Squeeze RNN with hybrid optimization: A novel approach for heart disease prediction using gene expression data

Abstract

Heart disease is a leading cause of death, imposing a considerable strain on individuals, families, and the healthcare system. Its onset is often linked to factors such as inadequate attention to diet, health, and lifestyle. Prompt diagnosis and early treatment are vital to enhancing patient survival and reducing mortality. In this work, a hybrid Deep Learning (DL) method named Squeeze Recurrent Neural Network with Political Deep Hunting Optimization (PDHO_SqueezeRNN) is proposed using gene expression data for detecting heart disease, where SqueezeRNN combines the SqueezeNet model and Recurrent Neural Network (RNN). At first, input data is forwarded to data transformation, which is achieved by Yeo Johnson transformation. Then, feature fusion is performed by Lorentzian metric and Deep Neural Network (DNN). Finally, heart disease is detected by the proposed PDHO_SqueezeRNN. By combining Political Optimizer (PO) and Deer Hunting Optimization (DHO), the PDHO algorithm is developed. Moreover, PDHO_SqueezeRNN achieved peak values of 95.20% for accuracy, 97.00% for sensitivity, and 95.90% for specificity, surpassing existing approaches.

Keywords

gene expression data heart disease detection deer hunting optimization political optimizer deep neural network

1. Introduction

Heart disease is also known as cardiac disease,¹ which is an acute disorder that requires suitable treatment and examination of the patient's information. The human brain can't evaluate an enormous amount of data, which is a noticeable support system for doctors working in the medical field, especially for heart disease.² The present world is experiencing a certain number of deaths, which are broadly caused by heart attacks or failure.³ Coronary Artery Disease (CAD) is an ischemic heart disease that causes angina. Until now, CAD is still a crucial disease, which is a threat to human life.^4–7 CAD has a greater risk than other diseases, like cancer and diabetes, which hold the record for more than 40% of deaths caused by heart disease.⁸ The number of patients with CAD reached 7.35 per million death rates internationally. CAD is caused by the accretion of plaque, which is composed of cholesterol, calcium, fatty deposits, and other substances in the blood, where these substances may create sclerosis and arterial stenosis.⁹ The oxygen-rich blood is prevented by arterial stenosis from reaching the heart, which leads to myocardial infarction and acute coronary syndrome.¹⁰ The severe stenosis may cause blood clots, which leads to abrupt cardiac arrest and abrupt hypoxia of the heart muscle.¹¹

Heart disease detection at the initial stage may essentially aid in preventing the failure.¹² Everyday practice by practitioners in the medical field creates prime databases, which may be evaluated to examine the supreme attributes for diagnosing the disease of heart.^3,13 The early prediction of failure reduces the death rate and also it may aid medical specialists in making suitable decisions for the patients. Thus, the investigation based on early detection is essential to detect the symptoms rapidly and may extend the life of patients. By enhancing computer technology, high throughput expression data may be removed.¹⁴ The measure of genomics from gene expression data provides rich details about the primary system of disease and thus detects the resultants of the disease. Based on expression data, immense work has been introduced for classifying the disease, detecting the medical results, and recognizing genes with strong therapeutic molecular signatures.¹⁵ In disease genes, the evaluation of gene expression levels indicates a reliable prototype in every disease.¹⁶ Due to the consequences of complex interactions, disease detection is essential to understand the system and discover the therapeutic targets.¹⁷

Recent research on Deep Learning (DL) in medical imaging enormously increased in the past years. DL is an essential strategy, wherein a greater number of hidden layers is employed to disclose the covert presence in the data.¹⁸ DL is also utilized to detect the diagnosis of other diseases.¹⁹ By employing Machine Learning (ML) schemes, practitioners in the medical field may obtain precious input about heart patients that enables them to provide suitable treatment to the patients.^2,20,21 With the endorsement of DL, an enormous number of investigators in the medical area endeavour to establish ML modules to aid the treatment of specific diseases.²² The ML model is employed for the real-world classification of heartbeat.²³ A deep genetic ensemble of classifiers has also been established to predict arrhythmia with electrocardiogram (ECG) signals.²⁴ Furthermore, the Convolutional Neural Network (CNN) module has been proven that it is an effective system employed in the evaluation of medical images and biomedical Nature language processing (NLP).¹⁴

The purpose of this work is to introduce a hybrid PDHO_SqueezeRNN. The Yeo-Johnson transformation is applied to the input data during the data transformation phase. Then, feature fusion is performed by Lorentzian metric and DNN. Heart disease detection is acquired by SqueezeRNN, which is trained by PDHO.

Proposed PDHO_SqueezeRNN for heart disease detection: A hybrid model named PDHO_SqueezeRNN is developed for detecting heart disease. Here, the hybrid network SqueezeRNN combines the SqueezeNet and RNN. The SqueezeRNN is trained using the PDHO module, which combines PO and DHO.

The following section of the work is organized as follows: Section 2 outlines the motivation and the existing work in the field. The devised PDHO_SqueezeRNN is defined along with the structural design in Section 3 and Section 4 elucidates the outcomes of the work. Finally, the developed method with upcoming work is explained in Section 5.

2. Motivation

The challenge of detecting heart disease using gene expression data has led researchers to create technologies built on this approach. So, for creating a new technology, this section elucidates the survey of previous strategies and reviews the benefits and limitations of existing methods.

2.1 Literature survey

Xiao, C., et al.¹¹ introduced a U-net Convolutional Neural Network (CNN). The result of this module was smooth, and it enhanced the efficacy while progressing the segmentation unit. In addition to that, it is applicable to utilize an enormous number of databases together with the presence and absence of a centerline. Ashraf, M., et al.² devised a Deep Neural Network (DNN) for creating an automated system for heart attack prediction. The DNN was employed for detecting heart disease and it effectually extracted the entire anomalies. However, this system failed to implement other DL modules to obtain extreme precision. Mehmood, A., et al.³ designed a method named Cardio Help, which predicts the probability of cardiovascular disease in a patient by incorporating a deep learning algorithm named CNN. This strategy focused on detecting the probability of heart disease by integrating the modern databases available at UCI Respiratory. It is alarmed with temporal data using CNN for predicting Heart Failure (HF) at an initial stage. Wang, Z., et al.¹⁴ presented Feature Re-arrangement based DL System (FRDLS). This method outperformed real-time data gathered from the Electronic Health Record (HER) system of Shanghai Shuguang Hospital. This module aids in promoting accurate detection.

Zhou, L., et al.¹⁵ designed a kernel partial least squares with the genetic algorithm (GA-KPLS) to detect patients with heart attack. It was a supreme model to enhance the prognosis of patients with various risk stages. Nevertheless, it failed to integrate multi-omics and clinical data for the enhancement of the final detection. Reddy, G.T., et al.²¹ devised Adaptive Genetic Algorithm with Fuzzy Logic (AGAFL). The system outperformed the preceding modules but it did not intend to examine other domains, like insurance, finance and so on. Zhao, X., et al.²⁵ developed DL for early risk prediction of heart disease. This module did not consider the issue of censoring and its sample should be retained like how to deal with the issue in the ML module. Nikdelfaz, O. and Jalili, S.,¹⁷ modelled a disease candidate genes prediction system, which comprises learning and prediction stages. This strategy failed to apply to other diseases. Even though, some other genomic information was not utilized to enhance this system like the PPI network. Torunn Melnes., et al.²⁶ developed gene expression profiles using the Nanostring Metabolic Pathways Panel (NMPP) in elderly event-free Familial Hypercholesterolemia (FH) patients for the detection of coronary heart disease. This method achieved potential persistent long-term effects in immune-related gene expression. However, this technique failed to evaluate specific genes as biomarkers for heart disease risk prediction in patients having FH. Vignesh Venkat., et al.²⁷ presented a new Findable, Accessible, Intelligent, and Reproducible (FAIR) approach using the Random Forest (RF) algorithm. This method achieved highly significant Heart Failure (HF), Atrial Fibrillation (AF) and other genes with demographic variables but failed to use a larger dataset to develop a robust model. Mengyi Sun and Linping Li²⁸ introduced Weighted Gene Co-expression Network Analysis (WGCNA) to identify biomarkers of Idiopathic Dilated Cardiomyopathy-induced heart failure (IDCM-HF) for predicting heart disease. This technique had specific diagnostic markers for the treatment of heart disease. However, it failed to recognize the roles of Extracellular Matrix (ECM) molecular pathways. Qinglan Ma., et al.²⁹ developed an ML technique for identifying marker genes for congenital heart disease of Different Cardiac Cell Types. This method achieved the ability to quantitatively and qualitatively identify specific gene biomarkers by providing a robust platform for exploring complex disease mechanisms but failed to decode the molecular complexity of congenital heart disease.

2.2 Challenges

The challenges faced while detecting heart disease by employing gene expression data are elaborated as follows,

In,¹¹ the dimension of the input image is not constrained in the devised module U-net CNN. However, it was not appropriate for elaborating medical images.

The DNN devised in² was surpassed in an enormous number of databases to recognize the true potential. Nevertheless, it attained minimal accuracy, which led to a problematic issue for this method.

In,¹⁴ the FRDLS approach was rapid and precise for heart disease detection and surpassed the unstable circumstances in medical information. Yet, this system did not execute multi-label, multi-class, and other detection activities.

Recently, heart disease prediction has been referred to as a complicated case in medical science. However, interpreting gene expression data is challenging when identifying genes to contribute to multi-genic disorders, such as atherosclerosis and cardiomyopathies.

3. Proposed squeeze fused recurrent neural network with political deep hunting optimization for heart disease detection

This work presents a PDHO_SqueezeRNN model by employing a hybrid DL technique for detecting heart disease. Here, SqueezeRNN is derived by combining the SqueezeNet model³⁰ and RNN,³¹ which is trained by PDHO, wherein the PDHO integrates DHO³² and PO.³³ Initially, the input gene expression data acquired from the database^34,35 is subjected to the data transformation unit to process the data by Yeo Johnson transformation. After that, the transformed data is allowed to the feature fusion stage, where feature fusion is performed using the Lorentzian metric and DNN.³⁶ Finally, the detection of heart disease is accomplished by implementing PDHO_SqueezeRNN. The block diagram of PDHO_SqueezeRNN for detecting heart disease is shown in Figure 1.

Figure 1.

Structure of PDHO_SqueezeRNN for heart disease detection.

3.1 Acquisition of data

Considering a typical source of data H with $^{'} n^{'}$ number of data that is represented by,

H = H_{1}, H_{2}, \dots . H_{m}, \dots H_{n}

(1)

Here,

H_{n}

is represented as the whole data and

m^{t h}

data is considered as the input gene expression data for the entire process that is illustrated by

H_{m}

3.2 Data transformation using Yeo Johnson transformation

Data transformation is adapting data from one format to another and it involves altering the values in the data to make it accurate, consistent, and suitable for the evaluation purpose. The input data $H_{m}$ is forwarded to data transformation to progress data by employing Yeo Johnson transformation. The data transformation output is represented as $T_{m}$ .

3.3 Feature fusion by Lorentzian and deep neural network

Feature fusion is a progression of merging more than one feature vector to acquire a single feature vector and it makes the resulting feature vector more effortlessly progressed than the exact feature vectors. The transformed data $T_{m}$ is passed to the feature fusion stage. This phase is performed by employing Lorentzian and DNN.

3.3.1 Feature fusion by Lorentzian

At first, arrange the features based on Lorentzian metrics with the DNN model, and the number of features to be selected for further process is formulated by,

F_{m} = \sum_{b = 1}^{K} \frac{λ}{h} F_{b}

(2)

Here,

F_{m}

implies fused feature,

F_{b}

refers feature.

where,

b = 1 + \frac{ℏ}{ƛ}, h = 1 to ƛ

(3)

Here,

ƛ

defines the ratio of total features to the number of features to be selected using

ƛ = \frac{ℏ}{K}

, where features to be selected are denoted by K and the total number of features is signified as

ℏ

3.3.2 Generating

λ

by employing DNN

In this module, $λ$ is generated by employing DNN architecture. In DNN, the dimension of the feature $100 \times 10$ is considered by training data. The feature is forwarded to the DNN for obtaining the target value. After that, training data is divided into classes as 0 and 1. The generation of $λ$ is illustrated in Figure 2. In this figure, $f_{1}, f_{2}, \dots . . f_{n}$ are specified as feature attributes, $t_{1}, t_{2}, \dots t_{n}$ are the average data and $F_{1}, F_{2}, \dots . . F_{n}$ are the values needed to generate $λ$ .

Figure 2.

Illustration of the $λ$ generation.

The value of $λ$ is computed by employing the following expression,

λ = K (t_{m}, ℵ)

(4)

Here, the average data belonging to the class is represented by

t_{m}

(a)

DNN architecture

A DNN³⁶ comprises input, output, and hidden layers. A neuron considers the vector, which computes a weighted sum to make the decision. The previous layer neurons are linked to neurons of subsequent layers in the fully connected neural network. The expression of the weighted sum is formulated by,

X^{ν} = E^{H} I^{ν - 1} + φ^{ν}

(5)

Here, the bias vector implies

φ

and activation map of the prior layer specifies

I^{ν - 1}

. In regards to escalating the convergence of the network, batch normalization is employed.

I^{ν} = ρ ({\tilde{M}}^{ν})

(6)

Here, the activation function is denoted as

ρ

. The rectified linear unit (ReLU) is used for the hidden layer as an activation function that is given as,

I^{ν} = R e L U ({\tilde{M}}^{ν}) = max (0, {\tilde{M}}^{ν})

(7)

ReLU neglects the vanishing gradient problem. The classification phase provides the possibility of the presence of various classes. The possibility of the dominant class provided by the softmax function is formulated by,

\hat{Υ} = \arg_{ψ} max {\frac{e^{Z_{ψ}^{O}}}{\sum_{ψ = 1}^{Ψ} e^{Z_{ψ}^{O}}}}

(8)

Here, the weighted sum of

ψ^{t h}

unit of the output layer is

Z_{ψ}^{O}

and neurons are deduced by approximately ∼2 to attain the deduction of dimension. In Figure 3, the illustration of DNN is formulated. The feature fusion output is specified as

F_{m}

Figure 3.

Structure of DNN.

3.4 Heart disease detection

The heart disease detection phase is achieved by employing the developed module PDHO_SqueezeRNN. Here, SqueezeRNN is achieved by the amalgamation of SqueezeNet and RNN as well as the PDHO is the amalgamation of PO and DHO.

3.4.1 Proposed PDHO_SqueezeRNN

This structural view explains the detection progression by employing the presented module PDHO_SqueezeRNN, which comprises three phases namely, SqueezeNet Model, SqueezeRNN model, and RNN model. In the SqueezeNet Model, input data $H_{m}$ is given to the SqueezeNet Model and the resultant $D_{m 1}$ and fused feature $F_{m}$ are forwarded to the second phase of SqueezeRNN, where the fusion and regression phases are carried out. The regression unit is utilized to authenticate the similarity of targeted and detected outcomes. In the third phase, the outcome of the SqueezeRNN $D_{m 2}$ is forwarded to the RNN model to attain the final detected output, which is indicated as $D_{m 3}$ . The three modules are briefly explained with their architecture and their expression in the following section. The structure of the SqueezeRNN is shown in Figure 4.

(a)
SqueezeNet module

Figure 4.
Schematic view of the SqueezeRNN.

In SqueezeNet,³⁰ 1D CNN is an alternative module of 2D CNN that considers 1D data as input. Generally, the hidden layer comprises of convolutional and pooling layer. The length L for 1D input data is indicated as $z \in ℜ^{L}$ , let $m = 1, 2, \dots . M$ with length $A$ , where $M$ indicates the convolutional kernels, a referred to as bias, then the resultant of $D_{m 1} \in ℜ^{A}$ with length $A$ is known as feature map with $M$ channels, which is computed as,
$D_{m 1} = α (s^{m} * H_{m} + a)$
(9)
Here, the activation function is denoted as $α$ and the convolution operation is specified as $$ . In this module, ReLU is considered as an activation function that refers $m (z) = max (0, z)$ . This function allows the network to acquire sparse illustrations in a simple manner that broadly arises up the training course. The length $A$ of the outcome is decided based on input beneath the convolution. If there is no padding, it is formulated as,
$A = c e i l (\frac{L - B + 1}{O})$
(10)
Here, the ceil function is indicated as $c e i l ()$ . If $B + 1$ is zero then,
$A = c e i l (\frac{L}{O})$
(11)
Apart from ReLU, the residual connection is also employed to bridge the issue of complexity, when the depth becomes deeper the network may suffer from the degradation issue and it may fail to acquire the supreme module with extreme complexity. This method is devised based on hypothesis. Normally, the number of residual units is 2 or 3 in the residual block. The input to $c^{t h}$ block is denoted as $z_{c}$ , from any block c to $c^{t h}$ block, the forward propagation is computed by,
$z_{C} = z_{c} + \sum_{e = 1}^{C - 1} M (z_{e}, V_{e})$
(12)
The expression above describes that residual connection is not only present in the single block but also present in between C and c, which is stated as,
$\frac{\partial β}{\partial z_{c}} = \frac{\partial β}{\partial z_{C}} \frac{\partial z_{C}}{\partial z_{c}} = \frac{\partial β}{\partial z_{C}} (1 + \frac{\partial}{\partial z_{C}} \sum_{e = 1}^{C - 1} M (z_{e}, V_{e}))$
(13)
The term $\frac{\partial}{\partial z_{C}} \sum_{e = 1}^{C - 1} M (z_{e}, V_{e})$ will not be always −1 for whole samples in mini-labels; the structure of residual alleviates the network's gradient-based learning.

To merge the channels to observe the coupling features, the residual network is adapted by altering the kernel of the first layer of convolution's second block into the squeeze kernel. Normally, the preceding layer of squeeze operation comprises feature maps and signal channels with the length of the signal. The resultant of this operation I is computed as,
$I = \sum_{m_{1} = 1}^{M_{1}} \sum_{e = 1}^{c} s_{e}^{m_{2}} z_{e}^{m_{1}}$
(14)
This can be interpreted as a weighted integration of feature maps from various channels. By deducing the loss in the training process, the finest integration of weight is accomplished. The structural design of SqueezeNet is shown in Figure 5. (b)
SqueezeRNN module

Figure 5.
The architecture of the squeezeNet model.

SqueezeRNN is designed by combining SqueezeNet and RNN. The outcome of the SqueezeNet module $D_{m 1}$ is forwarded to the hybrid module SqueezeRNN. Here, the fused feature vector $F_{m}$ is fed to the regression phase to determine the similarity of the targeted output. The arithmetic expression of the SqueezeRNN layer is illustrated below.
$Z = \sum_{o = 1}^{x} F_{m (o)} M_{o}$
(15)
Here, Z is indicated as the outcome from $d^{t h}$ interval.

By applying the fractional concept, the SqueezeRNN is formulated as,
$\begin{matrix} w (d + 1) = k Z + \frac{1}{2} D_{m 1} \end{matrix}$
(16)

$\begin{matrix} D_{m 2} = k * \sum_{o = 1}^{x} F_{m (o)} * M_{o} + D_{m 1} * M_{o} \end{matrix}$
(17)
Substitute equation (9) in equation (17), then the expression becomes,
$D_{m 2} = k * \sum_{o = 1}^{x} F_{m (o)} * M_{o} + α (s^{m} * H_{m} + a) * M_{o}$
(18)
Here, the constant is signified as k, $D_{m 2}$ refers SqueezeRNN layer's output, $M_{o}$ indicates weight. (c)
RNN model
RNN³¹ is an artificial neural network, which may progress the sequential data. It has a memory that saves the details from the preceding inputs and influences the present outcome. Here, in this module, the resultant of SqueezeRNN $D_{m 2}$ is then forwarded to the RNN module to obtain the detected output. (i)
Evaluate hidden state vector: The evaluation of reset gate, activation of forget gate, candidate and current hidden state is included in this stage. The expressions of these phases are as follows:
$q^{(1)} = ω [J_{q}^{(1)} y_{} + R_{q}^{(1)} g_{}^{(1)} + B_{q}^{(1)}]$
(19)
Equation (18) is reset gate expression together with weight matrices $J_{q}^{(1)}$ and $R_{q}^{(1)}$ , the bias vector is implied as $B_{q}^{(1)}$ , the hard sigmoid function is symbolized as $ω [\dots]$ . The initial state of the hidden layer is assumed as the null matrix that is $g_{< 01 >}^{(1)}$ .
$u^{(1)} = ω [J_{u}^{(1)} y_{} + R_{u}^{(1)} g_{}^{(1)} + B_{u}^{(1)}]$
(20)
Here, u is indicated as the forget gate, which is close to the reset gate.
${\tilde{g}}^{(1)} = \tan g [{\tilde{J}}^{(1)} y_{} + {\tilde{R}}^{(1)} (q^{(1)} \circ g_{}^{(1)}) + {\tilde{B}}^{(1)}]$
(21)
Here, the candidate's hidden state is signified as ${\tilde{g}}^{(1)}$ and Hadamard product symbolizes °. The parameters are all stored in the weighted matrices.
$g_{}^{(1)} = u^{(1)} \circ g_{}^{(1)} + (1 - u^{(1)}) {\tilde{g}}^{(1)}$
(22)
Here, the current hidden state is indicated by $g_{}^{(1)}$ . (ii)
Evaluation of hidden state variables: This stage is employed to examine the variables for subsequent Grated recurrent unit (GRU) with the aforementioned phases.
$\begin{matrix} q^{(j)} = ω [J_{q}^{(j)} y_{}^{(j - 1)} + R_{q}^{(j)} g_{}^{(j)} + B_{q}^{(j)}] \end{matrix}$
(23)

$\begin{matrix} u^{(j)} = ω [J_{u}^{(j)} y_{}^{(j)} + R_{u}^{(j 1)} g_{}^{(j - 1)} + B_{u}^{(j)}] \end{matrix}$
(24)

$\begin{matrix} {\tilde{g}}^{(j)} = \tan g [{\tilde{J}}^{(j)} y_{}^{(j - 1)} + {\tilde{R}}^{(j)} (q^{(j)} \circ g_{}^{(j)}) + {\tilde{B}}^{(j)}] \end{matrix}$
(25)

$\begin{matrix} g_{}^{(j)} = u^{(j)} \circ g_{}^{(j)} + (1 - u^{(j)}) {\tilde{g}}^{(j)} \end{matrix}$
(26)
(iii)
Evaluation of the first hidden layer of fully connected CNN: The hidden layer is expressed as,
$g^{U_{G R U} + 1} = \tan g [J^{U_{G R U} + 1} g_{p}^{U_{G R U}} + B^{U_{G R U} + 1}]$
(27)
Here, $J^{U_{G R U} + 1}$ illustrated as the weight matrix and $B^{U_{G R U} + 1}$ implies the dimensional bias vector. (iv)
Evaluation of subsequent hidden layers: The analysis of the subsequent layer is formulated by,
$g^{(j)} = \tan g [J^{(j)} g^{(j - 1)} + B^{(j)}]$
(28)
(v)
Evaluation of the resultant of the RNN module: The expression of the RNN module is computed by,
$D_{m 3} = J^{(U_{G R U} + U_{H L} + 1)} * {D_{m 2}}^{(U_{G R U} + U_{H L})} + B^{(U_{G R U} + U_{H L} + 1)}$
(29)
Substitute equation (18) in equation (29), then the expression is determined as,
$D_{m 3} = J^{(U_{G R U} + U_{H L} + 1)} * {[k * \sum_{o = 1}^{x} F_{m (o)} * M_{o} + α (s^{m} * H_{m} + a) * M_{o}]}^{(U_{G R U} + U_{H L})} + B^{(U_{G R U} + U_{H L} + 1)}$
(30)
Here, the weight matrix is signified as J, the bias vector is implied as B, the hyperparameter of GRU and the hidden layer is symbolized as $U_{G R U}$ and $U_{H L}$ . The output of RNN is represented as $D_{m 3}$ and architectural view of RNN is shown in Figure 6.

Figure 6.
Architectural view of RNN.
3.4.2 Training algorithm of PDHO_SqueezeRNN

The DHO³² module is the meta-heuristic scheme. Here, the hunters use a few techniques to capture the deer with a greater number of parameters, like position and wind angle. This type of behavior is integrated with the PO³³ technique to develop the proposed model PDHO, which is used to train the hybrid network SqueezeRNN. The training progression of this technique is elucidated as follows:

(a)
Solution Encoding
The solution encoding is used to optimize the solution given in search space $(χ)$ and outcomes are denoted as,
$χ = [1 \times δ]$
(31)
Here, the SqueezeRNN factor is $δ$ . (b)
Fitness measure
It analyzes the finest solution by the difference between the targeted outcome and the resultant of SqueezeRNN, which is computed by,
$G = \frac{1}{n} \sum_{m = 1}^{n} {[τ_{m} - D_{m 3}]}^{2}$
(32)
where, n implies the number of data samples, fitness value is indicated as G, $τ_{m}$ is the target output, and $D_{m 1}$ is the result of SqueezeRNN. (c)
Algorithmic steps
This section explains the algorithmic steps of PDHO_SqueezeRNN.

Step 1: Initialization

At first, initialization is performed by the population initialization of hunter, which is represented as,
$W = W_{1}, W_{2}, \dots \dots, W_{ϖ}; 1 < κ \leq ϖ$
(33)
Here, the entire count of hunters is denoted as $ϖ$ in the population W.

Step 2: Examine fitness

To examine the solution, fitness measure is utilized, which furnishes a high rate of prediction in predicting heart disease by employing equation (32).

Step 3: Initialization of parameters

The deer's angle and position are significant functions to recognize the fine locations of the hunters. The wind angle, circle, and circumference are considered as search space that is formulated as,
$ε_{r} = 2 π h$
(34)
where, h is signified as a random number and r is indicated as an existing iteration. The position angle is determined by,
$η_{t} = θ + π$
(35)
where, $θ$ is represented as the angle of wind.

Step 4: Upgrade the new location

At first, the candidate solution is considered by algorithm when the finest space location is unknown that examines the fitness factor as the best solution by assuming a position that is similar to the position of leader $W^{l e a d}$ and the position of successor $W^{s u c}$ . (i)
Propagation in terms of the position of leader
If an extreme location is evaluated, every individual aims to acquire the finest location and thus it begins the analysis of location update. Thus, the encompassing behavior is illustrated by,
$W_{r + 1} = W^{l e a d} - S . μ . | E \times W^{l e a d} - W_{r} |$
(36)
Here, the present iteration of the position is $W_{r}$ , and $W_{r + 1}$ is the next iteration. S and E are the coefficient vectors and $μ$ implies random numbers between wind speed from 0 to 2.

Considering $W^{l e a d} > W_{r}$ ,
$\begin{matrix} W_{r + 1} = W^{l e a d} - S . μ | E \times W^{l e a d} - W_{r} | \end{matrix}$
(37)

$\begin{matrix} W_{r + 1} = W^{l e a d} (1 - S . μ . E) + S . μ . W_{r} \end{matrix}$
(38)
The expression from PO is integrated with DHO to enhance the proposed module, which is represented by,
$\begin{matrix} W_{r + 1} = ℓ^{} + N (ℓ^{} - W_{r}) \end{matrix}$
(39)

$\begin{matrix} ℓ^{} = \frac{W_{t r 1} + N W_{r}}{1 + N} \end{matrix}$
(40)
Here, $ℓ^{}$ implies the leader position mentioned in equation (40); thus, it can be applied by substituting in equation (38),
$W_{r + 1} = \frac{W_{r + 1} + N {W_{r}}_{t}}{1 + N} (1 - S . μ . E) + S . μ . W_{r}$
(41)
where, $W_{r}$ is the position at the current iteration, $W_{r + 1}$ is the position at the next iteration, S and E are coefficient vectors, and $μ$ is a random number calculated based on the speed of the wind, where the values range from 0 to 2.

Therefore, the final update solution is represented as,
$W_{r + 1} = \frac{1 + N}{N + S . μ . E} [\frac{N}{1 + N} W_{r} (1 - S . μ . E) + S . μ . W_{r}]$
(42)
where, N lies in the range of 0 and 1. The coefficient vector is calculated by,
$\begin{matrix} S = \frac{1}{4} \log (r + \frac{1}{r_{max}}) P \end{matrix}$
(43)

$\begin{matrix} E = 2. I \end{matrix}$
(44)
Here, the maximum iteration is $r_{max}$ , the parameter is implied as P in the interval of −1 and 1, I is a random value in the range of 0 and 1. (ii)
Propagation in terms of the angle of position
For search space enhancement, the angle in the rule of update solution is considered to enlarge the belief. The computation of angle examines the location of the hunter, which is expressed as,
$Q_{r} = \frac{π}{8} \times h$
(45)
According to the variance between visual prey and wide angle, the upgraded position angle is stated as,
$X_{r} = ε_{r} - Q_{r}$
(46)
The position angle is expressed as,
$η_{r + 1} = η_{r} + X_{r}$
(47)
The update position is calculated by,
$W_{r + 1} = W^{l e a d} - μ . | C o s (γ) \times W^{l e a d} - W_{r} |$
(48)
where, $μ$ is the random number and $W^{l e a d}$ is the leader position. (iii)
Propagation in the course of successor
The rate of the vector E is below 1. Hence, upgrading the location following the position acquired the finest initial solution.
$W_{r + 1} = W^{s u c} - S . μ . | E \times W^{s u c} - W_{r} |$
(49)
where, $W^{s u c}$ is the successor position of search agent from the current population.

Step 5: Termination

The progression of this presented module continues unless the best solution is acquired.

Algorithm 1 illustrates the pseudo-code of PDHO.

4. Results and discussions

The PDHO_SqueezeRNN experimental outcomes are calculated and comparative discussions are analyzed with prevailing methods in the section.

4.1 Experimental setup

For implementing the PDHO_SqueezeRNN technique, the PYTHON tool is used in Windows 10 OS.

4.2 Dataset description

The global gene expression for the coronary artery disease database and the Merging heart disease database are taken to perform the assessments.

4.2.1 Global gene expression for coronary artery disease database

This database³⁴ contains a number of 394 differentially expressed genes, where 331 genes were found to be up-regulated and 63 genes were found to be down-regulated. From the North Indian population, 12 non-diabetic patients with CAD were selected for the prediction of heart disease from the dataset.

4.2.2 Merging heart disease database

In this dataset,³⁵ the data were collected using the Affymetrix Human Genome U133 Plus 2.0 array (GPL96) and the Affymetrix Human Genome U95 Version 2 array (GPL8300). Various heart diseases included in this dataset are Chronic and Congestive heart failure, Coronary and Acute ischemic heart disease, cardiovascular disease, and so on.

4.3 Data visualization

The data visualization in Figure 7 combines the global gene expression and heart disease datasets, with feature values depicted in various colors. The orange color represents normal feature values, whereas the green color represents abnormal feature values. Here, Figure 7(a) illustrates various feature values based on gene samples given in the global gene expression dataset. In this graph, GSM2601293 and GSM2601294 have equal normal feature values between 100,000 and 120,000 when compared with the other features. Similarly, GSM2601300 and GSM2601306 have abnormal feature values of 140,000. Figure 8(b) represents several feature values based on gene samples given in the merging heart disease dataset. The features, such as GPL6244.29, GPL6244.79, GPL570.18, GPL570.162, GPL11532.37, GPL11532.76, GPL11532.101, GPL11532.160 and GPL11532.179 represents abnormal patients, whereas GPL96.26, GPL570.7, GPL570.8, GPL570.87, GPL570.204, GPL11532.11, GPL11532.16, GPL11532.280 represents normal patients.

Figure 7.

Data visualization for heart disease detection, (a) feature value graph of global gene expression dataset, (b) feature value graph of merging heart disease dataset.

Figure 8.

Evaluation of PDHO_SqueezeRNN based on global gene expression altering training data (a) accuracy, (b) sensitivity and (c) specificity.

4.4 Performance measures

The PDHO_SqueezeRNN utilizes performance measures, like sensitivity, accuracy, and specificity.

4.4.1 Accuracy

It is defined as the degree of closeness among the measurement and original value that is computed as,

a c c = \frac{T_{n} + T_{p}}{T_{n} + T_{p} + O_{n} + O_{p}}

(49)

4.4.2 Sensitivity

It is referred to as the possibility of a test to exactly recognize the patients with a disease, which is computed by,

s e n = \frac{T_{p}}{T_{p} + O_{n}}

(50)

where,

T_{p}

indicates true positive and

O_{n}

represents false negative.

4.4.3 Specificity

It is defined as the possibility, that a disease-free individual will examine as negative, which is formulated by,

s p e c = \frac{T_{n}}{T_{n} + O_{p}}

(51)

Here, true negative is represented by

T_{n}

and false positive is specified by

O_{p}

4.5 Comparative analysis

In this section, the PDHO_SqueezeRNN comparison using Global gene expression and Merging heart disease with the alteration of training data and K-fold is deliberated. The conventional modules employed for the analysis are U-net CNN,¹¹ DNN,² Deep CNN,³ FRDLS,¹⁴ and PDHO-based Deep Q-network.

4.5.1 Analysis of PDHO_SqueezeRNN based on global gene expression

The assessment of PDHO_SqueezeRNN based on Global gene expression with the conventional schemes by altering training data and k-fold is elaborated in this section.

(a)
Evaluation of PDHO_SqueezeRNN by altering training data
In Figure 8, the evaluation of PDHO_SqueezeRNN by altering training data is designed. Figure 9(a) exploits the PDHO_SqueezeRNN with accuracy. When training data is 90%, the PDHO_SqueezeRNN gained an accuracy of 0.940. Here, the proposed method has the performance enhancement of 19.924% than U-net CNN, 12.650% than DNN, 13.762% than Deep CNN, 9.861% than FRDLS, and 3.942% than PDHO-based Deep Q-network. In Figure 8(b), the sensitivity of PDHO_SqueezeRNN is illustrated. With 90% of the training data, the PDHO_SqueezeRNN gained a sensitivity of 0.961. Here, the performance of the proposed method is 19.098%, 16.723%, 13.564%, 8.487%, and 2.459% higher than the performance of the existing methods. Figure 8(c) depicts the PDHO_SqueezeRNN in regards to specificity. If training data is assumed as 90%, then the specificity of PDHO_SqueezeRNN is 0.948. The performance gains while comparing existing schemes are 17.748%, 8.747%, 9.619%, 7.358%, and 6.261%. (b)
Evaluation of PDHO_SqueezeRNN altering k-fold
In Figure 9, analysis of PDHO_SqueezeRNN based on Global gene expression by altering k-fold is designed. Figure 9(a) enumerates PDHO_SqueezeRNN in terms of accuracy. With 9 as k-fold, PDHO_SqueezeRNN obtained an accuracy of 0.951. This represents a performance enhancement of 16.251% over U-net CNN, 14.729% over DNN, 10.104% over Deep CNN, 4.882% over FRDLS, and 2.711% over the PDHO-based Deep Q-network. In Figure 9(b), the sensitivity of PDHO_SqueezeRNN is illustrated. The PDHO_SqueezeRNN achieved a sensitivity of 0.969, showing a performance improvement of 17.338%, 13.975%, 10.730%, 4.494%, and 3.210% over prior models when evaluated with a 9-fold cross-validation. Figure 9(c) depicts PDHO-_SqueezeRNN in regards to specificity. With k-fold set to 9, the PDHO_SqueezeRNN model attained a specificity of 0.958, marking improvements of 17.493%, 14.172%, 10.675%, 5.735%, and 3.427% over traditional approaches.

Figure 9.
Evaluation of PDHO_SqueezeRNN based on global gene expression altering k-fold (a) accuracy, (b) sensitivity and (c) specificity.
4.5.2 Analysis of PDHO_SqueezeRNN based on merging heart disease

The evaluation of PDHO_SqueezeRNN using Merging heart disease is compared with the preceding modules by varying training data and k-fold is elucidated in this section.

(a)
Assessment of PDHO_SqueezeRNN altering training data
The assessment of PDHO_SqueezeRNN based on Merging heart disease is depicted in Figure 10. In Figure 10(a), the PDHO_SqueezeRNN with respect to accuracy is represented. When the training data is 90%, PDHO-_SqueezeRNN achieved an accuracy of 0.942, which shows a performance gain of 16.972%, 15.911%, 9.552%, 6.358% and 3.714% over other techniques. Figure 10(b) designs PDHO_SqueezeRNN on the basis of sensitivity. For 90% of training data, PDHO_SqueezeRNN gained a sensitivity of 0.963, showing a performance improvement of 18.761%, 17.723%, 14.214%, 8.376% and 4.767% over conventional models. The evaluation of PDHO_SqueezeRNN in regards of specificity is exploited in Figure 10(c). The PDHO_SqueezeRNN attained specificity as 0.947 when the training data = 90%, which demonstrates a performance increase of 17.396% over U-net CNN, 15.087% over DNN, 13.299% over Deep CNN, 8.161% over FRDLS, and 4.506% over PDHO-based Deep Q-network. (b)
Assessment of PDHO_SqueezeRNN altering k-fold

Figure 10.
Evaluation of PDHO_SqueezeRNN based on merging heart disease altering training data (a) accuracy, (b) sensitivity and (c) specificity.

In Figure 11, the valuation of PDHO_SqueezeRNN based on Merging heart disease altering k-fold is described. The accuracy of the PDHO_SqueezeRNN is shown in Figure 11(a). With 9 as k-fold, the PDHO-_SqueezeRNN gained an accuracy of 0.952, showing a performance improvement of 16.845%, 14.243%, 13.330%, 8.339%, and 4.426% over conventional models. Figure 11(b) enumerates the sensitivity of PDHO_SqueezeRNN. Using a 9-fold cross-validation approach, the PDHO_SqueezeRNN recorded an accuracy of 0.970, with performance improvements of 16.993%, 15.698%, 11.570%, 8.877%, and 6.672% compared to previous techniques. In Figure 11(c), the PDHO_SqueezeRNN with respect to specificity is illustrated. If the k-fold is 9, the specificity of PDHO_SqueezeRNN is 0.959, which shows a performance gain of 19.419% over U-net CNN, 16.085% over DNN, 12.641% over Deep CNN, 9.333% over FRDLS, and 6.928% over PDHO-based Deep Q-network.

Figure 11.
Evaluation of PDHO_SqueezeRNN based on merging heart disease altering k-fold (a) accuracy, (b) sensitivity and (c) specificity.
4.6 ROC analysis

The PDHO_SqueezeRNN comparison by global gene expression and merging heart disease datasets for heart disease detection is done using ROC analysis and is shown in Figure 12. In Figure 12(a), PDHO_SqueezeRNN based on global gene expression dataset, obtained TPR of 0.887 for 0.6 FPR, whereas other existing methods obtained TPR of 0.694, 0.741, 0.791, 0.817 and 0.831 for FPR of 0.6. The PDHO_SqueezeRNN achieved a maximum performance of 21.75% than U-net CNN technique utilized for heart disease detection. Similarly, in Figure 12(b), the TPR obtained by PDHO_SqueezeRNN for 0.2 FPR is 0.832, whereas existing techniques obtained TPR of 0.641, 0.687, 0.726, 0.754 and 0.792. The proposed model obtained a maximum performance of 12.74% than Deep CNN technique used for the detection of heart disease.

Figure 12.

Estimation of PDHO_SqueezeRNN using ROC analysis (a) global gene expression dataset (b) merging heart disease dataset.

4.7 Comparative discussion

Table 1 specifies the comparative discussion of PDHO_SqueezeRNN. From the below discussion, it is proved that PDHO_SqueezeRNN has outperformed other designed heart disease prediction models. In the global gene expression dataset, the proposed PDHO_SqueezeRNN model achieved a maximum accuracy of 94.00%, while the accuracy of U-Net CNN is 75.30%, DNN is 82.10%, Deep CNN is 81.10%, FRDLS is 84.80%, and the PDHO-based Deep Q-network is 90.30% for 90% of the training data. Similarly in k-fold, the specificity obtained by the existing technique is 79.00%, 82.20%, 85.60%, 90.30%, and 92.50%. On the other hand, the proposed model has a specificity value of 95.80%. In the Merging heart disease dataset, PDHO_SqueezeRNN obtained a maximum sensitivity of 97.00% in the K-fold analysis, while the other techniques have sensitivity values of 80.50%, 81.70%, 85.70%, 88.30% and 90.50%. Likewise, the proposed method obtained the maximum accuracy of 94.20% for 90% of the training data, whereas the accuracy of the existing methods, such as U-Net CNN is 78.20%, DNN is 79.20%, Deep CNN is 85.20%, FRDLS is 88.20%, and PDHO-based Deep Q-network is 90.70%.

Table 1.
Comparative discussion.

Metrics U-net Deep PDHO-based Proposed PDHO-

Database /Methods CNN DNN CNN FRDLS Deep Q-network _SqueezeRNN

Global gene expression Training data Accuracy 75.30% 82.10% 81.10% 84.80% 90.30% 94.00%

Sensitivity 77.70% 80.00% 83.10% 87.90% 93.70% 96.10%

Specificity 77.90% 86.50% 85.70% 87.80% 88.80% 94.80%

k-fold Accuracy 79.60% 81.10% 85.50% 90.40% 92.50% 95.10%

Sensitivity 80.10% 83.30% 86.50% 92.50% 93.80% 96.90%

Specificity 79.00% 82.20% 85.60% 90.30% 92.50% 95.80%

Merging heart disease Training data Accuracy 78.20% 79.20% 85.20% 88.20% 90.70% 94.20%

Sensitivity 78.20% 79.20% 82.60% 88.20% 91.70% 96.30%

Specificity 78.20% 80.40% 82.10% 87.00% 90.50% 94.70%

k-fold Accuracy 79.10% 81.60% 82.50% 87.20% 91.00% 95.20%

Sensitivity 80.50% 81.70% 85.70% 88.30% 90.50% 97.00%

Specificity 77.30% 80.50% 83.80% 86.90% 89.20% 95.90%

	Metrics	U-net		Deep		PDHO-based	Proposed PDHO-
Global gene expression	Training data	Accuracy	75.30%	82.10%	81.10%	84.80%	90.30%	94.00%
Sensitivity	77.70%	80.00%	83.10%	87.90%	93.70%	96.10%
Specificity	77.90%	86.50%	85.70%	87.80%	88.80%	94.80%
k-fold	Accuracy	79.60%	81.10%	85.50%	90.40%	92.50%	95.10%
Sensitivity	80.10%	83.30%	86.50%	92.50%	93.80%	96.90%
Specificity	79.00%	82.20%	85.60%	90.30%	92.50%	95.80%
Merging heart disease	Training data	Accuracy	78.20%	79.20%	85.20%	88.20%	90.70%	94.20%
Sensitivity	78.20%	79.20%	82.60%	88.20%	91.70%	96.30%
Specificity	78.20%	80.40%	82.10%	87.00%	90.50%	94.70%
k-fold	Accuracy	79.10%	81.60%	82.50%	87.20%	91.00%	95.20%
Sensitivity	80.50%	81.70%	85.70%	88.30%	90.50%	97.00%
Specificity	77.30%	80.50%	83.80%	86.90%	89.20%	95.90%

5. Conclusion

Heart disease is considered a crucial health challenge that impacts millions of lives per year. Early and accurate prediction of heart disease can significantly reduce these numbers by enabling timely intervention and management. Accordingly, a novel technique, named PDHO_SqueezeRNN is proposed for detecting heart disease. Here, the input is forwarded from the database to the data transformation phase to process the data by Yeo Johnson transformation. Then, the transformed data is fed to the feature fusion stage that is performed by Lorentzian metrics and DNN. At last, the detection of heart disease is performed by employing SqueezeRNN, which integrates the SqueezeNet model and RNN. Moreover, SqueezeRNN is trained by the PDHO, which is the integration of DHO and PO. The developed PDHO_SqueezeRNN technique overcame the designed models and attained superior results with the performance metrics that include accuracy, sensitivity, and specificity with supreme values of 95.20%, 97.00%, and 95.90% in K-fold analysis. In the future, the proposed module will be extended to analyze additional diagnostic datasets, such as those for cancer and brain disorders, to evaluate its accuracy.

Footnotes

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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		Metrics	U-net		Deep		PDHO-based	Proposed PDHO-
Database		/Methods	CNN	DNN	CNN	FRDLS	Deep Q-network	_SqueezeRNN
Global gene expression	Training data	Accuracy	75.30%	82.10%	81.10%	84.80%	90.30%	94.00%
		Sensitivity	77.70%	80.00%	83.10%	87.90%	93.70%	96.10%
		Specificity	77.90%	86.50%	85.70%	87.80%	88.80%	94.80%
	k-fold	Accuracy	79.60%	81.10%	85.50%	90.40%	92.50%	95.10%
		Sensitivity	80.10%	83.30%	86.50%	92.50%	93.80%	96.90%
		Specificity	79.00%	82.20%	85.60%	90.30%	92.50%	95.80%
Merging heart disease	Training data	Accuracy	78.20%	79.20%	85.20%	88.20%	90.70%	94.20%
		Sensitivity	78.20%	79.20%	82.60%	88.20%	91.70%	96.30%
		Specificity	78.20%	80.40%	82.10%	87.00%	90.50%	94.70%
	k-fold	Accuracy	79.10%	81.60%	82.50%	87.20%	91.00%	95.20%
		Sensitivity	80.50%	81.70%	85.70%	88.30%	90.50%	97.00%
		Specificity	77.30%	80.50%	83.80%	86.90%	89.20%	95.90%