Five public datasets, including the Z-Alizadeh Sani dataset [35], the Hungary dataset [36], the Cleveland dataset [36], the Long Beach–Virginia dataset [36], and Switzerland datasets [36], which contain 303, 293, 303, 200, and 123 patients, respectively, with 54, 14, 14, 14 and 14 attributes, respectively, were collected and used in this study. For the Z-Alizadeh Sani dataset, 54 clinical features were divided into four groups: demographics, symptoms and examination, electrocardiogram (ECG), laboratory, and echo features, as shown in Table 1.

Other four datasets include 14 attributes: age, gender, chest pain type, resting blood pressure, serum cholesterol, fasting blood glucose, resting ECG results, acquisition of maximal heart rate, exercise angina pectoris, ST depression, slope of peak exercise ST segments, number of major blood vessels, thalassemias (thal) and cardiac diagnosis.

Patients were classified as having CHD if they had a diameter narrowing greater than or equal to 50%. Otherwise, they were considered normal. As a result, each of the five datasets was divided into two groups: the CHD group and the normal group. The numbers of two groups for each of the five datasets are shown in Table 2 (Ref. [35, 36]).

Data preprocessing method: For dichotomous data, such as gender (male or female), obesity (yes or no), left ventricular hypertrophy (yes or no), etc., the values are quantized as 1 and 0, respectively. The dataset we collected and used in this study is small and unsuitable for convolutional neural networks. In addition, compared with convolutional neural network (CNN), MLP has fewer layers and fewer training parameters, which requires less time. Some studies have also shown that when the amount of data is small, the performance of the CNN-based and MLP-based models is comparable. Thus, considering the amount of data in this paper and the CNN and MLP characteristics, MLP was used to establish the CHD detection model. For the missing numeric data values, the average of the existing value for the attribute in the category (CHD or normal) is used to complete the missing values. For the missing categorical data values, the integer data within the quantization range of the category were randomly generated. Four datasets, the Hungary dataset, Cleveland dataset, Long Beach–Virginia dataset, and Switzerland datasets, were merged into a mixed dataset. To eliminate inconsistencies, the numeric data in each dataset were normalized to (0,1) and then merged.

Singular value decomposition-based feature selection method: After data preprocessing for missing data filling with average values, features were selected with the SVD method. SVD is an algorithm widely used in machine learning, which has important applications in dimensionality reduction and feature extraction. The basic principle is to decompose a complex matrix into three matrixes: the left singular vector matrix, the singular value matrix, and the right singular vector matrix. The product of these three matrices is equal to that of the original matrix under certain conditions, which provides great convenience for analyzing and processing data.

Any matrix A can be decomposed into the product of three matrices, as shown in Eqn. 1.

(1)$$A=U\sum V^T$$

where U is an orthogonal matrix and is a diagonal matrix.

The singular value matrix is a diagonal matrix in which the diagonal elements are singular values. These values can reflect the important features of the original matrix. By retaining the largest singular values and their corresponding left and right singular vectors, we can reconstruct the original matrix approximately to achieve dimensionality reduction and feature extraction of data. Through SVD decomposition, the dimensionality reduction of the data can be achieved by the largest singular values and their corresponding left and right singular vectors.

SVD can reveal the potential association of CHD features, which helps to improve the accuracy and efficiency of CHD prediction. This study represents the CHD data as a vector matrix, and the SVD method is used for dimensionality reduction and feature extraction. Specifically, we decompose the CHD data matrix using the SVD method to obtain its feature vectors and singular values. Then, the number of principal components to be retained is selected based on the magnitude of the singular values to acquire a downscaled representation of the data. As a result, 10 features were chosen from the original attributes and used to establish the CHD detection model.

MLP, an artificial neural network with one input layer, multiple hidden layers, and one output layer, as shown in Fig. 2. The MLP has numerous layers of nodes, each fully connected to the next. In addition to the input nodes, each node is a neuron with a nonlinear activation function. A backpropagation algorithm is used to train MLPs. The MLP method can implement nonlinear discriminant and learn any nonlinear input function. A previous studyfound a nonlinear relationship between clinical factors, such as age, weight, sex, etc., and CHD [22]. The MLP is a universal estimator, which can used to estimate nonlinear functions. Therefore, we used the MLP method in this study to establish the CHD prediction model. The number of features selected determines the number of neurons in the input layer; it was set to 10 in this study. The number of hidden layers was set as 5.

CHD prediction model: Since the samples in this study are small, a 5-fold cross-validation method was used to establish the CHD prediction model. Specifically, the stochastic gradient descent method samples were used in the training process, meaning the cross-entropy loss function was applied to optimize the model. The flowchart of this CHD prediction model is shown in Fig. 3. On one hand, in model building, the larger the test set, the smaller the randomness in the measure of model quality, and the more reliable the model performance analysis results are. Due to the small dataset used in this study, a smaller training dataset means a poorer model if we get a large test set by partitioning out more training data. On the other hand, the core of cross-validation is to divide the dataset multiple times and average the results of numerous evaluations, which can eliminate the adverse effects such as overfitting caused by the imbalance of the data in a single partition, and obtain a more reasonable and accurate evaluation of the model. Compared with the traditional model evaluation method (dividing a fixed training set and test set), the advantage of cross-validation is to avoid the problems caused by unreasonable dataset division. The CHD dataset used in this paper is small, meaning it is easy to overfit due to the unreasonable division of the dataset when training the model, so it is more advantageous to use the cross-validation method to evaluate the model. Thus, a 5-fold cross-validation method was used to solve this problem and establish the CHD detection model. Specifically, the normal and diseased samples were divided into five subsets, and then four subsets were used as the training set and the remaining subset as the test set. Then, these were cycled five times until all samples were tested.

Accuracy, precision, recall, F₁-score, and AUC values are used to assess the performance of the CHD prediction model established in this study.

Accuracy is the proportion of samples correctly predicted by the model. The calculation method is shown in Eqn. 2.

(2)$$Accuracy=\frac{TP+TN}{TP+TN+FP+FN}$$

Precision is a measure of the ability of the classifier to identify samples correctly; precision expresses the proportion of samples that are correctly predicted out of the samples identified as positive samples, often called the check rate [37]. The calculation method is shown in Eqn. 3.

(3)$$Precision=\frac{TP}{TP+FP}$$

The recall represents the percentage of all predicted positive samples that can be correctly predicted, usually called the check-perfect rate [38]. The calculation method is shown in Eqn. 4.

(4)$$Recall=\frac{TP}{TP+FN}$$

In Eqns. 2,3,4, TP is the true positive number. Actual represents a positive sample labeled by professional doctors, and the prediction is a positive sample assessed by model. TP indicates that the classifier correctly predicts positive samples. TN is the true negative number. The actual sample is negative, and the prediction is negative. TN indicates that the classifier correctly predicted a negative sample as a negative sample. FP is the false positive number: an actual negative sample predicted a positive sample. FP indicates that the classifier incorrectly predicted a negative sample as a positive sample, also known as a “false positive”. FN is the false negative number: the actual positive sample predicted the negative sample. FN indicates that the classifier incorrectly predicted a positive sample as a negative sample, also known as a “false negative”.

The F₁-score is a composite evaluation metric, the reconciled average precision rate and recall rate [39], as shown in Eqn. 5.

(5)$$F_1=\frac{2\mathrm{·}Precision\mathrm{·}Recall}{Precision+Recall}$$

The precision and recall rates are calculated using Eqns. 3,4, and then these rates are summed to compute the F₁-score; the higher the F₁-score, the better the performance of the classification model.

To analyze and compare the performance of the CHD prediction model proposed in this study, we also established four other CHD prediction models: MLP without SVD, random tree, random forest, and logistic; the results are shown in Table 3.

From Table 3, we can see that compared to the other three models established using SVD-based selection features, our model achieved the best performance with an accuracy of 94.39%, a precision of 94.5%, a recall of 94.4%, F₁-score of 94.4%, and AUC of 98.2%. The AUC values for our proposed model were 13.7% and 1.2% higher than the random tree-based and random forest-based models, respectively, and the same versus the logistic-based model. In addition, we also compared the performance of models established using the MLP method with all features, features selected with the PCA method, and features selected with the SVD method. The results showed that the performance of the SVD-based features method was better than that of the other two. The accuracy of the SVD-based model was 7.3% and 0.5% higher than the all-features- and PCA-based models, respectively.

The visualization performances of the different models established in this study are shown in Fig. 4, whereby Fig. 4a shows the performance of models established with SVD-based features using random tree, random forest, and logistic, respectively. Fig. 4b shows the performances of the models built using the MLP method with all PCA- and SVD-based features, respectively.

Fig. 4a illustrates that the accuracy, precision, recall, F₁-score, and AUC performances of our proposed model are the highest among the analyzed models. A possible reason is that the MLP method can learn the nonlinear function of the input and implement nonlinear discriminant. Fig. 4b demonstrates that all performance indicators for our proposed model are higher in the three models established with different features. A possible reason is that SVD can reveal the potential association of attributes and can improve the performance of the CHD prediction model.

Fig. 5 shows the ROC curves for the CHD prediction models. Fig. 5a shows the receiver operating characteristic (ROC) curves of the models established with different classifiers using SVD-selected features. Fig. 5a illustrates that the ROC curves of the MLP + SVD-based and logistic + SVD-based models are close to coincident, which means no significant difference occurred in the AUC values between the two methods. The AUC value of the MLP + SVD-based model is higher than those for the random forest + SVD and random tree-based models. Fig. 5b shows the ROC curves of the models built with a classifier of the MLP using features selected for the SVD method and all features and features selected for the PCA method. From Fig. 5b, we can see that the AUC value of the SVD-selected features is higher than for all features-based and PCA-based models.

Table 4 shows the confusion matrix computed using the prediction score of the proposed model. The overall prediction accuracy of the proposed model was 94.4%; that is, 286 of the 303 patients were correctly classified, while 5.61% (17/303) patients were misclassified, which corresponds to an 88.89% (80/90) prediction ‘sensitivity’ with a 96.71% (206/213) prediction ‘specificity’. The positive predictive value (PPV) of the risk model was 91.95% (80/87), and the negative predictive value (NPV) was 95.37% (206/216).

We performed the Hosmer–Lemeshow test and calculated a p-value of 0.162 and a chi-square of 7.902, which indicates the effectiveness of the proposed model performs well.

For each sample, there is one disease prediction. A total of 303 predictions were computed using the leave one case out (LOCO) method. These predictions were divided into three groups, with 101 sample predictions in each group, and the number of diseased and non-diseased samples in each group was calculated. The first group was used as the baseline, and the odds ratio value and the corresponding 95% confidence interval values were calculated, as shown in Table 5.

As shown in Table 5, the odds ratio (OR) values increased from 1 to 1.1485 and then to 1.5570, which means the CHD prediction scores increased as the cases were determined to have CHD.

To explore the influence of hyperparameters on the performance of the model, the learning rate was gradually increased from 0.05 to 0.5 at intervals of 0.05, and the changes in model performance indicators are shown in Fig. 6a. As illustrated in Fig. 6a when the learning rate is set to 0.1, the performance of the model is better than others. Similarly, the performance indicators are shown in Fig. 6b for when the momentum is gradually increased from 0.05 to 0.5 at intervals of 0.05. As can be seen from Fig. 6b, when the momentum is set to 0.05, the performance of the model is better than others. Thus, the learning rate and the momentum were set to 0.1 and 0.05, respectively.

To compare and analyze the performance and robustness of our proposed method, we tested our method on a constructed dataset that mixed with four well-known public cardiology datasets: Hungary, Cleveland, Long Beach–Virginia, and Switzerland, which contained 293, 303, 200, and 123 samples, respectively. Moreover, the samples in each of the four datasets have 14 attributes. Thus, 920 cases are contained in this mixed dataset, each with 14 attributes. After data preprocessing, which comprised filling missing data and normalization, the SVD method was applied to extract features from this mixed dataset. Then, machine learning methods, including random tree, random forest, logistic, and our MLP, were used to establish the CHD detection model. In addition, we used all attributes without SVD to construct the CHD detection model; the results are shown in Table 6, and visualization of these results is shown in Fig. 7.

From Table 6, we can see that the accuracy, precision, recall, F₁-score, and AUC of our proposed model was 96.63%, 96.5%, 97.4%, 97%, and 99.1%, respectively, which are all higher than the models established using random tree, random forest, logistic, and the MLP without SVD. Specifically, the accuracy, precision, recall, F₁-score, and AUC of our proposed model are higher by 2.61%–7.06%, 3.3%–6.6%, 3%–6%, 3.6%–6.4%%, and 0.9%–9.7%, respectively, than the other four CHD prediction models established in this study.

From Fig. 7, we can see that the performance indicators for the accuracy, precision, recall, F₁-score, and AUC of our proposed model are the highest of the five CHD prediction models. The experimental results show that the SVD and MLP-based model performs well in predicting heart disease, outperforming the other methods in accuracy, recall, and F₁ values, and has a higher predictive performance. This indicates that SVD can extract important features from the data and input them into the MLP model for effective classification and prediction.

Table 7 shows the confusion matrix calculated using the prediction score of the proposed model on the mixed dataset. The accuracy of the proposed model was 96.63%; that is, 889 of the 920 cases were correctly classified, while 3.37% (31/920) cases were misclassified. Moreover, the sensitivity and specificity values were 96.8% (393/406) and 96.5% (496/514), respectively. The PPV of the risk model was 95.62% (393/411), and the NPV was 97.45% (496/509).

To analyze and compare the SVD method contribution to the performance of the CHD prediction model, we established the CHD prediction model with all 14 attributes and features extracted by the SVD method and tested it on four well-known cardiology datasets. The performances of the CHD prediction models on the different datasets are shown in Table 8; visualization of these results is shown in Fig. 8.

From Table 8, we can see that the performance of the CHD detection model established using SVD-based selected features is better on each of the four datasets than the model built using all features. Specifically, the AUC values of our proposed model achieved 97.50%, 100.00%, 100.00%, and 99.70% on the Cleveland, Hungarian, Switzerland, and Long Beach–Virginia datasets, respectively, which is 11.1%, 16.2%, 22.5%, and 19.8% higher, respectively, than the model built using all features. The precision, recall, and F₁-score values of our proposed model on the four datasets are 5.2%–17.3%, 4.3%–16%, and 4.8%–16.6% higher, respectively, than the model built using all features.

From Fig. 8, we can see that for each of the four datasets, the performance indicators of our proposed model are all higher than the model built with all features. These results indicate that introducing the SVD method for feature extraction and further model construction helps improve its performance. This may be due to their existing redundancy and correlation between attributes in the dataset that affect the performance of the model. The SVD method can reduce dimensions and extract data features. In addition, the potential association between characteristics of the CHD dataset can be revealed using the SVD method, thus helping to improve the performance of the model.