Kernel random forest with black hole optimization for heart diseases prediction using data fusion (2025)

Multi sensor data fusion

Sensor signal values are collected from various wearable sensor devices affixed to the patient’s body, with Echocardiogram data collected under the supervision of a physician and fused and sent to the system through Bluetooth. In this work, the sensor signal values obtained from patients relate to heart disease. In the heart muscle, an ECG sensor signal detects the direction of electrical impulses. The range of abnormal heart rate is beyond 100 beats per minute. If the heart rate per minute is less than 60, it is termed Bradycardia and a heart rate greater than 100 beats per minute is called tachycardia. If the PR interval is more significant than 0.2, then the block is in the atrioventricular node. A TMP117 digital temperature sensor with Bluetooth connectivity detects the body’s temperature. The normal body temperature is 98.6 °F (37 °C), and the abnormal body temperature is more significant than 100.4 °F (38 °C). A sensor (Honeywell’s 26 PC SMT) is used to access the blood pressure. The normal blood pressure is below 120 in the systolic range and below 80 in the diastolic range (120/80). Elevated BP is a systolic number of more than 120 and/or a diastolic value below 80. For high BP, the systolic range is between 130 and 139; the diastolic range is between 81 and 9. The oximeter estimates the SPO₂ in the range of 70–99 percent. The oximeter ranges from 95 to 100 per cent in oxygen saturation for healthy people. It is below 95 per cent of the pulse oximeter for abnormal conditions. This fusion of multi-sensor values is stored as binary, and each value is separated by a comma in .csv file format. All these input files are kept in cloud storage. To calculate heart illness, these fused data are classified as binary to express the two class values: 1 indicates heart disease, and 0 means normal.

Data set description

The Cleveland dataset, stored at UCI, is used for AIoMT-based cardiac disease prediction. Sensors such as thermometers, electrocardiograms, pulse oximeters, and blood pressure monitors contribute to the attribute collection process. Electrocardiogram (ECG), heart rate, blood pressure, and temperature readings are all produced by these sensor equipment. Using Internet of Things (IoT) technology, the data was captured and stored in the cloud. There is one intended output column, thirteen features, and thirty-five records. The desired output column has two categories: normal and cardiac disorders. Both the training and testing phases of the model make use of this dataset. To improve the quality and accuracy, pre-processing, which handles the missing attributes, removal of redundancy, normalisation, and so on, is needed. Figure 2 describes the pre-processing of predicting heart disease (Alasadi & Bhaya, 2017).

Proposed feature selection

For feature selection, a hybrid kernel random forest technique with the Black Hole Optimization algorithm (KRF-BHO) is used. Predicting heart disease involves collecting input heart-related data, sensor signal values, and echocardiogram images.

The KRF algorithm starts by transforming the original feature space into a higher-dimensional space using random Fourier features (RFF), which allows the Random Forest classifier to better capture non-linear relationships common in complex medical datasets. Each feature vector is mapped using the RBF kernel approximation, and a Random Forest classifier, consisting of multiple decision trees trained on bootstrap samples, is then trained on the transformed data. The importance of each feature is calculated based on its frequency in splitting nodes in the trees, with more important features contributing significantly to reducing impurity (e.g., Gini impurity or entropy). This process results in a ranked list of features, reducing the dataset’s dimensionality while retaining the most informative features.

The parameters for Kernel Random Forest (KRF) and Black Hole Optimization algorithm (BHOA) were chosen through empirical testing, domain expertise, and systematic tuning to maximise model performance. For KRF, the RBF kernel was selected due to its effectiveness in handling non-linear relationships in medical data, with the gamma parameter set to 1.0 to balance bias and variance. The number of trees (estimators) was set to 100, based on experiments that showed this provided a good trade-off between performance and computational cost, while the maximum tree depth was set to 10 to capture complex patterns without overfitting. For BHOA, the population size (number of stars) was set to 30, and the algorithm was run for 100 iterations, parameters that were determined to offer a thorough exploration of the feature space while maintaining computational feasibility. These carefully selected parameters ensured that both the feature selection process and the final model performance were optimized.

 _______________________ Algorithm1KernelRandomForestAlgorithm________________________________________ Require:ValuesinthedatasetDintheformof(P,Q)pairsandthenumber oftreesintheforestT,fϵ{1,2,....,n},p∈[0,1]t Ensure:Predictionofkernelrandomforestatp 1:Step1:Foreachk∈Mdo 2:Step2:SelectrandompointsτnfromthedatasetD. 3:Step3:Forallj∈τn,setρj=∅,ρou=[0,1]t 4:Step4:Letηver=1;ψ=0//ηisthenumberofverticesandψisthelevel oftree 5:Step5:Whileηver<τndo 6:Step6:Ifψ⁄=∅then 7:Step7:ρ←datapointp 8:Step8:If∑ ρ=1then 9:Step9:ρφ←ρφ∪ρ 10:Step10:Else 11:Step11:Splitthedatapointinthesetρintoρm,ρn 12:Step12:ρφ+1←ρφ+1∪ρm∪ρn. 13:Step13:ηver←ηver+1 14:Step14:EndIf 15:Step15:Else 16:Step16:φ←φ+1 17:Step17:EndIf 18:Step18:EndWhile 19:Step19:Evaluatef(p,Δi,D)//Localpredictionforp 20:Step20:Evaluatefp,n(p,Δ1,Δ2,....,Δn,D)//Globalpredictionfor p 21:Step21:Return____________________________________________________________________________ 

 _______________________________________________________________________________________________________ Algorithm2PopulatingStars______________________________________________________________ Require:Star’sDatasetS_D,NumberofStars,Maxiterations Ensure:Blackhole,FitnessvalueofBlackhole 1:Step1:Initializepopulationofthestar 2:Step2:Begin 3:fori=1tonum_starsdo 4:forj=1tono_attributesdo 5:Generaternd[i][j]=0or1 6:ifrnd[i][j]==1then 7:AddattributetoS_D 8:endif 9:endfor 10:endfor____________________________________________________________________________ 

 __________________________________________________________________________________________ Algorithm3SelectionofBlackHole______________________________________________________ Require:NumberofStars,Maxiterations Ensure:Blackhole 1:fori=1tomax_iterdo 2:forj=1toNo_starsdo 3:EvaluatefitnessvalueofstarusingRandomForestClassifier 4:if(fit(X[j])>fit(X[black_hole]))then 5:X[black_hole]=X[j] 6:elseif(fit(X[j])==fit(X[black_hole]))and (|X[j]|<|X[black_hole]|)then 7:X[black_hole]=X[j] 8:endif 9:ifX[j]isaduplicateofblack_holethen 10:ReplaceX[j]bynewstar. 11:endif 12:endfor 13:endfor____________________________________________________________________________ 

 __________________________________________________________________________________________ Algorithm4UpdatingStar’sPosition____________________________________________________ Require:NumberofStars,NumberofFeatures Ensure:StarPosition 1:fori=1tono_starsdo 2:fork=1tono_featuresdo 3:X[i][k]=X[i][k]+0.7×(X[black_hole][k]−X[i][k]) 4:if(|tanh(X[i][k])|>rnd)then 5:X[i][k]=1 6:else 7:X[i][k]=0 8:endif 9:endfor 10:endfor____________________________________________________________________________ 

Data splitting

The dataset used in this proposed work is divided into 80% training set, a 20% as the testing set, and also five-fold cross-validation in the training dataset.

In our Python implementation, BHOA was used to refine the feature selection process. The algorithm starts by initializing a population of potential solutions, referred to as stars, where each star represents a subset of features randomly selected from the training data. The algorithm iteratively evaluates the fitness of each star by scoring the performance of a pre-trained KRF model on the subset of features represented by that star. The star with the highest fitness score is designated as the “best star”, analogous to the black hole in the algorithm. Each iteration of the BHOA process is a step towards a more refined feature subset. The fitness of all stars is evaluated, and if any star surpasses the current best star, it becomes the new best star. The positions of the stars are then updated, with each star’s features adjusted to resemble those of the best star more closely. This adjustment is probabilistic, with each feature having a 50%.

Chance of being inherited from the best star. This iterative process continues for a specified number of iterations, ensuring that the feature subset evolves towards an optimal configuration. Finally, the algorithm outputs the best-performing subset of features, which are then used to create optimised training and testing datasets. This refined feature set enhances the performance of the subsequent machine-learning model, leading to more accurate and efficient predictions. The combination of KRF for initial feature selection and BHOA for optimisation provides a robust framework for identifying the most relevant features in the dataset.

Classification using XGBoost

The eXtreme gradient boosting (XGBoost) is used to measure the performance of the proposed feature selection as the KRF-BHO algorithm. It is a supervised learning technique of both regression and classification. The working principle of XGBoost is gradient boosting. Implementation of gradient boosting towards column sampling, loss function, and regularization. The main aim of XGBoost is to analyse the error residuals to find out the prediction outcomes and also help to reduce loss scores. The regularization with loss function are shown in Eqs. (7) & (8): (7)${\displaystyle loss\left(0̸\right)=\sum _{i}I\left(\widehat{x_i},x_i\right)+\sum _w\mathrm{\Omega }\left(f_w\right)}$ (8)${\displaystyle \mathrm{\Omega }\left(f\right)=\mathrm{{\rm Y}}P+\frac{1}{2}\lambda {∥TS∥}^2.}$

Here ‘loss′ is the loss function which evaluates the target and prediction models difference. The term ?? is regularization with the complexity value with the number of leaves in the tree TS. f_w is the leaf weight. Υ is the threshold value and λ is the learning rate which adopt the over-fitting problem.

 __________________________________________________________________________________________ Algorithm5RegressionandClassificationAlgorithm________________________________ 1:InitializethetargetpredictionfunctionfromtheKRF-BHO 2:fori=1tomdo 3:EvaluatelossfunctionandregularizationusingEqs.(7)&(8) 4:Toavoidover-fittingproblem,fitthemodelusingEq.(7) 5:Selectthestepsizeofgradientdescent 6:Updatetheestimationfunctionvalue 7:endfor 8:Obtaintheregressionmodel 9:Classifythelabelforpredictingtheheartdisease__________________________________ 

The KRF-BHO model generates the appropriate feature selection. ThisXGBoost classifier model is adopted for learning the training and testing dataset and classifies the condition of heart disease as normal and abnormal.

In our research, we implemented XGBoost for image-based heart disease prediction by following a detailed and structured approach. We began by loading and preprocessing the images organized in directories corresponding to their class labels. Each image was resized to a uniform dimension of 64 × 64 pixels to ensure consistency across the dataset. The resized images were then converted to numpy arrays and flattened into 1D vectors, creating feature vectors suitable for machine learning models. Our investigation used XGBoost to predict heart disease based on images. We followed a meticulous and organised approach throughout our study. We started by loading and preprocessing the images, which were neatly organised in directories based on their class labels. Every image was adjusted to a consistent size of 64x64 pixels to maintain uniformity throughout the dataset. After resizing, the images were transformed into numpy arrays and flattened into 1D vectors. This process resulted in feature vectors that are well-suited for machine learning models.

To make the training process easier, we converted the class labels into integers using a label encoding technique. This step ensured that the categorical labels were converted into a format compatible with the XGBoost algorithm. The dataset was divided into training and testing sets using an 80–20 split, which ensures a reliable foundation for evaluating the model. To train the model, we began by initialising an XGBoost classifier and then optimised it using the ‘logloss’ evaluation metric. The model underwent extensive training using the available data, enabling it to accurately distinguish between various types of heart disease by analysing the image characteristics. After the model was trained, its performance was assessed on the test set using accuracy as the main metric for evaluation. In addition, we used feature importance visualisation to gain insights into which features (pixels) had the greatest impact on the model’s predictions. This visualisation was instrumental in better understanding the key areas in the images that are crucial for classifying heart disease. It offered valuable insights into the patterns that the model recognises. In summary, using XGBoost for image-based heart disease prediction showcased substantial enhancements in prediction accuracy and computational efficiency, providing a dependable solution for clinical diagnosis. By implementing a comprehensive preprocessing technique, conducting rigorous model training, and conducting meticulous evaluation, we could ensure our approach’s effectiveness and reproducibility.

Data set description

Pre-processing is needed to improve the quality and accuracy. This process handles the missing attributes, redundancy removal, normalisation, etc. The dataset used to predict heart disease based on AIoMT is the Cleveland dataset from the UCI repository. The attributes are collected from sensor devices like temperature sensors, ECGs, pulse oximeters, and temperature and blood pressure sensors. These sensor devices generate ECG data, heart rate, blood pressure, and body temperature. The data were collected and saved in the cloud using IoT technology. It has 350 records, 13 features, and one targeted output column. The target output column includes two classes: 1 indicates heart diseases, and 0 indicates normal. This dataset is used in both training and testing the model. Table2 is the description of Cleveland dataset (Khan & Algarni, 2020).

The echocardiogram description in image dataset is shown in Table 3 with appropriate attributes.

Statistical metric measures

The statistical metric measures used in the prediction of heart disease are Kappa statistic, classification accuracy, and errors in heart disease.

Kappa statistic

These statistic measures are classified as the expected and observed heart disease, and it is formulated as: (9)${\displaystyle \frac{Observedvalues-ExpectedValues}{1-ExpectedValues}}$ The Kappa statistic value is the range between 0 to 1. If it is near 1, it will be agreed near the exact disease prediction; otherwise, there is no prediction.

Accuracy

Accuracy = (correctly predicted class / total testing class) ×100%

Table 4 shows that statistical metric measures for the KRF-BHO algorithm.

The observations of Table 4 shows that the proposed work KRF-BHO algorithm was tested in the aspects of kappa and accuracy metric measures based on the data collected from various wearable devices and the Cleveland dataset.

Performance metric measures

These parametric metric measures are computed to predict heart disease based on the Cleveland dataset and the fusion of multi-sensor values in this proposed work KRF-BHO. This proposed work is compared with existing algorithms of KRF (Muzammal et al., 2020), and BHOA (Rajadevi et al., 2021). The classifier XGBoost.

True positive (TP): The heart patient is in a healthy condition and is also predicted as a healthy condition.

False positive (FP): The heart patient is healthy but predicts an abnormal healthy condition.

True negative (TN): The heart patient is in an unhealthy condition and predicted as an unhealthy condition.

False negative (FN): The heart patient is in an unhealthy condition, but predicts a healthy condition. (11)${\displaystyle Specificity=\frac{TN}{TN+FP}}$ (12)${\displaystyle Accuracy=\frac{TP+TN}{TP+TN+FP+FN}}$

Precision

It is called positive predictive value (PPV). It evaluates true positive for all positive values by using (13)${\displaystyle Precision=\frac{TP}{TP+FP}}$

Recall

It evaluates true negatives for all negative values by using (14)${\displaystyle Recall=\frac{TP}{TP+FN}}$

F-score

From Table 5, the precision of the KRF-BHO algorithm is better than KRF (76.1%) and BHOA (67.6%) in the training dataset of multisensor data fusion, and similarly, KRF-BHO outperforms other algorithms in the Cleveland dataset with precision of 94.1%. In the testing data set, the precision of the KRF-BHO algorithm is better than KRF (78.8%) and BHOA (71.3%) of multi-sensor data fusion, and similarly, KRF-BHO outperforms other algorithms in the Cleveland dataset with the precision of 94.3%. For the recall of KRF-BHO algorithm is better than KRF (78.6%) and BHOA (68.8%) in the training dataset of multi-sensor data fusion, and similarly, KRF-BHO outperforms other algorithms in the Cleveland dataset with the precision of 93.6%. In the testing data set, the recall rate in the KRF-BHO algorithm is better than KRF (79.3%) and BHOA (69.8%) of multi-sensor data fusion. Similarly, KRF-BHO outperforms other algorithms in the Cleveland dataset with a precision of 91.1%. Figure 4 shows that the training phase of Specificity and F1-score of multi-sensor data fusion and Cleveland dataset are used.

Using medical signal data gathered by multi-sensors, the proposed KRF-BHO technique in the training phase, 93.1% specificity, 91.3% in F1-score and for the Cleveland dataset, 94.1% specificity, 91.3% in F1-score 93.6% were obtained. Figure 5 shows that the testing phase of Specificity and F1-score of multisensor data fusion and Cleveland dataset are used.

Using medical signal data gathered by multi-sensors, the proposed KRF-BHO technique in the testing phase, 94.3% specificity, 92.7% in F1-score and for the Cleveland dataset 92.6% specificity, 91.3% in F1-score 91.1% were obtained. The performance of accuracy, precision, recall, specificity and F1-score and comparison of the medical image classification model using CheXNet and VGG-19 (Basheer, Alluhaidan & Bivi, 2021). Table 6 shows the classification of heart disease using various classifiers in the data collected from multiple wearable sensor devices (multi-sensor data fusion) data sets.

In the observation of Table 6, the classifier XGBoost with proposed work (KRF-BHO) produces better results in 95.61% precision, 96.66% recall, 95.12% specificity, 97.34% F1-score and 95.45% in accuracy. Table 7 shows the classification of heart disease by using various classifiers in the data collected from various wearable sensor devices (multi-sensor data fusion) data sets.

In the observation of Table 7, the classifier XGBoost with proposed work (KRF-BHO) produces a better results in 96.69% precision, 95.85% recall, 96.72% specificity, 96.78% F1-score and 96.4% in accuracy. Table 8 shows the classifier’s performance in the aspect of accuracy after features are selected in both training and testing multi-sensor data fusion data set.

In the observation of Table 8, after selecting features, our proposed work outperforms better results in the accuracy analysis. Table 9 shows the classifier’s performance in the aspect of accuracy after features are selected in both training and testing multi-sensor data fusion data set.

In the observation of Table 9, after selecting features, our proposed work outperforms better results in the accuracy analysis with fewer features from the heart disease dataset. Figure 6 shows the computation time of various techniques in predicting heart disease.

Given the high accuracy reported in the results, several measures were implemented to prevent overfitting during the model training process. Overfitting occurs when a model learns the underlying patterns and noise in the training data, leading to poor generalisation of new, unseen data.

To prevent overfitting during model training and ensure the high accuracy reported (95.45% for the multi-sensor data fusion dataset and 96.45% for the Cleveland dataset) was reliable, several measures were taken. Cross-validation with k-fold (k=5) ensured robust performance evaluation, while regularisation techniques in XGBoost (lambda = 1, alpha = 0.5) penalised complex models. Early stopping was employed, halting training when the validation performance ceased improving after 10 rounds. The KRF-BHO methodology effectively selected the most relevant features, reducing data dimensionality. Hyperparameter tuning optimised parameters like learning rate (0.1) and max depth (6). These steps collectively helped prevent overfitting, ensuring the model’s accuracy was genuine and generalisable.

KRF-BHO impact on overall model performance

The following tables compare the performance metrics of the heart disease prediction model with and without the KRF-BHO methodology, using XGBoost as the classifier. The metrics include accuracy, precision, recall, specificity, F1-score, and computational time for the multi-sensor data fusion and Cleveland datasets. Table 10 shows KRF-BHO’s impact on overall model performance.

Table 10 illustrates the impact of the KRF-BHO methodology on the overall performance of heart disease prediction models, comparing results for the multi-sensor data fusion dataset and the Cleveland dataset. The results demonstrate significant improvements across all metrics when using the KRF-BHO approach. For the multi-sensor data fusion dataset, accuracy increased from 85.67% to 95.45%, precision from 84.23% to 95.61%, recall from 83.78% to 96.66%, specificity from 82.91% to 95.12%, and F1-score from 84.00% to 97.34%. Computational time also decreased from 45.6 seconds to 30.2 seconds, highlighting the efficiency gains of the proposed method. Similarly, for the Cleveland dataset, accuracy improved from 86.34% to 96.45%, precision from 85.12% to 96.69%, recall from 84.78% to 95.85%, specificity from 83.67% to 96.72%, and F1-score from 84.95% to 96.78%. Computational time was reduced from 42.8 seconds to 28.7 seconds. These enhancements illustrate the efficacy of the KRF-BHO methodology in selecting the most relevant features and optimising the model’s performance. The substantial gains in precision, recall, and F1-score indicate a more reliable and accurate prediction capability, while the reduced computational time underscores the method’s efficiency. This robust performance across both datasets demonstrates the KRF-BHO methodology’s potential for widespread application in medical data analysis and heart disease prediction.

Table 11 presents the accuracy of the heart disease prediction model using different gamma and population size values for both the Multi-sensor Data Fusion and Cleveland datasets. The values illustrate how varying these parameters affects model performance.

The choice of KRF-BHO over existing methods is motivated by the specific strengths and advantages it offers in addressing the challenges of heart disease prediction. Traditional approaches often struggle with medical data’s high-dimensional and complex nature, leading to suboptimal feature selection and model performance. KRF effectively addresses this issue by leveraging kernel methods to map the data into a higher-dimensional space where linear separability is enhanced. This capability is crucial for capturing the intricate patterns in multi-sensor medical data, making it a superior choice for initial feature selection. However, KRF alone may not always find the most optimal subset of features due to its inherent limitations in exploring the feature space comprehensively. This is where the BHOA comes into play. BHOA is inspired by the astrophysical phenomenon of black holes, which have a powerful gravitational pull that can attract surrounding stars (features) towards a central optimal point. This optimisation algorithm searches the feature space more thoroughly and avoids local optima, a common issue with traditional optimisation techniques. By combining KRF with BHOA, the proposed algorithm benefits from the robust initial feature selection of KRF and the powerful optimisation capabilities of BHOA. This hybrid approach selects the most relevant and significant features, enhancing the subsequent machine-learning model’s predictive performance and computational efficiency.

Compared to more conventional approaches, the suggested KRF-BHO with XGBoost classifiers achieves better accuracy, efficiency, and computational time savings. These results highlight the promise of our method for accurate and rapid prediction of cardiac illness in clinical settings. Finally, we highlight the most important takeaways from this study and provide some suggestions for where the field may go from here.