including cell lines from nine types of cancer: non‐small‐cell lung, leukaemia, central nervous system, colon, renal, ovarian, breast and prostate. As a whole, synergy is assessed for 293,565 drug combination cell line tuples, which presents a matrix completeness of 91.35%. Each centre uses its own process and some drugs are missing from the mixture pool with respect to the assessment institute. While there is no overlap between drug combination‐cell line tuples involving the three institutes, it is extremely hard to calculate inter‐centre group consequences, and thus we should use information from various assessment institutes separately [41].

The combination gain is computed in NCI‐ALMANAC by the alleged ComboScore (a revised variation of the Bliss independence model). The dose‐response matrix of the utilised drug combination cell line tuple provides the benefit (or loss) of the consequence attained by the combination of theoretically estimated value. Significant values of ComboScore show a synergistic combination, although the negative match an antagonistic influence (those solely additive acquire a zero ComboScore) (For more details please see [39]).

4.2 Validation analysis

We have initially divided data into two completely isolated parts depending upon the fraction (e.g. 50% for training and remaining 50% for testing). Thereafter, to validate the drug synergy prediction models, the training data is divided into ten chunks. First nine chunks are used to train the drug synergy prediction models. Finally, the tenth chunk is used to validate the models. Fig. 4 shows the actual working of the drug synergy prediction model.

Fig. 4.

Actual working of the proposed drug synergy prediction model

Tables 1, 2–3 show the comparative analysis of the proposed and competitive models. These tables indicate that the proposed model outperforms competitive models in terms of root mean squared error, accuracy and coefficient of determination, respectively.

Table 1.

Analysis of training accuracy

Dataset	20%	40%	60%	80%	90%
DT	$88.1\pm 0.6$	$91.8\pm 0.8$	$87.7\pm 0.9$	$88.5\pm 0.4$	$89.3\pm 0.4$
RF	$89.3\pm 0.9$	$92.4\pm 0.8$	$88.4\pm 0.8$	$89.8\pm 0.2$	$90.6\pm 0.4$
L1‐SVM	$90.2\pm 0.6$	$92.7\pm 0.8$	$89.0\pm 0.4$	$89.8\pm 0.6$	$91.1\pm 0.9$
L2‐SVM	$90.2\pm 0.7$	$92.7\pm 0.9$	$89.0\pm 0.4$	$89.8\pm 0.1$	$91.1\pm 0.2$
ANN	$93.7\pm 0.8$	$94.6\pm 0.8$	$91.4\pm 0.9$	$93.6\pm 0.9$	$93.4\pm 0.8$
kNN	$94.3\pm 0.8$	$95.4\pm 0.8$	$91.9\pm 0.7$	$94.6\pm 0.9$	$94.3\pm 0.9$
CNN	$95.0\pm 0.9$	$96.3\pm 0.9$	$93.6\pm 0.6$	$95.9\pm 0.8$	$96.1\pm 0.9$
LSTM	$95.9\pm 0.9$	$96.5\pm 0.9$	$94.4\pm 0.7$	$96.6\pm 0.9$	$96.2\pm 0.7$
ANFIS	$97.1\pm 0.9$	$97.8\pm 0.8$	$95.1\pm 0.9$	$98.6\pm 0.9$	$96.9\pm 0.8$
proposed	$98.4\pm 0.7$	$99.4\pm 0.4$	$97.3\pm 0.8$	$99.4\pm 0.5$	$98.5\pm 0.6$

Table 2.

Analysis of training coefficient of determination

Dataset	20%	40%	60%	80%	90%
DT	$0.87\pm 0.08$	$0.87\pm 0.04$	$0.82\pm 0.02$	$0.82\pm 0.06$	$0.84\pm 0.07$
RF	$0.88\pm 0.01$	$0.87\pm 0.02$	$0.83\pm 0.06$	$0.83\pm 0.04$	$0.84\pm 0.03$
L1‐SVM	$0.88\pm 0.06$	$0.88\pm 0.02$	$0.83\pm 0.06$	$0.83\pm 0.02$	$0.85\pm 0.09$
L2‐SVM	$0.90\pm 0.03$	$0.89\pm 0.07$	$0.85\pm 0.02$	$0.85\pm 0.09$	$0.86\pm 0.08$
ANN	$0.91\pm 0.04$	$0.90\pm 0.02$	$0.86\pm 0.09$	$0.86\pm 0.05$	$0.87\pm 0.07$
kNN	$0.92\pm 0.01$	$0.91\pm 0.03$	$0.87\pm 0.09$	$0.87\pm 0.06$	$0.88\pm 0.05$
CNN	$0.93\pm 0.02$	$0.92\pm 0.03$	$0.88\pm 0.06$	$0.88\pm 0.05$	$0.89\pm 0.04$
LSTM	$0.94\pm 0.03$	$0.93\pm 0.04$	$0.89\pm 0.06$	$0.89\pm 0.07$	$0.90\pm 0.05$
ANFIS	$0.94\pm 0.03$	$0.94\pm 0.04$	$0.90\pm 0.05$	$0.90\pm 0.05$	$0.92\pm 0.04$
proposed	$0.97\pm 0.02$	$0.96\pm 0.03$	$0.92\pm 0.04$	$0.94\pm 0.05$	$0.95\pm 0.04$

Table 3.

Training analysis of root mean squared error

Dataset	20%	40%	60%	80%	90%
DT	$4.6\pm 0.54$	$4.6\pm 0.76$	$5.1\pm 0.44$	$4.5\pm 0.89$	$4.1\pm 0.66$
RF	$5.5\pm 0.82$	$4.3\pm 0.41$	$4.5\pm 0.69$	$4.0\pm 0.79$	$6.3\pm 0.65$
L1‐SVM	$5.0\pm 0.70$	$6.1\pm 0.55$	$4.4\pm 0.83$	$3.3\pm 0.46$	$3.6\pm 0.67$
L2‐SVM	$4.7\pm 0.54$	$4.8\pm 0.51$	$4.7\pm 0.78$	$4.3\pm 0.71$	$4.9\pm 0.88$
ANN	$3.2\pm 0.63$	$3.9\pm 0.88$	$3.7\pm 0.44$	$2.9\pm 0.73$	$5.8\pm 0.49$
kNN	$4.4\pm 0.77$	$4.1\pm 0.81$	$4.1\pm 0.62$	$6.8\pm 0.58$	$5.9\pm 0.64$
CNN	$6.0\pm 0.82$	$4.5\pm 0.68$	$4.3\pm 0.57$	$4.7\pm 0.87$	$5.2\pm 0.91$
LSTM	$3.3\pm 0.95$	$4.6\pm 0.86$	$5.0\pm 0.78$	$5.6\pm 0.69$	$4.5\pm 0.72$
ANFIS	$2.0\pm 0.45$	$3.7\pm 0.43$	$2.4\pm 0.39$	$2.2\pm 0.47$	$3.3\pm 0.49$
proposed	$1.7\pm 0.31$	$2.0\pm 0.39$	$1.1\pm 0.27$	$1.2\pm 0.29$	$2.2\pm 0.41$

4.3 Verification analysis

This section discusses the comparative analysis between the proposed and competitive machine learning models. We have initially divided data into two completely isolated parts depending upon the fraction (e.g. 50% for training and remaining 50% for testing). Thereafter, all the models are trained on the training dataset. All the trained models are then verified using the remaining 50% of testing dataset. Similarly, depending upon the fractions, every time, the training data and testing data have no similarity between them. The main objective is to compute the performance of the proposed model. Tables 4, 5–6 depict the performance analysis of the competitive and the proposed machine learning models. It is observed that the proposed model outperforms competitive models in terms of accuracy, coefficient of determination and root mean squared error, respectively.

Table 4.

Analysis of testing accuracy

Dataset	20%	40%	60%	80%	90%
DT	$91.3\pm 0.8$	$89.4\pm 0.9$	$90.5\pm 0.9$	$89.8\pm 0.6$	$88.1\pm 0.7$
RF	$92.6\pm 0.6$	$90.9\pm 0.8$	$91.9\pm 0.9$	$90.1\pm 0.5$	$89.8\pm 0.8$
L1‐SVM	$93.1\pm 0.8$	$90.6\pm 0.0$	$91.3\pm 0.6$	$91.7\pm 0.2$	$90.2\pm 0.9$
L2‐SVM	$93.1\pm 0.7$	$90.6\pm 0.7$	$91.3\pm 0.1$	$91.7\pm 0.9$	$90.2\pm 0.4$
ANN	$93.5\pm 0.8$	$93.9\pm 0.6$	$92.6\pm 0.6$	$95.9\pm 0.7$	$93.6\pm 0.8$
kNN	$94.2\pm 0.7$	$94.7\pm 0.6$	$93.4\pm 0.1$	$96.3\pm 0.8$	$94.3\pm 0.6$
CNN	$95.8\pm 0.7$	$96.7\pm 0.9$	$94.1\pm 0.7$	$98.3\pm 0.8$	$95.2\pm 0.8$
LSTM	$96.1\pm 0.9$	$97.1\pm 0.6$	$94.6\pm 0.8$	$98.5\pm 0.8$	$95.2\pm 0.0$
ANFIS	$96.9\pm 0.7$	$98.0\pm 0.8$	$96.1\pm 0.8$	$99.0\pm 0.7$	$97.4\pm 0.8$
proposed	$98.1\pm 0.8$	$98.4\pm 0.8$	$98.2\pm 0.9$	$99.1\pm 0.7$	$98.2\pm 0.6$

Table 5.

Analysis of coefficient of determination

Dataset	20%	40%	60%	80%	90%
DT	$0.81\pm 0.08$	$0.84\pm 0.07$	$0.82\pm 0.07$	$0.88\pm 0.07$	$0.90\pm 0.06$
RF	$0.81\pm 0.07$	$0.84\pm 0.06$	$0.82\pm 0.07$	$0.89\pm 0.06$	$0.90\pm 0.05$
L1‐SVM	$0.82\pm 0.08$	$0.85\pm 0.07$	$0.83\pm 0.06$	$0.89\pm 0.06$	$0.91\pm 0.05$
L2‐SVM	$0.83\pm 0.07$	$0.86\pm 0.08$	$0.84\pm 0.06$	$0.91\pm 0.05$	$0.92\pm 0.03$
ANN	$0.84\pm 0.09$	$0.87\pm 0.04$	$0.85\pm 0.11$	$0.92\pm 0.06$	$0.93\pm 0.04$
kNN	$0.85\pm 0.10$	$0.88\pm 0.09$	$0.86\pm 0.11$	$0.93\pm 0.05$	$0.94\pm 0.04$
CNN	$0.86\pm 0.11$	$0.90\pm 0.08$	$0.87\pm 0.10$	$0.94\pm 0.03$	$0.89\pm 0.08$
LSTM	$0.87\pm 0.11$	$0.91\pm 0.07$	$0.88\pm 0.10$	$0.91\pm 0.07$	$0.92\pm 0.06$
ANFIS	$0.89\pm 0.09$	$0.92\pm 0.06$	$0.90\pm 0.07$	$0.96\pm 0.03$	$0.98\pm 0.01$
proposed	$0.95\pm 0.04$	$0.96\pm 0.03$	$0.96\pm 0.02$	$0.98\pm 0.01$	$0.98\pm 0.71$

Table 6.

Analysis of root mean squared error

Dataset	20%	40%	60%	80%	90%
DT	$5.1\pm 0.63$	$5.4\pm 0.78$	$3.7\pm 0.47$	$3.0\pm 0.68$	$4.8\pm 0.74$
RF	$3.1\pm 0.49$	$3.7\pm 0.91$	$4.4\pm 0.96$	$3.8\pm 0.91$	$4.5\pm 0.87$
L1‐SVM	$5.6\pm 0.41$	$4.8\pm 0.37$	$3.3\pm 0.81$	$5.5\pm 0.76$	$5.1\pm 0.84$
L2‐SVM	$4.6\pm 0.47$	$3.3\pm 0.91$	$4.7\pm 0.74$	$6.3\pm 0.35$	$4.9\pm 0.76$
ANN	$4.4\pm 0.65$	$3.9\pm 0.61$	$3.8\pm 0.45$	$4.9\pm 0.47$	$5.0\pm 0.57$
kNN	$6.3\pm 0.39$	$6.5\pm 0.48$	$5.4\pm 0.51$	$3.5\pm 0.55$	$4.4\pm 0.41$
CNN	$4.0\pm 0.49$	$4.8\pm 0.45$	$4.1\pm 0.39$	$4.7\pm 0.38$	$4.6\pm 0.29$
LSTM	$5.3\pm 0.34$	$4.3\pm 0.29$	$4.1\pm 0.37$	$5.7\pm 0.26$	$4.8\pm 0.29$
ANFIS	$3.9\pm 0.23$	$2.9\pm 0.31$	$2.4\pm 0.29$	$2.5\pm 0.34$	$3.0\pm 0.27$
proposed	$2.5\pm 0.24$	$1.9\pm 0.27$	$1.6\pm 0.19$	$1.9\pm 0.28$	$2.6\pm 0.32$

5 Conclusions and perspectives

An integrated deep‐learning model has been proposed to predict the DDI score. The proposed model has integrated the RNNs, CNNs and MDNs. Extensive experiments have been conducted by considering a benchmark DDI dataset. Comparative analysis has been performed between the proposed and competitive machine learning models. It has been observed that the proposed model outperforms competitive models in terms of root mean square error, coefficient of determination and accuracy by 2.7352, 2.8202 and 3.4927, respectively. Therefore, the proposed model is applicable for real‐time applications.