Optimization Based Approach for Heart Disease Classification

2.1 Dataset

The University of California, Irvine (UCI) provided the Cleveland dataset (UCI, 1990), which comprises four separate datasets related to heart disease, for this investigation. Six of the 303 patient data instances in it contain missing values. There are six cases of missing items in the Cleveland Heart Disease dataset. The presence (num = 1 or 2 or 3 or 4) and absence (num = 0) of the heart illness were the two classifications into which the diagnosis characteristic (num) for heart disease was divided. Class distributions showed that 54% of participants did not have heart disease, and 46% did [8]. Table 2 illustrates Cleveland dataset.

Table 2. Cleveland heart disease dataset [8]

There are 14 characteristics and 270 samples in the Statlog dataset (Table 3) [9]. These characteristics are comparable to Cleveland's. The dataset has no missing values, and 150 samples are part of groups 0 (healthy patients) and 1 (disease patients).  

Table 3. Statlog heart disease dataset [9]

2.2 Boruta algorithm

The RF classification approach is the foundation of the Boruta algorithm. Random Forest uses a Z-score to determine the important scores. The Z-score must be revised to determine a feature's importance appropriately. In addition, we require additional criteria to distinguish between significant aspects and those that do not concern the dependent variable. The Boruta algorithm is required in this situation. It makes an effort to compile every intriguing and relevant aspect. The following stages are how it operates [10, 11]:

•Initially, it generates shadow features, sometimes called permuted copies, duplicates of the original features with randomly fixed values. The dataset now includes these features.

•After that, all of these characteristics are used to train the model. The importance of each feature is then determined by computing the feature importance measure, also known as mean decrease accuracy. The greater its worth, the greater its significance.

•The value of the Z-score is assessed. It determines if a true characteristic is more essential than the best of its shadow features at every iteration. Whether a feature's Z-score exceeds the highest Z-score of its shadow features determines this. The dataset's irrelevant characteristics are eliminated, which lowers the model's performance.

•As such, the elements that remain are rejected and significant. The set number of random forest runs can be increased if any remaining questionable features exist.

2.3 Binary Harris hawks optimizer

HHO is a cutting-edge optimizer miming the movements and responses of a hawk and rabbit's hunting process. As demonstrated in the HHO original work, this optimizer's fundamental mathematical underpinnings enable it to effectively handle various restricted and unconstrained situations [12].

The primary method used by Harris hawks to pursue prey is the "surprise pounce," sometimes referred to as the "seven kills" approach. This is a cunning approach where some hawks shift to attack from different angles while simultaneously focusing on one animal that is thought to be running away from the covering. This attack can be finished swiftly by stopping the stunned target in seconds, but the "seven kills" might consist of many fast rushes near the target over minutes, depending on the target's ability to flee [13].

2.3.1 Exploration-phase

During this stage, two techniques are used to update the Hawks search agents, with each strategy having an equal chance of being chosen. In HHO, agents perch in random locations (tall trees) or about the positions of the prey and other close individuals. Eq. (1) provides a mathematical formulation of these tactics [13-15].

$\begin{array}{cc}A(t+1)= \left\{\begin{array}{l}A_{r n d}(t)-r d_1\left|A_{r n d}(t)-r d_2 A(t)\right| & p \geq 0.5 \\ \left(A_{h t d}(t)-A_{\text {avg }}(t)\right)-r d_3\left(L_{b n d}+r d_4\left(U_{b n d}-L_{b n d}\right)\right) & p<0.5\end{array}\right.\end{array}$              (1)

where A(t+1) presents the vector of hawk position in iteration t, A(t) indicates the vector position of hawk, $A_{h t d}(t)$ is the location of hunted rabbit. p, rd1, rd2, rd3, and rd4 are random numbers in range (0,1). $L_{b n d}$ and $U_{b n d}$ are lower and upper bound. The mean position of the current generation of individuals, which can be calculated using Eq. (2).

$A_{\text {avg }}(t)=\frac{1}{M} \sum_{i=1}^M A_i(t)$             (2)

where, M refers to entire number of hawks, $A_i(t)$ indicates the location of each hawk at iteration t.

2.3.2 Exploration to exploitation transition

Generally speaking, an algorithm needs a proper method to transition from exploration to exploitation to balance the fundamental searching behaviours. In HHO, this portion of the search process is controlled by the vanishing energy of the prey, which is reduced by the escaping behaviour. Eq. (3) is used to formulate the energy of the escaping prey.

$P=2 P_O\left(1-\frac{t}{T_{\max }}\right)$              (3)

where, $T_{\max }$ is maximum iteration, P indicates the power of rabbit run-out.

2.3.3 Exploitation phase

In this phase, the Harris’ hawks perform the surprise pounce (seven kills as called in the study [15]). By launching an assault on the target identified in the earlier stage. On the other hand, prey frequently try to get away from hazardous circumstances. As a result, many pursuit techniques are used in actual circumstances. Four potential strategies are suggested in the HHO to mimic the attacking stage based on the tactics of pursuing Harris' hawks and the victim's evasive actions. Prey always has a natural tendency to flee from hazardous conditions. The notation rd indicates the chance to flee; if the target escapes successfully, rd<0.5; otherwise, rd>=0.5.

If p≥0.5 and rd≥0.5 that means the prey has high energy, and utilizing some haphazard tricky rebounds to run away but last, it can't. Meanwhile the Harris`s hawks (HH) surround it to make the prey tired and the perform the ''surprise pounce". The action modeled as Eqs. (4) and (5).

$A(t+1)=\Delta A(t)-P\left|K A_{h t d}(t)-A(t)\right|$                  (4)

$\Delta A(t)=A_{h t d}(t)-A(t)$              (5)

where, $\Delta A(t)$ is the difference between current position and the hawk's position vector. The arbitrary bounce force is $K=2\left(1-r d_5\right)$.  

At this point, p≤0.5 and rd≥0.5, indicating that the prey is quite tired and exhibiting some runaway energy. In addition, HH closely surrounds the intended victim to execute the "surprise pounce finally". As a result, the present location is changed using Eq. (6).

$\Delta A(t+1)=A_{h t d}(t)-P\left|\Delta A_{h t d}(t)\right|$              (6)

where, P is greater than or equal to 0.5, and rd is less than 0.5, the prey has sufficient energy to flee; thus, establishing a soft blockage before the "surprise pounce" makes this strategy superior to the others. The equation below is used to execute the soft:

$B=A_{h t d}(t)-p\left|K A_{h t d}(t)-A(t)\right|$               (7)

They hypothesized that the hawks would plummet based on the LF-based shapes using the following law:

$C=B+S_{r d m} \times L F(G)$               (8)

where, G is the problem space, LF is levy flight function, and $S_{r d m}$ is arbitrary vector of size $1 \times F$.

$L F(\alpha)=0.01 \times \frac{l \times \mu}{|m|^{\frac{1}{\alpha}}} \cdot \alpha=\left(\frac{\theta(1+\alpha) \times \sin \left(\frac{\pi \alpha}{2}\right)}{\theta\left(\frac{1+\alpha}{2}\right) \times \alpha \times 2\left(\frac{\alpha-1}{2}\right)}\right)^{\frac{2}{\alpha}}$                 (9)

where, l and m are arbitrary values in (0,1), and ɑ is the default constant adjusted to 1.5.

The final method for altering hawk positions during the soft blockage stage.

$A(t+1)=\left\{\begin{array}{l}B \text { if } F(B)<F(A(t)) \\ C \text { if } F(C)<F(A(t))\end{array}\right.$             (10)

where, B and C are got by Eqs. (7) and (8), respectively.

When p<0.5 and rd<0.5, the prey lacks the energy to flee, resulting in a hard blockage before the "surprise pounce" to catch and kill the animal. This phase on the prey side is identical to the soft blockade, except the hawks try to minimize the distance between their average location and the fleeing prey. Thus, the following are employed in the hard blockage case:

$A(t+1)=\left\{\begin{array}{l}B \text { if } F(B)<F(A(t)) \\ C \text { if } F(C)<F(A(t))\end{array}\right.$                  (11)

where, B and C are extracted using Eqs. (12) and (13).

$B=A_{h t d}(t)-p\left|K A(t)-A_n(t)\right|$                     (12)

$C=B+S_{r d m} \times L F(G)$                (13)

The pseudo code of HHO algorithm is listed below.

2.4 Logistic regression algorithm

In machine learning classification algorithms, logistic regression analyzes datasets with categorical dependent variables (DVs) as well as independent variables (IVs) [16]. Linear regression provides continuous numerical output, but logistic regression uses the logistic sigmoid function to yield a probability value that may be assigned to two or more discrete classes [17].

The cost function is limited using logistic regression to a range between 0 and 1. Eq. (14) yields a probability estimate between 0 and 1, where z represents the function's input and e denotes the natural log's base [18, 19].

$\sigma(z)=\frac{1}{1+e^{-z}}$            (14)

The provided data set shows that 1 denotes a high risk of coronary heart disease during the next ten years, whereas 0 denotes no risk at all. The logistic model's independent variables are as x₁, x₂, …, x_n [19].

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Figure 1. Logistic regression [19]

This is accomplished by using the log odds of the occurrence ln(P/1−P), where P is the probability of the event that represents the CHD risk. P always falls between 0 and 1, as a result.

The formula has two inputs, z and e, which are natural log bases. Input is z, and output is between 0 and 1 (probability estimate). Figure 1 demonstrates the logistic regression [19].

In the provided data set, a value of 1 denotes a high risk of coronary heart disease during the next ten years, whereas a value of 0 denotes no heart risks at all. The logistic model's independent variables are represented as x₁, x₂, x₃, ..., and x_n [19].

$\log \left(\frac{p}{1-p}\right)=\beta_0+\beta_1 x_1+\beta_2 x_2 \ldots \ldots+\beta_n x_n$           (15)

Logistic regression attains this by taking the log odds of the event ln(P/1−P), where P represents the probability of the event being related to coronary heart disease. Therefore, P always in range (0 and 1).

2.5 Random forest (RF)

Basic classifiers in RF are hierarchical and tree-structured. The dimensions of text data are often very large. There are a lot of unnecessary features in the dataset. Only a few significant features are helpful for the classifier model. By using a simple fixed probability, the RF algorithm determines the most relevant feature [20, 21]. By mapping a random sample of feature subspaces to the RF technique, Breiman built a number of decision trees based on sample data subsets. The RF algorithm connected with a collection of training documents D and N_f attributes can be demonstrated as bellow [22, 23]:

-First, a predefined probability sample of D₁, D₂, ... D_K was taken with replacement.

Create a decision tree model for every document that D_K has. Utilizing its subspace of the m-try dimension, the training papers are randomly selected from the available features. Determine every conceivable probability using the m-try characteristics. The leaf node generates the optimal data split. A procedure will be carried out repeatedly until the saturation threshold is met.

Utllize the high probability value to determine the classification outcome after combining the K number of unpruned trees, h₁(X₁), h₂(X₂), … into the RF.

2.6 Evaluation metrics

Accuracy used to determine the most effective model for forecasting individuals with heart disease. The metrics were calculated as [24, 25]:

$Accuracy =\frac{T P R+T N R}{T P R+T N R+F P R+F N R}$              (16)

At the preprocessing step the UCI-Cleveland dataset is examined for missing values 6 records are removed. Heart Statlog dataset is examined for missing values and filled missing values with mean. The dataset is scaled using the Standard scaler. Then PCA is applied. The PCA results are illustrated in Figure 3.

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Figure 3. Explained variance ratio of principal component vector for Statlog dataset

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Figure 4. Fitness of proposed HHO-algorithm of Statlog dataset

In PCA, the highly correlated features are kept together to transform the data into a lower-dimensional space. PCA is computed by first normalizing data, computing a Covariance matrix, Eigenvectors, and eigenvalues, and then sorting features based on eigenvalues. In this work, we first apply PCA as a filter feature selection method and select the best features. Then, the dataset with selected features is forwarded to the wrapper feature selection BHHO algorithm to perform a hybrid PCA-BHHO algorithm. The least irrelevant feature is removed by using PCA as a filter method before performing the BHHO algorithm, which enhances computational efficiency and increases system performance.

The last feature based on PCA results is removed then results is fed to the BHHO algorithm. The HHO algorithm parameters are set as number of iterations is 100, beta is 1.5, and threshold is 0.5. Figure 4 demonstrates the fitness function of the BHHO algorithm.

The proposed PCA-HHO algorithm is achieved an accuracy of 90.14%. Nine features are selected and they are trestbps, fbs, thalach, restecg, slope, old peak, Thal, Chol, and Ca.

The PCA results of heart disease dataset is demonstrated in Figure 5. The result of proposed PCA-HHO algorithm is achieved an accuracy of 89.33%. Nine features are selected and they are CP, trestbps, thalach, restecg, slope, old peak, Thal, Chol, and Ca. Figure 6 demonstrates the fitness function of the BHHO algorithm.

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Figure 5. Explained variance ratio of principal component vector for Cleveland heart disease dataset

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Figure 6. Fitness of proposed HHO-algorithm Cleveland heart disease dataset

Boruta algorithm with RF are used on Statlog and Cleveland heart disease dataset and attained an accuracy of 90.14%, 87.64, respectively. Accuracy of proposed PCA-HHO algorithm and Boruta algorithm are demonstrated in Figure 7.

Comparison between related work and proposed model are demonstrated in Table 4.

For the Statlog dataset, the proposed PCA-BHHO algorithm achieved an accuracy of 92.59%, whereas Boruta and RF attained an accuracy of 90.14%. Liu et al. [3] used the RFRS technique and achieved an accuracy of 92.59%. Albert et al. [5] used the Smote & BOML algorithm and achieved an accuracy of 86.7%.

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Figure 7. Comparison of proposed BHHO-algorithm and Boruta algorithm

Table 4. An accuracy comparison of model proposed with previous works

For the Cleveland dataset, Khemphila and Boonjing [4] used an algorithm and attained an accuracy of 82%. Das et al. [6] employed the NN algorithm for classification and achieved an accuracy of 89.01%. Weng et al. [7] utilized the KNN algorithm for classification and achieved an accuracy of 79.2%. The proposed PCA-BHHO algorithm achieved an accuracy of 87.64%, whereas the Boruta and RF algorithm attained an accuracy of 87.64%.

It comes to patient care, nurses are the experts. They are more knowledgeable about a patient's current state than medical professionals and hospital managers. They are the first to notice whether a patient's condition is getting worse or when they are in agony. Because of this, nurses must be able to solve problems and make decisions that affect patient outcomes. In nursing, clinical decision-making is an active process of evaluating a patient's status and making evidence-based decisions about their care. A group of medical professionals collaborate to analyze the situation and decide on the best course of action. To acknowledge patients as their own best advocates and authorities on their own physical and mental health requirements, clinical decision-making also involves patients and their families. It is useful to provide the nurses with a decision-making system to check the patients for suspicious in heart disease as a first step when check patients.