Cloud computing-based framework for heart disease classification using quantum machine learning approach

3.1 Cloud-based HD classification model

The present study suggests the development of a cloud-based system for classifying HDs and that can monitor health data from remote users and identify their HD category. The technology is sufficiently adaptable to support the diagnosis and classification of a wide range of disorders when applied to the consumer health data stored on cloud servers. Nonetheless, we primarily focused on a single instance of application, which included classifying the illness as either “normal” or “abnormal.” Figure 1 displays the general layout of the proposed architecture. In the architecture, patients visit a rural healthcare facility, where a practitioner collects data via wearable devices, performs imaging tests and medical history assessments, conducts surveys, obtains electronic records of health, and then transmits all information to a doctor, who then uploads it to a cloud platform for analysis.

3.2 Dataset collected

The HD dataset sourced from Kaggle is as a comprehensive compilation of HD-related data. The dataset merges information from five distinct datasets into a unified dataset. This merger extends across 12 common features, making it the most extensive HD dataset available for research purposes [23]. The five constituent datasets utilized for this are the Cleveland, Hungarian, Switzerland, Long Beach VA, and Statlog (Heart) datasets [24]. These datasets include male and female patients, resulting in a total of 1,190 records. Among these records are 11 distinctive features and a single target variable. The dataset accounts for 629 instances of HD and 561 instances of normal cardiac health. The age range of the patients included in the dataset is 57–60 years. Importantly, this dataset does not have any missing values. This dataset comprises a diverse set of features, incorporating six nominal and five numeric variables. For a comprehensive understanding of the dataset’s attributes, their description and that of the features included in the dataset on HD are presented in Table 2.

3.3 Data preprocessing

In the preparation of the HD classification dataset, denoted as “Cleveland_statlog_Hungary,” several critical data preprocessing steps were employed to ensure data quality and enhance its suitability for classification tasks. The following primary processes were included.

3.4 Feature extraction

Feature extraction is a significant stage in HD classification because it helps identify the most relevant features that can be utilized to train ML methods. Some feature extraction methods are used in HD classification such as the PCA technique, and it is a powerful tool utilized in ML to identify the most influential factors contributing to HD prediction. By reducing the dataset complexity, PCA enhances the overall performance of ML techniques. Essentially, PCA is a feature extraction technique that identifies the primary components within the data and uses them to transform its underlying structure.

PCA relies on a series of X-unit vectors, each of which represents the orientation of the line that provides the best match. After the first X1 components, all the others are perpendicular to each other. The first PC represents the axis along which data’s anticipated variance is maximized. By contrast, the data projections’ variance reaches the maximum in a path perpendicular to the initial X1 main components. PCA is a well-liked method for simplifying data by identifying its key drivers of variance. This method may be used for predictive modeling and exploratory data analysis. A lower-dimensional data collection can be constructed while keeping as much variance as possible by mapping every information point to only the first few major components. With PCA, a long list of variables can be shortened to a manageable subset that still accounts for the bulk of the original set. Overall, PCA is a potent technique that is extensively utilized because of its ability to improve the efficiency of ML algorithms. Based on the findings, PCA is computed as follows:

1. Standardizations: The continuous beginning variables are spread out such that they all have an equal impact on the study. The average and standard deviation for each factor are determined, and standardized data may be expressed as equation (5) by subtracting the mean from every parameter of the standard deviation.

   (5) Z = x − μ σ .

   Here, µ = {µ1, µ2, … µm} represents the mean of the independent features, while σ = {σ ₁, σ ₂, … σ _m } represents the standard deviation of the independent features. Z denotes the z-score, x denotes the original value, μ denotes the mean of the dataset, and σ denotes the standard deviation of the dataset. The z-score serves as a measure of the number of standard deviations of a value from the mean. A positive z-score indicates that the value exceeds the mean, and a negative z-score suggests that the value falls below the mean. The z-score proves valuable in statistical analyses, such as hypothesis testing and confidence interval estimation, because it enables the comparison of values from disparate datasets that may possess different means and standard deviations.

2. Covariance matrix calculation: The covariance matrix is calculated to identify the correlations between variables. The covariance matrix is calculated as follows:

where C is the covariance matrix, n is the number of observations, and X is the standardized data matrix. The eigenvalues and the eigenvectors are calculated. The equation used to calculate the covariance matrix of a dataset is a measure of the relationship between variables in a dataset. The equation measures how much the variables in the dataset are related to each other and helps in identifying the direction of the highest variance, which can be useful in PCA and other dimensionality reduction techniques to calculate the eigenvalues and eigenvectors of the covariance matrix following these steps:

• The covariance matrix (C) is calculated using equation (6).

• The eigenvalues (λ) and eigenvectors (v) of the covariance matrix (C) are determined using appropriate numerical methods such as QR decomposition or singular value decomposition.

1. The most minor and most significant values of that feature in the collection data are determined. The covariance matrix’s eigenvectors and eigenvalues are determined. Each eigenvector is a direction in which the data change remarkably, and its corresponding eigenvalue is the magnitude of that eigenvector’s fluctuation. The eigenvectors and the eigenvalues can be calculated using the following equation:

   (7) C × V = λ × V ,

   where v is the eigenvector, λ is the eigenvalue, and C is the covariance matrix. The relationship between the eigenvector and eigenvalue of the covariance matrix is a pivotal concept in the examination of multivariate data and linear transformations.

2. The primary components and the eigenvectors with the largest eigenvalues are selected. The original data are transformed into a lower-dimensional space using PCA, where the immediate members stand in for the directions along which the data fluctuate the most.

3. Visualization of results: The results are visualized using a scatter plot. A scatter plot of the data along the first and second main components of interest (x-axis and y-axis, respectively) is generated. Figure 2 shows that each point’s hue reflects a different dependent variable.

A 3D scatter plot of statistics inside the predominant thing space is generated. This form of plot is beneficial for visualizing records with three dimensions. The x-axis in Figure 3 represents the most essential aspect, the y-axis represents the second most important, and the z-axis is the 0.33 most important. The identification of patterns or connections in the statistics may be facilitated by the correspondence of each factor’s color to the variable of interest.

Figure 2

Visualization of results.

Figure 3

3D data visualization.

3.5 Feature selection

Selecting the most important input variables or features from a huge dataset is an essential part of ML. Reducing the data’s dimensionality in this manner can improve the performance of prediction models. With only the most pertinent details included, the model can zero in on what is essential in determining the outcome. Overfitting, which occurs when a model is extremely complicated and catches noise rather than underlying patterns, may also be avoided in this way. Different approaches are used for selecting features; the approach is dependent on the dataset and the current situation. A strong technique utilized in feature selection is the SVM-RFE approach, which employs SVM for evaluating features based on nonlinear kernels and for survival analysis. Figure 4 indicates that this approach aids in improving a classifier’s performance by selecting the most important features and discarding the rest.

Figure 4

SVM-RFE steps.

The SVM-RFE technique is often used in disciplines such as ML and data mining. Users can boost the precision of their models for classification and hence the quality of their findings by employing this approach. To maximize a predictive model’s efficacy, the role that feature selection plays in ML must be appreciated. The following equation describes the SVM-RFE algorithm:

In this equation, w represents the weight vector, b is the bias term, C is the regularization parameter, and y_i is the dependent variable. The SVM-RFE method is an iterative algorithm that works backward from an initial set of features. In each round, the method fits a simple linear SVM and ranks the features based on their importance. The process is repeated until a feature-sorted list is obtained. Through SVM training using the feature subsets of the sorted list and evaluating the subsets using cross-validation, the optimal feature subsets can be identified. The SVM-RFE method consists of the steps presented in Figure 4.

3.6 Data splitting

Data splitting is a fundamental strategy in assessing ML algorithms. Overfitting may be avoided by splitting the dataset into training and testing sets, generating an accurate testing set, simulating the model’s behavior on simulated data, and assessing the results. Typically, 80% of the data is used for training, while 20% is used for testing. By using this proportion, the dataset would generate a training set with 952 records and a testing set with 238 records [2]. Figure 5 illustrates how the separation of training and testing datasets facilitates the training and assessment of different ML classifiers.

Figure 5

Split the dataset.

3.7 Classification stage

The study demonstrates the contribution of ML classification algorithms, including the ANN, SVM, QNN, QSVM, and bagging applied to QSVM, to the overall findings of the research. Following the dataset preparation process described in the previous two sections, ML techniques and quantum ML were used to implement categorization algorithms. The Scikit-Learn package must be utilized in the development of ML algorithms, and the Qiskit package uses QML. Regression, classification, and clustering are just a few of the ML algorithms included in the library, which is quite important in this field. The proposed system is implemented using a few of the functions offered by this library. The proposed system uses many Python libraries, including Google, in its implementation.

• Colab: This library is used for the free Jupyter Notebook environment on Google Cloud servers known as Colab Notebooks.

• NumPy library: This library is used for computing numerical data.

• Pandas is a library for analyzing and manipulating data.

• Matplotlib: This library is for making graphs, plots, and charts.

• Seaborn: This is a matplotlib-based data visualization package.

• Cv2: OpenCV is a well-known library for programming in real-time computer vision.

• The Python library file system is the OS.

3.7.3 QNN

QNNs are a type of quantum algorithm that may be taught variation ally with classical optimizers; they are based on specified quantum circuits [25]. A feature map (with input parameters) and an ansatz (with trainable weights) are components of these circuits. Like their classical analogs, QNNs are employed in ML to uncover previously unseen patterns in data. Once the data are placed in the quantum state, it is processed by quantum gates whose weights can be changed and learned again. Backpropagation may be used to train the weights using the measured value of this state as input to a loss function. Numerous research studies have implemented QNNs for cardiovascular risk prediction, machine translation, and function approximation. The QNN algorithm is structured as follows:

• Through the use of cross-validation, the dataset is partitioned into a training dataset and a testing dataset.

• Before analysis, the data are preprocessed using RFE, PCA, and min–max normalization.

• A feature map of two qubit maps conventional feature vectors will use to quantum spaces.

• In a QNN network, a parametrized quantum circuit obtains the input data and weights as parameters.

• A string of binary results is produced in a bulk form.

The QNN model is trained on the data, and cross-validation iterators are used to evaluate the model’s efficacy. QNNs may be regarded through the lens of both quantum computing and classical ML, and they can be used for various ML tasks, such as classification, regression, and optimization, as shown in Figure 6. The quantum data are decoded back into a standard value of 0 or 1 by the binary measurements. The QNN algorithm is presented as Algorithm 3.

Algorithm 3: QNN Algorithm steps
Input: Training data
Output: A class label for feature vector
Begin
Step 1: Initialize the weights and biases for the input layer, hidden layer(s), and output layer.
Step 2: Set the learning rate and the number of epochs.
Step 3: Load classical data into a quantum state using quantum feature maps.
Step 4: Process the quantum state with quantum gates parametrized by trainable weights.
Step 5: Calculate the error between the predicted output and the actual output.
Step 6: Backpropagate the error through the network to update the weights and biases.
Step 7: Repeat steps 3–6 until the error is minimized or a maximum number of epochs is reached.
Step 8: Use the trained QNN to classify the output for new input data.
End

Figure 6

Architecture of quantum neural network.

Figure 6 depicts the QNN’s input, output, and hidden units. One occlusion layer is employed in this case. Each hidden-layer node represents three states, where r is the quantum level. For simplicity, we assume that n _i means the input to the input layer, O _j represents the output of the hidden layer, and O _k represents the output of the output layer, representing the learning rate, which is a small random value.

As an illustration, n _i represents the input layer, while O _j and O _k describe the hidden and output layers’ output, respectively. W _ij represents a weight on the input layer, while W _kj represents a weight on the hidden layer, and Figure 7 displays these relationships.

Figure 7

QNN classifier outline.

3.7.4 Quantum support vector machine (QSVM)

The SVM technique has a quantum counterpart in the QSVM approach. The Pegasos method, a fundamentally predicted subgradient solver for SVM, is used to train the classifier in the QSVM method. When applied to the SVM method, the quantum kernel technique accelerates the learning process, as seen in the QSVM algorithm. For processing on a quantum computer, the quantum kernel method uses quantum map features to convert standard data to quantum states. After training the QSVM classifier on a data set, its efficacy may be evaluated on a separate test data set. The classical-quantum (CQ) approach encodes classical data so that a quantum computer can handle it, enabling the mapping of conventional vectors of features to quantum spaces. The CQ method converts classical information into quantum states using a 5-qubit feature map. Figure 8 depicts the QSVM algorithm’s structure; the dataset is split between the training and testing datasets (in 80:20 proportion) after being preprocessed with RFE and min–max normalization. Computing the inner outcome of the quantum map features is how the quantum kernel transforms the quantum state of the collected information points into a space of higher dimension. To develop a QSVM for classification, a ZFeatureMap and a quantum kernel with a state vector simulator backend are used. The random seed of the algorithm is set to 12345. The CQ technique can be used to train the QSVM algorithm by encoding classical data to be processed by a quantum computer. The CQ technique employs a 5-qubit feature map to map classical feature vectors to quantum spaces. The quantum kernel changes the data points of the quantum state into a space with more dimensions by determining the inner outcome of the quantum map’s features. The model’s accuracy is determined by applying the QSVM classifier trained on the data to the test data and then analyzing the results. The QSVM algorithm is presented in Algorithm 4.

Algorithm 4: The QSVM steps
Input: Training data
Output: A class label for feature vector
Begin
Step 1: Prepare the input, hidden layer(s), and output layers by setting their initial weights and biases.
Step 2: The epochs number and the learning rate may be adjusted.
Step3: Dividing a test dataset and a training dataset with an 80:20 split
Step 4: Preprocessing the dataset with RFE and min–max normalization.
Step 5: Applying a 5-qubit feature map to translate conventional feature vectors into quantum spaces.
Step 6: We take the inner result of the quantum map features to project the state of quantum data points into a higher dimensional space.
Step 7: The training data were used to fine-tune the QSVM classifier.
Step 8: Use the test data to determine how well the model performs.
Step 9: Decode the quantum information into its equivalent binary measurement (a standard value of 0 or 1) for each classical input.
End

Figure 8

Outline of the QSVM.

The QSVM quantum kernel uses a quantum map of features to convert conventional vectors of features to quantum spaces. The traditional feature vector (x) is transformed into a quantum state | ( x ) ( x ) | utilizing a quantum feature map. The quantum kernel then uses the internal result of the quantum map’s characteristics to project the quantum state’s data points into a space with extra dimensions, where xi and xj are n-dimensional inputs, ( x ) is the quantum feature map, and kernel matrix K is defined as Kij = | ( xi ) | ( xj ) | 2 . Quantum kernels may be used with standard classical kernel learning methods, like SVM and clustering. The QSVM training algorithm is an optional algorithm offered by the qiskit-machine-learning package. This algorithm is like SVM but has a quantum kernel. The outline of the QSVM is presented in Figure 8.

3.8 Proposed bagging QSVM method for HD diagnosis

HD classification is a crucial task in medical research, and ML methods have been extensively employed to improve classification models. Ensemble learning approaches, such as bagging, can be used to enhance the performance of HD model classification. To aggregate the classifications of many models trained on various parts of the same dataset, a technique called “bagging” is used. A new model relies on a bagging ensemble process built on top of the QSVM to efficiently classify HDs. The method utilizes a random method of splitting the dataset into smaller pieces. If the classification algorithm is not performing well in identifying the HD risk, using an ensemble strategy like boosting or bagging can help. Combining the best features of bagging and the QSVM algorithm, bagging-QSVM is an ensemble learning method that can make models work better. For this method, 100 separate QSVM models are trained on different parts of the dataset. The final output of the ensemble model is then generated by averaging the predictions of these models. After training the models, the ensemble model provides the final result by averaging the forecasts and assigning the majority vote to the class with the most votes. In each bootstrap sample utilized in the bagging model, some occurrences from the original dataset are duplicated or disregarded. Each bootstrap sample in a bagging model replicates the original dataset or skips part of the occurrences. This approach generates many subsamples of a dataset for use in model training. The bagging ensemble approach averages the predictions of several models, which is very useful when working with high-variance models because it helps reduce the model’s variance. When used in statistical learning or model fitting, the bagging ensemble method is an example of ensemble learning that integrates many models to enhance prediction performance. The bagging-QSVM algorithm is presented in Algorithm 5.

Figure 9 presents a schematic description of the bagging-QSVM model:

• The first step in converting conventional data into a quantum state is to define the quantum feature map.

• In step two, the quantum feature map is used as an input parameter in constructing a new instance of the QSVM class.

• Third, the QSVM instance is used as the basis estimator to create a new instance of the bagging classification class.

• Fourth, the fit technique is used to adjust the bagging classification instance to the input data.

• The classification approach is employed to make predictions on newly collected information.

Figure 9

Bagging-QSVM model.

The bagging method keeps the QSVM algorithm from overfitting the data. The bagging approach produces several subsets of the original dataset by randomly picking data with replacement. A QSVM model is trained independently on each subgroup, and then, the models’ combined predictions are utilized to create a final classification.

4.1 SVM results

When the models were trained on the comprehensive HD dataset, the achieved outcomes were are follows: accuracy of 73.1%, precision of 68% to abnormal and 79% to class normal, recall of 77% to class abnormal and 70% to class normal, F1 score of 72% to class abnormal and 74% to class normal, sensitivity of 80%, macro average of 73%, and average weight of 74%. All the results are summarized in Table 3.

The classifier achieved a success rate of 73% in accurately categorizing the cases, as evidenced by its overall accuracy of 0.73. Nonetheless, accuracy alone may not provide a comprehensive understanding of the classifier’s performance. In terms of predicting the absence of HD, the classifier displayed a precision of 0.68 and exhibited a precision of 0.79 in predicting the presence of HD. Precision, which refers to the percentage of correctly anticipated occurrences for a given class, was appropriately exemplified. A high level of accuracy is indicated by a low occurrence of false positives. Specifically, the recall for identifying the presence of HD was 0.70, while the recall for determining its absence was 0.77. Recall is also referred to as sensitivity or true positive rate and measures the percentage of correctly predicted occurrences of actual positivity. A strong recall is indicated by a low rate of false negatives. On the one hand, in the case of forecasting the absence of cardiac disease, the F1 score, which is the harmonic mean of accuracy and recall, was reported to be 0.72. On the other hand, for predicting the presence of cardiac disease, the F1 score was reported to be 0.74. The F1 score provides a balanced metric that combines precision and recall. This metric is particularly useful in situations where the dataset is unbalanced. From the analysis of the performance metrics, we can infer that the classifier categorizes cases of HD. This is evident from the high accuracy, recall, and F1 score for both the absence and presence of cardiac disease, indicating a good balance between true positives and negatives. However, these metrics have different applications and are inversely related to each other. By examining these indicators, the effectiveness of the SVM model can be assessed, and areas that may require improvement can be identified.

The evaluation of the SVM classification algorithm for disease prediction pertaining to the heart involves the examination of a confusion matrix and the receiver operating characteristic (ROC) graph. The actual and predicted values are represented in Figure 10. The parity between the number of actual predictions from the normal and abnormal classes demonstrates the accuracy of the system. The ROC for the SVM is presented in Figure 11. This evaluation reveals the capability of the SVM in diagnosing patients with and without HD based on the classification analysis.

Figure 10

Confusion matrix the SVM model.

Figure 11

ROC curve of the SVM model.

The precision of the model for the normal class surpasses that of the abnormal class, suggesting that the likelihood of correct classification is greater when predicting a normal class than when predicting an abnormal class. Meanwhile, the recall of the model for the abnormal class outperforms that for the normal class, indicating that the model exhibits superior identification capabilities for abnormal cases compared with normal cases. Moreover, the F1 score of the model for the abnormal class exceeds that of the normal class, signifying that the model’s predictive capabilities are more accurate for the abnormal class than for the normal class. In terms of iteration, the model underwent more iterations for the normal class than for the abnormal class. This particular observation implies that the model received more training in the normal class, possibly contributing to the higher precision observed for the normal class than that for the abnormal class. The model’s accuracy is 0.73, indicating that it has accurately predicted 73% of the data. The SVM model demonstrated a satisfactory accuracy level of 0.73. However, when considering the precision, the recall, and the F1 score, the model’s performance varied between the abnormal and normal classes. The analysis of the results suggests that the model is more adept at identifying abnormal cases than normal cases, indicating a bias toward the normal class during training. Consequently, adjustments to the hyperparameters and fine-tuning of the model may be necessary to enhance the model’s performance.

4.2 ANN results

The following findings were obtained after training the models on the comprehensive HD dataset: accuracy of 83.61%, precision of 82% to abnormal and 0.85% to normal, recall of 81% to abnormal and 85% to normal, F1 score of 82% to abnormal and 85% to normal, and sensitivity of 80% in the ANN model. All the results are summarized in Table 4.

The ANN classifier attained an accuracy of 0.84, indicating that it accurately classified 84% of the instances in the dataset. For abnormal cases, the precision is 0.82, denoting that 82% of the instances was predicted as not having HD were true negatives. For normal cases, the precision was 0.85, indicating that 85% of the instances predicted as having HD were true positives. In the case of abnormalities, the recall stood at 0.81, meaning that 81% of the instances without HD were correctly identified. For normal cases, the recall was 0.85, indicating that 85% of the instances with HD were correctly identified. The F1 score, a harmonic mean of precision and recall, was presumably calculated for both classes. The analysis of the performance metrics suggests that the ANN classifier exhibits commendable performance in the field of HD classification research, characterized by high precision, recall, and accuracy for both classes. The classifier’s balanced performance is further evidenced by its consistent macro average precision, recall, and F1 score. The confusion matrix can offer additional insights into the classifier’s performance by illustrating the number of true positives, true negatives, false positives, and false negatives for each class. The problem consists of abnormal and normal cases, and the model generated predictions for 238 cases.

The performance of the ANN classification algorithm shown in Figure 12 was assessed using a confusion matrix and an ROC graph. In terms of performance metrics analysis, several insights can be drawn. First, the confusion matrix displays the combination of the actual and predicted values. This matrix reveals that the number of actual predictions was equal for the positive and negative classes, indicating the accuracy of the system. Second, the ROC curve is a graphical depiction of the performance of a binary classifier system as its recognition threshold is varied. Figure 13 presents the ROC curve for the ANN classifier, demonstrating the classifier’s high sensitivity and specificity in diagnosing patients with and without HD on the basis of the classification evaluation.

Figure 12

Confusion matrix of the ANN model.

Figure 13

ROC curve of the ANN model.

The precision score for the normal category was 0.82, while the precision score for the abnormal category was 0.85. These scores indicate that the model’s false positive predictions decreased, thus showcasing its proficiency in predicting positive cases. Furthermore, the recall score for the normal category was 0.81, and that for the abnormal category was 0.85. These scores suggest that the model’s false negative predictions were minimized, demonstrating its capability to identify positive cases. In addition, the F1 score for the normal category was 0.82, and that for the abnormal category was 0.85. These scores imply that the model’s false positive and false negative predictions decreased, thereby highlighting its aptitude for predicting and identifying positive cases. Precision, recall, and F1-score are significant metrics employed to evaluate the performance of a classification model. The iteration number pertains to the frequency with which a model is trained on the dataset. Depending on the nature of the problem and the available data, a certain measure or collection of metrics may be more suitable.

4.3 QNN results

The outcomes were as follows: accuracy of 77%, precision of 76% to class 0 and 77% to class 1, recall of 73% to class 0 and 79% to class 1, F1 score of 75% to class 0 and 78% to class 1, macro average of 0.77%, and average weight of 77% in the QSVM model. All the results are summarized in Table 5.

For predicting cardiac issues, the QNN classifier achieved a total accuracy rating of 0.77. This result proves that the classifier accurately classified HD patients. However, to fully grasp the classifier’s capabilities, the accuracy and recall for both the negative and positive categories must be examined. The respective precision and recall were 0.76 and 0.73 for the negative class, which represents those who do not have HD. Based on these measures, the classifier accurately identified healthy individuals. The respective accuracy and recall were 0.77 and 0.79 for the positive class, which represents those with HD. Based on these measurements, the classifier is also reasonably reliable in identifying people with HD. For the negative class, the F1 score was 0.75, and for the positive class, the F1 score was 0.78. F1 is a value that combines precision and recall. The results demonstrate that the ratio of accuracy to recall is satisfactory for both groups. The iteration value for the abnormal was determined to be 107. These metrics were derived by evaluating the confusion matrix and ROC graph of the QNN classifier in predicting HD. Thus, the QNN classifier achieved an overall performance of 0.77 in the prediction of HD, accompanied by reasonably reliable precision and recall for both the positive and negative classes. The F1 score level for both classes was commendable, thereby signifying a favorable balance between precision and recall. These metrics were obtained by assessing the confusion matrix and ROC graph of the QNN classifier for HD prediction, as illustrated in Figures 14 and 15.

Figure 14

Confusion matrix of the QNN model.

Figure 15

ROC curve of the QNN model.

Cross-validation constitutes a methodology employed for assessing the efficacy of a model by subjecting it to the examination of a portion of the data that were not employed during the training process. In the context of a QNN, the outcomes of cross-validation can be used to determine the optimal collection of parameter values. This implies that the parameters of the network can be modified to enhance its performance based on the outcomes of cross-validation, as depicted in Figure 16.

Figure 16

Cross-validation QNN model.

The analysis of these metrics indicates that the model exhibits a reduced number of false positive and false negative predictions for the normal category compared with the abnormal category. The F1 score serves as a means to strike a balance between precision and recall. Moreover, it signifies that the model manifests a lower occurrence of false positive and false negative predictions for the normal category than for the abnormal category. The accuracy of the model stands at 0.76, indicating that it accurately predicts the class of 76% of the data points. Precision, recall, F1 score, and accuracy are pivotal metrics employed to assess the performance of a classification model. These metrics offer valuable insights into the accuracy and quantity of the model’s positive predictions and the equilibrium between precision and recall. The selection of appropriate metric(s) is contingent on the problem domain and the dataset at hand.

4.4 Quantum support vector classifier results

The following results were obtained: accuracy of 85%, precision of 79% to class 0 and 91% to normal, recall of 90% to class 0 and 81% to class 1, F1 score of 84% to class 0 and 85% to class 1, macro average of 0.85, and average weight of 86% in the QSVM model. All the results are summarized in Table 6.

The measure known as recall, sensitivity, or true positive rate provides a quantitative assessment of the proportion of true positive predictions among all positive cases in the dataset. In an abnormal setting, the model correctly classified 90% of people as having no cardiac illness (recall = 0.90). The recall for normality was 0.81, indicating that the algorithm correctly identified 81% of people with HD. These recall values demonstrate the classifier’s ability to catch negative and positive examples accurately. The F1 score must be considered for a thorough investigation. The F1 score is the harmonic average of accuracy and recall and is a balanced statistic for assessing classifier performance. With an F1 score of 0.84, anomalies were classified with a good mix of accuracy and recall. Table 5 shows the accuracy and recall of the QSVM method, which lets us test how well it works in real life and find any problems. The total accuracy of the QSVM classifier on the dataset was 84%. The classifier achieved a precision of 0.79 for abnormality (no HD) and 0.91 for normalcy (HD). The recall for abnormal cases was 0.90, and that for normal cases was 0.81. Specifically, the F1 score for class 0 was 0.84, showing an excellent equilibrium between accuracy and recall. A more thorough investigation of a classifier’s efficacy may be conducted if its performance is measured across various parameters. Precision is the proportion of genuine positive predictions relative to all positive predictions made by the model, whereas accuracy describes how well the classifier can predict class labels. In contrast, recall quantifies the proportion of correct positive predictions relative to the total number of positive cases in a dataset. Finally, the F1 score is a balanced indication of classifier performance because it takes the harmonic mean of accuracy and recall.

Using a quantum kernel, the QSVM method accelerates the SVM’s learning process, making it a QML algorithm. The Qiskit ML library includes a score function for determining the QSVM model’s precision. Both accuracy and recall must be considered while analyzing the QSVM model’s results. Comparatively, recall measures the percentage of correct responses among all recorded positives, while precision measures the rate of correct answers among all projected positives. The F1 score is a harmonic average of accuracy and recall and offers a balanced evaluation of the algorithm’s performance. The model performed well in normal and atypical situations, as indicated by a comparable F1 score. With incredible accuracy and F1 scores in both normal and abnormal cases, the QSVM model seems a viable strategy for predicting HD. However, the model’s accuracy might shift depending on the characteristics utilized for categorization and the data set. Common and valid approaches can be used to check how well binary classification methods, like QSVM, work for predicting HD. These approaches include confusion matrices and ROC curves, which show how well other models work. These methods can potentially enhance the HD prediction model’s accuracy and generalizability, which in turn will aid in halting the disease progression. ROC curves and confusion matrices test how well the QSVM algorithm works for classifying HD cases. These resources help determine whether a binary classification method performs as expected. The results of the confusion matrix and ROC curves are presented in Figures 17 and 18.

Figure 17

Confusion matrix of the QSVM model.

Figure 18

ROC curve of the QSVM model.

4.5 Experimental results of the proposed bagging model for HD diagnosis

The accuracy, precision, recall, F1 score, and average weight using bagging-QSVM were all determined to be optimal when the proposed method was implemented in the dataset and tested. Table 7 summarizes the results.

The proposed approach achieved an accuracy of 100% when applied to the dataset, indicating that all data points were correctly classified. The precision for both the abnormal and normal classes was 100%, indicating that all predicted positive instances for both classes were positive. The recall for both abnormal and normal classes was 100%, indicating that the actual positive instances for both classes were correctly identified. The F1 score for both abnormal and normal classes was 100%, which is a harmonic mean of precision and recall, indicating a perfect balance between the two metrics. The macro average for precision, recall, and F1 score was 100%, indicating that the performance across both classes was excellent. The average weighted precision, recall, and F1 score in bagging-QSVM were also 100%, indicating a high level of performance across all classes.

The provided data appear to represent the evaluation measures of a model that has undergone training using the bagging technique along with QSVM. This specific model achieved a precision, recall, and F1 score of 1.00 for both the regular and abnormal categories. The accuracy of the model was also 1.00, indicating that the model did not made any incorrect predictions. For the regular and abnormal categories, the number of iterations was 107 and 131, respectively. In addition, the macro and weighted average for this model was 1.00. Bagging, a meta-algorithm within the domain of ML, was developed to improve the stability and accuracy of statistical classification and regression algorithms. This technique involves training multiple models on different subsets of the training data and then merging their predictions to generate a final prediction. While bagging enhances prediction accuracy, it does so at the expense of interpretability. Considering the aforementioned information, the model trained using bagging in conjunction with QSVM performs exceptionally well on the given task. The outcomes indicate that the bagging-QSVM model performed better than other ML methods, with precision, recall, and F1 scores of 1.00 as shown in Figures 19 and 20.

Figure 19

Confusion matrix of the bagging-QSVM model.

Figure 20

ROC curve of the bagging-QSVM model.

According to the findings of the experiment, the accuracy achieved by QSVM was recorded as 84.8%, whereas traditional SVM achieved an accuracy of 73.1%. Likewise, QNN demonstrated an accuracy of 76.5% in contrast to the 83.6% achieved by ANN. Therefore, QSVM and QNN exhibited the highest levels of performance among the quantum classifiers, with accuracies of 84.8 and 76.5%, respectively. On the one hand, this observation underscores the superior outcomes that quantum classifiers can generate compared with their classical classifier counterparts. On the other hand, the proposed model, known as bagging-QSVM, uses ensemble learning to show considerable improvements over previous quantum and classical classifiers. The bagging-QSVM surpasses all other methods, attaining an accuracy rate of 100%. Ensemble learning contributes to the optimization of quantum classifiers, as shown in Table 8.

4.6 Comparison of the state of the arts

The results of the proposed method, which utilizes ensemble learning bagging-QSVM, were discussed and compared with the findings of related works. According to the data presented in Table 8, the proposed approach achieved a remarkable accuracy rate of 100%, surpassing the results of the study by Asif et al. [26], who achieved an accuracy of 98.15%. Furthermore, the precision, recall, F1 score, and Cohen’s kappa values for the proposed approach were 96.27, 98.72, 97.48, and 95.07%, respectively. Meanwhile, Kumari and Muthulakshmi [27] secured a position with an accuracy of 95.33%, precision of 99.18%, recall of 97.90%, and F1 score of 98.53% [9], with an accuracy of 90.16%, precision of 0.90%, recall of 0.90%, and F1 score of 0.90%. With their stacked classifier, [27] attained an accuracy of 86.49%, precision of 87.32%, recall of 86.02%, and F1 score of 86.01%. The ROC-area under the curve (AUC) for their model was 99. The ML ensemble method also performed admirably, with an F1 score of 88.70%, a precision and recall of 88.02%, and an accuracy of 88.70%. This model obtained a ROC-AUC of 93. In the study by [18], instance-based quantum DL and ML were used to obtain 98 and 83.6% accuracy rates, respectively. The bagging-QSVM model outperformed all other classifiers with 100% accuracy, precision, recall, and F1 score. Both binary and regression classification modeling objectives were used to evaluate the outcomes. The results show that better predictions may be obtained using bagging, which employs many models with high variation but low bias. Overall, the bagging-QSVM model demonstrated superior performance over other ensemble learning models when applied to HD prediction. Bagging, as a powerful ensemble learning method, effectively reduces variance and enhances model accuracy. In addition, QSVM, a quantum classifier with proven superiority over other quantum classifiers, can be effectively incorporated into the bagging model to achieve high-performance outcomes. Table 9 compares the results of the proposed approach with those of related works for HD prediction and shows that the proposed method achieved the highest accuracy and performance measures. The bagging-QSVM model used in the proposed method outperforms other classifiers and can be used to achieve high performance.

AI-based approaches have many uses, including detecting several diseases [29,30]. The proposed approach is to improve the accuracy and efficiency of HD classification by using cloud computing and quantum computing. While the cloud computing based on the framework that uses QML to classify heart diseases has great promise, it does have some significant limitations. First, there are not a lot of practical, scalable quantum processors available, and the science behind quantum computing is still in its early stages. This is a problem when trying to use large-scale QML algorithms to classify all forms of cardiac disease. Second, there may be compatibility problems with the current conventional infrastructure when integrating quantum techniques into cloud platforms, which might make deployment and interoperability more complicated. Last but not least, protecting private medical information in the cloud requires a comprehensive solution to the security issues surrounding quantum computing, including the possibility that quantum algorithms are susceptible to specific kinds of assaults. To overcome these constraints and properly utilize this unique method of heart disease categorization, there has to be continuous progress in quantum computing, improvements in integration strategies, and stronger security measures.