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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>AutoML PyCaret and SHAP explainable AI for ECG signal classification based on amplitude variability</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Dmytro Tymoshchuk</string-name>
          <email>dmytro.tymoshchuk@gmail.com</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Iryna Didych</string-name>
          <email>iryna.didych1101@gmail.com</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Andriy Sverstiuk</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Lyubomyr Mosiy</string-name>
          <email>lmosiy@gmail.com</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Yuri Palianytsia</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>I. Horbachevsky Ternopil National Medical University</institution>
          ,
          <addr-line>Maidan Voli St., 1, Ternopil, 46002</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Ternopil Ivan Puluj National Technical University</institution>
          ,
          <addr-line>Ruska str. 56, Ternopil, 46001</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>Cardiovascular diseases remain the leading cause of global mortality, necessitating advanced non-invasive diagnostic tools. Traditional electrocardiogram (ECG) analysis often focuses on temporal rhythm parameters, frequently overlooking the diagnostic potential of cycle-to-cycle amplitude variability of characteristic waves. In this work, we propose a novel information technology that integrates mathematical modeling of amplitude variability with automated machine learning (AutoML) and explainable artificial intelligence (SHAP). Utilizing open PhysioNet databases, we extracted ten statistical descriptors of amplitude variability to form a dataset comprising four classes: normal, pacemaker, arrhythmias, and morphological abnormalities. The Random Forest model, optimized via the PyCaret library, demonstrated superior performance, achieving an accuracy of over 95% and an Area Under the Curve (AUC) exceeding 0.96 across all classes. Furthermore, SHAP analysis identified Skewness and Kurtosis as the most critical features driving the model's predictions, providing both global and local interpretability. The results confirm that combining amplitude variability descriptors with explainable AutoML frameworks significantly enhances diagnostic precision and transparency, ofering a robust foundation for reliable clinical decision support systems.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;ECG signal</kwd>
        <kwd>amplitude variability</kwd>
        <kwd>machine learning</kwd>
        <kwd>AutoML</kwd>
        <kwd>PyCaret</kwd>
        <kwd>explainable AI</kwd>
        <kwd>SHAP</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>Cardiovascular disease (CVD) remains the leading cause of mortality worldwide, accounting for more
than 17.9 million deaths annually, according to the World Health Organization (WHO).
Electrocardiography, as a non-invasive method of recording the electrical activity of the heart, plays a fundamental
role in the early diagnosis and monitoring of cardiac pathologies. The electrocardiogram (ECG) contains
critical information about the functional state of the myocardium, encoded in the morphology of the
characteristic P, Q, R, S, and T waves and their temporal relationships.</p>
      <p>Traditional methods of ECG analysis primarily focus on temporal parameters of heart rhythm (RR
intervals, heart rate variability) or morphological features of individual cardiac cycles. However, the
cycle-to-cycle amplitude variability of characteristic ECG waves remains insuficiently studied, despite
its potential diagnostic value. The amplitude variability function, which reflects the dynamic changes
in the amplitude values of the P, Q, R, S, and T waves between successive cardiac cycles, may serve as a
sensitive indicator of early pathological alterations in the cardiovascular system (CVS) that precede the
clinical manifestation of disease.</p>
      <p>
        Machine learning is already being applied across a wide range of domains, including finance [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ],
cybersecurity [
        <xref ref-type="bibr" rid="ref2 ref3">2, 3</xref>
        ], transportation [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], medicine [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], materials science [
        <xref ref-type="bibr" rid="ref6 ref7">6, 7</xref>
        ], and energy [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. The
integration of machine learning and artificial intelligence methods into cardiac diagnostics opens up
unprecedented opportunities for the prediction and early detection of heart disease. Recent studies
demonstrate that deep learning algorithms achieve high accuracy in ECG classification, significantly
outperforming traditional approaches. Advanced AI architectures are capable of automatically
detecting complex patterns and hidden regularities in ECG data that often remain invisible during visual
interpretation or conventional analysis [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ].
      </p>
      <p>The main contribution of this study is the development and experimental validation of an information
technology for cardiovascular disease diagnosis based on ECG amplitude variability using AutoML
(PyCaret) and Explainable AI (SHAP), which ensures high classification accuracy and interpretability of
results.</p>
      <p>The remainder of this paper is organized as follows. Section 2 reviews recent research in the field of
ECG analysis. Section 3 describes the datasets and the methodology for model development. Section 4
presents the experimental results and discussion. Finally, Section 5 summarizes the conclusions and
outlines future research directions.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related works</title>
      <p>The current state of research in the field of cardiac signal analysis is characterized by the rapid
development of artificial intelligence and machine learning methods for the diagnosis of cardiovascular
diseases (CVDs). This systematic review covers key scientific works published between 2024 and 2025,
demonstrating a variety of approaches ranging from traditional algorithms to innovative deep learning
architectures.</p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ], the authors proposed a new approach to detecting atrial fibrillation and normal sinus rhythm
using the concept of TinyML (Embedded Machine Learning). The researchers developed a highly
eficient system based on convolutional neural networks, adapted to run on the ESP32 microcontroller.
A distinctive feature of their approach is the use of preprocessing of data from the PTB-XL database,
including filtering and segmentation of time records into individual heart cycles. The experimental
results demonstrate high eficiency: the model achieved an accuracy of 94.1% during training and 94.04%
during testing, while the inference accuracy on the microcontroller was 99.33% when using data from a
patient simulator. This research opens up new prospects for the creation of portable diagnostic devices
with low energy consumption.
      </p>
      <p>
        Article [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] presents a comprehensive study of the impact of one-dimensional convolutional neural
networks on the accuracy of heart rate metrics for electrocardiogram and ballistocardiography (BCG)
signals. The researchers focused on the critical problem of motion artifacts, which negatively afect the
reliability of vital information such as heart rate. The proposed method for detecting motion artifacts
is based on a 1D CNN architecture that analyzes one-second segments of data and classifies them as
clean or noisy. The results of the experiments showed a classification accuracy of 95.9% for ECG and
91.1% for BCG signals. The most impressive achievement is the increase in the sensitivity of detection
algorithms: from 75% to 98.5% for ECG and from 72.1% to 94.5% for BCG for signals contaminated at 0
dB signal-to-noise ratio.
      </p>
      <p>
        In their work [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ], researchers presented an innovative methodology for predicting heart disease
using convolutional neural networks on an expanded PTB-XL+ database. The authors emphasize the
importance of automating ECG analysis, as traditional subjective interpretation is labor-intensive and
prone to errors. The developed CNN model demonstrates the ability to independently study features
from raw data, making it a potentially practical tool for improving diagnostic eficiency. Experimental
validation showed an average accuracy of 77.89% in identifying patterns of various heart diseases,
including arrhythmias, ischemic heart disease, and myocardial infarction. The results confirm the
promise of CNN approaches for improving clinical decision support systems.
      </p>
      <p>
        Scientists in [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ] presented a fundamentally new approach to the classification of cardiac signals by
developing an optional multimodal architecture with multiscale receptive fields of a CNN-enhanced
transformer. The key innovation is the introduction of switchable modal experts for staged
representation: the first stage extracts modality-specific features and balances intermodal relationships,
while the second stage captures cross-modal interaction information in a shared latent space. The
uniqueness of the architecture lies in its flexibility—thanks to switchable modal experts, the model
can be applied to both multimodal and unimodal data. The researchers also solved the problem of
performance imbalance between transformers and CNNs by combining the advantages of CNNs to
build a CNN-enhanced transformer with improved patch embedding and the integration of convolution
and residual connections.
      </p>
      <p>
        The authors [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ] developed an advanced deep learning approach for accurate ECG analysis, which
involves both wave delineation and beat-type classification tasks. The researchers integrated two new
schemes into the deep learning model. The first scheme represents an adaptive beat segmentation
method that determines the optimal duration for each heartbeat based on RR intervals, mitigating
segmentation errors from traditional fixed-period segmentation. The second scheme incorporates
information about the relative heart rate of the target beat compared to neighboring beats, improving
the model’s ability to accurately detect premature atrial contractions (PACs). Comprehensive evaluations
on the PhysioNet QT, MIT-BIH Arrhythmia, and real-world wearable device datasets demonstrated
high performance: 99.81% sensitivity for normal beats, 99.08% for premature ventricular contractions,
and 97.83% for PACs. For wave delineation, F1 scores of 0.9842 for non-wave segments, 0.9798 for P
waves, 0.9749 for QRS complexes, and 0.9848 for T waves were achieved.
      </p>
      <p>
        Publication [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ] presents a novel machine learning approach for ECG classification using scattering
wavelet features. The research methodology includes preprocessing of ECG segments followed by
wavelet scattering to extract low-variance features with reduced dimensions. Key features are selected
using the Minimum Redundancy and Maximum Relevance (MRMR) algorithm, chosen after a
comparative analysis of various feature selection algorithms. The researchers conducted a comprehensive
comparative analysis of various machine learning models: Support Vector Machine (SVM), K-Nearest
Neighbor (KNN), decision trees, and artificial neural networks with 10-fold cross-validation. Among
the twenty models studied, cubic SVM demonstrated the highest accuracy of 99.84%, which indicates
the efectiveness of combining wavelet dispersion with optimized machine learning algorithms.
      </p>
      <p>
        Researchers [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ] developed a complex methodology for detecting and classifying heart murmurs based
on statistically significant features obtained from comparing spectrogram images of phonocardiogram
recordings. The authors used short-time Fourier transform (STFT) to generate spectrograms of PCG
signals, which were then compared using Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity
Index Matrix (SSIM). Statistical analysis showed that the SSIM and PSNR similarity indices independently
provided 88.23% and 87.94% accuracy, respectively, for distinguishing normal heart sounds from murmurs
with a P-value of 2.05 × 10 −19 . The best classification results were achieved using a coarse tree with
PCA: 85% accuracy during training and 92.50% during testing for the classification of normal heart
sounds and diferent types of murmurs.
      </p>
      <p>
        Scientists in [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] proposed a comprehensive method for processing cardiac signals that combines
wavelet analysis with deep learning algorithms based on artificial intelligence. The scientists used
continuous wavelet transforms to calculate scalograms of various cardiac pathologies, creating diferent
types of these signals. The artificial intelligence architecture uses two well-known neural networks,
GoogLeNet and SqueezeNet, which have been suficiently trained in similar applications such as image
processing and machine vision. The experimental patient data for the simulation were obtained from
the Massachusetts Institute of Technology’s standard PhysioNet medical engineering dataset.
      </p>
      <p>In publication [18], the author presented an efective 34-layer ResNet deep network for classifying
three types of cardiovascular diseases based on features extracted from the time-frequency domain
in the form of scalograms. The researcher combined the proposed ResNet-34 model with transfer
learning techniques, demonstrating improved results. The algorithms were compared with other deep
networks, such as two diferent structures of a convolutional neural network (CNN) and a recurrent
neural network (RNN), as well as with a classifier based on Sparse Non-Negative Matrix Factorization
(SNMF) dictionary learning. The results showed that the ResNet-34-based model has better performance
across various evaluation criteria, such as accuracy, sensitivity, and reliability.</p>
      <p>Work [19] presented an innovative approach to ECG classification using spiking neural networks
(SNNs) with an attention mechanism. The key innovation is the adaptation of trained parameters from
artificial neural networks (ANN) to SNN using leaky integrate-and-fire (LIF) neurons. This transfer
learning strategy not only leverages the advantages of both types of neural network models but also
solves the training problems associated with SNNs. Spiking neural networks, which more accurately
mimic brain neural activity through spiking processing, ofer a promising path for energy-eficient
computing models. Experimental evaluation on two publicly available ECG benchmark datasets showed
an overall accuracy of 93.8% on the MIT-BIH Arrhythmia dataset and 85.8% on the PhysioNet Challenge
2017 dataset. These results highlight the potential of SNNs in medical diagnostics, ofering a path to
more accurate, eficient, and less resource-intensive analyses of heart disease.</p>
      <p>In publication [20], researchers proposed a hybrid approach for ECG classification based on machine
learning using various digital diferentiators and two-dimensional complex wavelet transform (DTCWT).
The study presents a systematic approach to classifying ECGs into six diferent classes based on
annotations from the MIT-BIH Arrhythmia database. The methodology includes manual feature
extraction using DTCWT to capture critical information from ECGs. Four innovative digital filters
are used to diferentiate ECGs in order to further enhance the discriminatory power of the extracted
features. The Pan-Tompkins algorithm has been improved using these digital diferentiators, increasing
its efectiveness in detecting QRS complexes.</p>
      <p>The paper [21] presents a methodological framework for clustering classification for accurate
processing of medical time series. The authors integrated agglomerative hierarchical clustering with
representations of Hilbert vector spaces of medical signals and biological sequences. The proposed
method demonstrated 96% success in classifying protein sequences by function and efectively identified
families in a large set of proteins. In the analysis of cardiac signals, the method retained 0.996 variance
in a compressed 6-dimensional space, accurately classifying 87.4% of simulated atrial fibrillation groups
and 99.91% of major groups when conduction direction was excluded.</p>
      <p>Researchers in [22] developed an innovative approach for classifying heart sounds using harmonic
and percussive spectral features from phonocardiograms with a deep feedforward artificial neural
network. The methodology includes advanced digital signal processing techniques applied to PCG
recordings from the PhysioNet 2016 dataset. A distinctive feature of the approach is the use of
harmonicpercussive source separation (HPSS) to extract separate harmonic and percussive spectral features. The
feature set consists of 164 attributes, including Chroma STFT, Chroma CENS, mel-frequency cepstral
coeficients (MFCC), and statistical features optimized by the ROC-AUC feature selection method. The
proposed model achieved a validation accuracy of 93.40% with a sensitivity of 82.40% and a specificity
of 80.60%. These results highlight the efectiveness of harmonic features and the reliability of artificial
neural networks in classifying heart sounds, especially in resource-constrained environments.</p>
      <p>In [23], researchers presented an innovative concept for regenerating cardiac signals using
regenerative artificial intelligence. This approach represents a novel use of AI for deep analysis of complex
electrical signals generated by the heart. Through advanced AI algorithms, it becomes possible to
perform a more in-depth analysis of ECGs, revealing patterns, anomalies, and biomarkers that might
otherwise go unnoticed. The goal of cardiac signal regeneration is to identify early signs of heart
damage and monitor the heart’s ability to regenerate or recover over time. The classification model
demonstrates high accuracy for all heartbeat classes, ranging from 93.85% to 99.16%, indicating its
efectiveness in detecting and classifying various types of arrhythmias.</p>
      <p>Specialists in [24] have developed a three-phase structure for real-time diagnosis of heart disease
through behavioral changes in the ECG. The innovative approach first identifies sudden changes in
ECG behavior and then determines the cause of these changes through disease classification. The
preprocessing stage is integrated with a change point detection (CPD) module, making the structure fully
end-to-end and adaptive. The CPD model uses an autoencoder to capture the essential characteristics
of ECG in latent space, which are then combined with other temporal features to improve the accuracy
of the stack ensemble classifier.</p>
      <p>Scientists [25] proposed an alternative approach using end-to-end classification models to remotely
obtain a discrete representation of cardiac signals from facial video recordings. Unlike traditional
computer vision solutions, which estimate cardiac signals by detecting physical manifestations of
heartbeat (such as changes in facial color due to changes in blood oxygenation), the authors introduced
a method for discretizing cardiac signals—an innovative preprocessing approach with limited precedents
in the health monitoring literature. The results showed that the proposed method outperforms the
baseline model on the UBFC-rPPG dataset, reducing the cross-dataset root mean square error from
2.33 to 1.63 beats per minute. Additionally, the approach reduces the computational complexity of
post-processing the model output, improving its suitability for real-time applications and deployment
on resource-constrained systems.</p>
      <p>The aim of our research is to develop information technology for cardiac diagnostics based on
the amplitude variability of characteristic ECG waves, using automated machine learning (AutoML)
and interpretable artificial intelligence (SHAP) methods to improve the accuracy and reliability of
cardiovascular disease diagnosis.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Materials and methods</title>
      <p>This study used open datasets from PhysioNet. The dataset [26] contained 12-lead electrocardiograms
of 45,152 patients recorded at a sampling rate of 500 Hz. This database includes recordings of various
common heart rhythm disorders and additional cardiovascular diseases, all of which were annotated
by highly qualified experts. The data [ 27] were generated from a set of long-term ECG recordings of
15 patients (11 men aged 22 to 71 and 4 women aged 54 to 63) with severe congestive heart failure.
The dataset [28] contained more than 100 15-minute two-lead ECG recordings. The recordings were
accompanied by annotations of the onset, peak, and end of P waves, QRS complexes, T waves, and,
where present, U waves for 30–50 selected cardiac cycles in each recording.</p>
      <p>To create a dataset for training and testing machine learning models, ECGs were processed using
a mathematical model of amplitude variability, which takes into account the amplitude values of
characteristic ECG waves (P, QRS, and T) [29]. The resulting dataset contained 651 samples. To build a
machine learning model, ten statistical descriptors of ECG amplitude variability were used as input
features:
• Mean (arithmetic mean) is a measure of the central tendency of the distribution of amplitude
variability;
• Median is a robust characteristic of the central tendency, resistant to the presence of outliers;
• Mode is the most frequently occurring value of amplitude variability;
• Standard Deviation is a measure of dispersion relative to the mean value;
• Sample Variance is the square of the standard deviation, reflecting variability;
• Kurtosis is an indicator of the peakedness (sharpness) of the distribution;
• Skewness is a measure of the asymmetry of the distribution;
• Range is the diference between the maximum and minimum values;
• Minimum is the smallest value of amplitude variability;
• Maximum is the largest value of amplitude variability.</p>
      <p>The following symbols were introduced into the dataset: Mean-Mean, Median-Med, Mode-Mo,
Standard Deviation-StD, Sample Variance-SV, Kurtosis-Kur, Skewness-Sk, Range-Ra, Minimum-Min,
and Maximum-Max. The initial parameter was the diagnosis, from which four classes were formed:
class 1 is the conditional norm, class 2 is the conditional norm with an implanted pacemaker, class 3
is arrhythmias, and class 4 is morphological abnormalities. Within the scope of this study, the term
morphological abnormalities refers to pathological conditions accompanied by structural changes in
the myocardium and/or the cardiac conduction system, which manifest themselves in the form of
persistent morphological abnormalities on the ECG. This group includes ischemic heart disease with a
history of myocardial infarction (scarring), bundle branch block (complete and incomplete), myocardial
hypertrophy, and cardiomyopathies.</p>
      <p>To ensure the accuracy of the forecasting quality assessment, the formed set was randomly divided
into two unequal parts in a 70/30 ratio, where 70% of the samples were included in the training sample,
and the remaining 30% in the test sample. This approach ensured, on the one hand, a suficient amount
of data for efective model training and, on the other hand, created conditions for reliable and objective
verification of their predictive ability on new, previously unknown examples.</p>
      <p>In this work, the machine learning model was formed using AutoML. The idea behind the AutoML
PyCaret method is to create an automated process for building a machine learning model that covers all
key stages from initial data preparation to obtaining the final optimized model [ 30]. The main goal of
this approach is to minimize manual intervention by the researcher and significantly accelerate model
development while maintaining high accuracy, stability of forecasts, and reproducibility of results. The
implementation of PyCaret-type AutoML includes several sequential steps: preliminary data processing,
automatic testing of a wide range of machine learning algorithms, evaluation of their efectiveness
using a unified set of metrics, and model ranking. Based on this ranking, the best model is automatically
selected, which can be further optimized using internal hyperparameter tuning mechanisms (additional
training). Thanks to this concept, PyCaret significantly improves the eficiency of the machine learning
model creation process, making it transparent, reproducible, and resistant to overfitting. In addition,
the use of a single integrated platform simplifies the comparison of diferent approaches and ensures
easy integration into further application systems.</p>
      <p>For a deeper understanding of the mechanisms of the constructed model, SHAP analysis (SHapley
Additive exPlanations) was applied, which is based on the concept of Shapley values (cooperative game
theory) [31]. This method belongs to the class of explainable artificial intelligence (Explainable AI)
approaches and allows us to quantitatively assess the contribution of each input feature to the formation
of a forecast. At the global level, SHAP allows us to determine the relative importance of features across
the entire sample and identify the most influential input features. At the local level, the analysis provides
an interpretation of predictions for individual observations, explaining which features and with what
intensity influenced the final decision of the model. This two-level interpretation makes it possible to
analyze the overall behavior of the algorithm. It also allows for the diagnosis of individual cases to
verify the correctness of predictions. The use of SHAP increases the transparency and explainability of
the model, which is particularly important in multi-class classification tasks with uneven distribution of
samples and complex nonlinear dependencies between features. This helps to increase confidence in the
results obtained and allows for more informed decisions based on machine learning model predictions.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Results and discussion</title>
      <p>In the AutoML system we developed, implemented using the PyCaret library, we built a fully automated
process for machine learning model construction that covers all stages — from preliminary data
processing to obtaining the final classifier. During the preliminary data processing stage, automatic checks were
performed to detect and impute missing values: for numerical features, missing values were replaced
using the strategy=‘mean’ principle, and for categorical features, using the strategy=‘most_frequent’
principle. This approach ensured the correctness and consistency of further training. Next, an
automatic comparison of a number of classification algorithms was performed, including Random Forest,
ExtraTrees, CatBoost, XGBoost, LightGBM, GradientBoosting, multilayer perceptron (MLP), Logistic
Regression, Ridge Classifier, and support vector machine (SVM). Each model was evaluated using a
unified set of metrics (Accuracy, AUC, Recall, Precision, F1-score, Kappa, MCC), the results of which
are shown in Table 1.</p>
      <p>Accuracy, recall, specificity, precision, F-score, and G-Mean were calculated using standard methods
based on basic classification parameters: true positives (TP), true negatives (TN), false positives (FP),
and false negatives (FN). For a more comprehensive evaluation of multi-class classification performance,
Cohen’s Kappa coeficient of agreement and the Matthews correlation coeficient (MCC) were
additionally employed. Both metrics are derived from the complete confusion matrix and enable assessment
of prediction balance and reliability even under conditions of class imbalance. Each metric reflects a
separate aspect of the model’s performance:
• Accuracy is the total proportion of correctly classified examples;
• Recall measures the model’s ability to correctly identify objects of the target class;
• Specificity reflects the ability to correctly identify negative cases;
• Precision represents the proportion of correctly predicted positive examples;
• F-score is a balanced assessment that combines Precision and Recall;
• G-Mean is a metric reflecting the balance between Recall and Specificity;
• AUC is the area under the ROC curve;
• Cohen’s Kappa is a coeficient that measures the degree of agreement beyond chance;
• MCC (Matthews Correlation Coeficient) is a robust metric that takes into account all four
elements of the confusion matrix and is particularly suitable for imbalanced datasets.</p>
      <p>Based on the results of comparison, the Random Forest Classifier model proved to be the most optimal,
demonstrating the best balance. To increase the reliability and accuracy of predictions, the selected
model was additionally integrated into the probability calibration procedure. To do this, it was wrapped
in CalibratedClassifierCV using sigmoid calibration and 5-fold cross-validation (cv=5, ensemble=True).
The ensemble=True option means that the model is calibrated on each fold and averages the results,
providing more stable probability estimates at the output. This approach improves the correspondence
between the predicted probabilities and the actual frequencies of class occurrence, reducing the model’s
overconfidence. The random forest is built with hyperparameters selected by AutoML for optimal
performance. Specifically, the model contains 240 trees (n_estimators=240) with a maximum tree depth
limited to 7 levels (max_depth=7). To prevent overfitting, a restriction is applied to the minimum number
of samples in the split node – no less than 10 (min_samples_split=10), and in the leaf – no less than
6 (min_samples_leaf=6). The requirement for a minimum reduction in impurity (impurity criterion)
during splitting was set at 0.02 (min_impurity_decrease=0.02), which guarantees that only statistically
significant splits are performed. The Gini criterion (criterion=‘gini’) was used to evaluate the quality of
the splits. The model did not limit the number of features when selecting splits (max_features=1.0, i.e.,
all available features at each node are considered), which may increase the completeness of information
use. Other parameters remained at their default values: in particular, bootstrap sampling was used to
build each tree (bootstrap=True), and a fixed random seed (random_state=42) was used to ensure the
reproducibility of the results. The selected configuration — a calibrated Random Forest as part of the
PyCaret pipeline — provides not only high classification accuracy but also reliable class probability
estimates. This is confirmed by balanced performance indicators for all four classes, which demonstrate
the reliability and generalizability of the model. Thus, the model we have built is the result of an
automated optimization process and provides high-quality multi-class classification.</p>
      <p>Figure 1 shows a diagram of the formed pipeline. The initial stage is numerical_imputer, where the
SimpleImputer algorithm can be used for the numerical features Mean, Med, Mo, StD, SV, Kur, Sk, Ra, Min,
and Max. The next step is categorical_imputer. The final part of the pipeline is CalibratedClassifierCV,
which implements probability calibration for the base RandomForestClassifier algorithm.</p>
      <p>The pipeline shown combines the stages of preliminary data processing and modeling into a single
integrated system. This ensures reproducibility, consistency of all steps, and reliability of forecasts,
creating a solid foundation for further analysis of classification results.</p>
      <p>Figure 2 shows the confusion matrix and its normalized version in percentages (normalized confusion
matrix), constructed to evaluate the classification quality of the Random Forest model.</p>
      <p>The first matrix shows the absolute values of correctly and incorrectly classified objects in each
class, while the second shows relative values in percentage terms. Analysis of the results shows that
most objects are correctly assigned to their categories, as evidenced by the high values on the main
diagonal. The use of the confusion matrix in two variants, namely absolute and normalized, allows for a
comprehensive assessment of the model’s performance: on the one hand, in terms of the actual number
of correctly and incorrectly classified samples, and on the other hand, taking into account the relative
proportions for each class. This allows us to objectively confirm the high eficiency of the constructed
model in the task of multi-class classification.</p>
      <p>Figure 3 shows the Precision–Recall and ROC curves with the corresponding AUC values for the
multi-class classification of the Random Forest model.</p>
      <p>The Precision–Recall curves demonstrate the stability and reliability of the model in the multi-class
classification task, confirming its ability to provide high-quality predictions for all four classes. They
maintain an accuracy level above 0.9 across a wide range of Recall, indicating the model’s efectiveness
in detecting objects of each class with a minimum number of false positives. The most consistent results
are observed for class 2, which demonstrates the highest stability of indicators. The ROC curves for
all four classes are located close to the upper left corner of the graph, confirming the high accuracy
of classification. The area under the curve (AUC) exceeds 0.96 in each case, reaching a maximum
(a)
(a)
(b)
(b)
Class
1
2
3
4</p>
      <p>TP
62
53
33
34</p>
      <p>TN
126
137
154
157</p>
      <p>FP
5
6
2
1
3
0
7
4
0.9591
0.9693
0.9540
0.9744</p>
      <p>The analysis of the indicators shows that the constructed model provides high-quality multi-class
value of 0.99459 for class 2. This indicates the model’s ability to reliably separate positive and negative
samples regardless of the selected classification threshold. Thus, the combination of Precision–Recall
and ROC analysis results confirms the efectiveness of training and the high generalization ability of
the constructed model.</p>
      <p>For a more detailed assessment of the classification quality, a set of standard metrics was calculated,
the results of which are presented in Table 2.
classification. The Accuracy value for all classes exceeds 95%, which confirms the consistency between
predictions and actual labels. High Recall and Specificity values demonstrate the model’s ability to
detect positive and negative examples equally efectively, minimizing the number of false positives and
false negatives. The Precision and F1-Score indicators remain consistently high, reflecting the balance
between Precision and Recall. Additionally, high G-Mean values indicate the balance of the model’s
performance in a multi-class task and uneven distribution of examples.</p>
      <p>Figure 4 shows the importance rating of input features determined using SHAP analysis for the
constructed model. Sk and Kur have the greatest impact on decision-making and are key factors for
classification. Min, Ra, and Max are of secondary importance. Other characteristics have a relatively
low impact on the model’s results.</p>
      <p>For a more in-depth interpretation of the classification results, Figure 5 shows SHAP summary
diagrams for each of the four classes.</p>
      <p>Unlike the global feature importance ranking, which only indicates their relative contribution, these
diagrams allow us to assess not only the degree but also the direction of the influence of individual
parameters on the probability of belonging to a particular class. The horizontal axis reflects the
magnitude of the SHAP value, where positive values indicate an increase in the sample’s belonging
to the current class, while negative values indicate a decrease in the probability of its classification.
Each point corresponds to a separate example from the sample; for better visualization with a large
number of observations, the points are partially scattered vertically. The left axis shows the names of
the features, sorted by decreasing importance according to the global ranking, and the color scale from
blue to red reflects the magnitude of the feature’s value (low or high, respectively).</p>
      <p>The generalized SHAP graphs for the four classes show clear diferences in both the strength of the
features’ influence and the direction of this influence on the probability of a sample belonging to each
class. For class 1, Sk and Kur dominate. High Sk and Kur values can shift the prediction to the right or
left, i.e., increase or decrease the probability of class 1, while low Sk values decrease it and low Kur
values increase it. Large Min values mainly increase the probability of class 1, while small ones decrease
it. For Ra, the opposite picture to Min prevails. Other statistics — SV, Max, StD, Med, Mo, and Mean —
make mostly small contributions in terms of modulus. For class 2, Sk is again the leading factor, but the
pattern is diferent: most points with low Sk values are concentrated in the right half-plane, i.e., they
increase the probability of belonging to class 2, while an increase in Sk mostly shifts the forecast to
the left. At the same time, Kur shows classic monotonicity: higher values increase the probability of
class 2, while lower values decrease it. Large Min values increase the probability of class 2, while small
values decrease it. Other features provide additional adjustment for class 2 assignment. The profile of
class 3 contrasts with the first two. The strongest predictor is Min. Low Min values shift the forecast
to the right, increasing the probability of class 3, while high values decrease it. A similar pattern is
observed for Kur. Low values of Ra, SV, Max, and StD decrease the probability of class 3, while high
values increase it. For the rest of the indicators, the picture is mixed. Class 4 is again dominated by Sk
and Kur. High Sk values mainly shift the prediction to the right, i.e., increase the probability of class 4,
while low Sk values decrease it. High Kur values can shift the prediction to the right or left, i.e., increase
or decrease the probability of class 4, while low values decrease it. Small Min values shift the prediction
to the left, decreasing the probability of class 4, while large values mainly increase it. An increase in
Ra, StD, SV, and Max indicators is usually accompanied by negative SHAP values, while a decrease is
accompanied by positive values. For the rest of the indicators, the picture is mixed.</p>
      <p>Thus, the results of the SHAP summary diagrams confirm that the model relies primarily on the
statistical characteristics of data distribution (Sk and Kur) in the classification process, and the direction
of their influence varies depending on the class. This makes it possible not only to identify key features,
but also to understand the specifics of their impact on the formation of predictions, which increases the
transparency and explainability of the classification results. At the same time, the patterns obtained
reflect only the generalized influence of features, while for individual examples it may difer significantly.
Therefore, for a deeper understanding of the model’s individual decisions, it is advisable to analyze
SHAP waterfall plots, which illustrate the contribution of each feature to the formation of a forecast at
the local level.</p>
      <p>Figure 6 shows SHAP waterfall diagrams for one sample (Sample 42) in each of the four classes,
illustrating the detailed distribution of the contributions of individual features to the final decision of
the model.</p>
      <p>Each column reflects the magnitude of the feature’s influence: red segments indicate a positive
contribution to the probability of belonging to the current class, while blue segments indicate a negative
contribution. The SHAP waterfall plots for sample 42 show how the model arrives at an individual
prediction  () step by step from the base class estimate [ ( )] thanks to the contributions of
individual features. The diagrams clearly show that for class 1 (a), there is a dominant negative influence
of Sk and Kur, which significantly reduce the predicted probability. In class 2 (b), the Sk indicator has
the greatest negative efect, while the rest of the features have a secondary contribution. For class 3 (c),
almost all features have a negative impact on the probability of the selected class. In contrast, class
4 (d) shows the opposite situation. The Sk and Kur indicators provide the most significant positive
contribution, significantly shifting the model’s prediction in favor of this class. Other features have a
mostly positive but insignificant impact. Thus, waterfall diagrams allow us to track not only the relative
importance of features, but also the specific direction of their influence on the model’s decision for
individual examples, providing a deeper interpretation of the classifier’s performance at the local level.
This ultimately leads to the sample being assigned to this class with a probability of 0.898.</p>
      <p>The use of SHAP analysis provided a comprehensive understanding of the model’s mechanisms by
combining global and local interpretations of its decisions. SHAP analysis ensured the transparency
and explainability of the classification results, allowing us to identify key predictors and assess their
role in decision-making. The results obtained further confirm the sensitivity of the amplitude variability
function to changes in the state of the human cardiovascular system and allow, on its basis, the use of
additional informative features in the form of the above statistical estimates for cardiac diagnostics.</p>
      <p>The proposed machine learning method has formed the basis for the development of an information
technology for cardiological diagnostics. However, it should be noted that the diagnostic specificity
of this technology is limited, since not all cardiovascular pathologies manifest through changes in
the amplitude of ECG waves. In particular, certain rhythm disturbances, conduction abnormalities,
or ischemic conditions may have only a minimal efect on amplitude variability, which restricts the
universality of the method.</p>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>The study developed and experimentally tested an information technology for automated diagnosis of
cardiovascular pathologies based on the amplitude variability of ECG waves, combined with AutoML
(PyCaret) and explainable artificial intelligence (SHAP). The use of AutoML ensured an eficient and
reproducible model development process that minimizes manual intervention by the researcher. Among
the tested algorithms, Random Forest with probability calibration indicates the highest performance,
achieving high Accuracy (over 95%) and AUC (over 0.96) values for all classes. This demonstrates
the model’s ability to reliably distinguish between normal, pacemaker patients, arrhythmias, and
morphological abnormalities. SHAP analysis enabled the identification of the key features that most
influence the model’s decisions and allowed tracking their impact at both global and local levels.
Specifically, Skewness (Sk) and Kurtosis (Kur) were identified as the dominant predictors afecting
classification probability. This interpretation increased the transparency and trust in predictions, which
is especially important for medical applications. The results confirm the feasibility of integrating
AutoML and explainable AI into cardiac diagnostics, opening up prospects for the creation of reliable,
interpretable, and practically applicable clinical decision support systems. This study has a limitation,
as the proposed machine learning–based diagnostic technology relies on ECG amplitude variability,
which does not capture all cardiovascular pathologies.</p>
      <p>In subsequent studies, appropriate ML methods will be applied, and SHAP analysis will be performed
for the time variability function, taking into account the amplitudes of characteristic ECG waves.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>The authors would like to thank the ERASMUS-EDU-2025-CBHE project “Digital Transformation and
Curriculum Development for Healthcare Teams” (Digi-CHange - 101233888 – GAP-101233888) for the
idea, inspiration and funds that made this work possible.</p>
    </sec>
    <sec id="sec-7">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the authors used Grammarly in order to grammar and spell check,
and improve the text readability. After using the tool, the authors reviewed and edited the content as
needed to take full responsibility for the publication’s content.
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