MnL–TWA: Manifold Learning Approach for T–Wave Alternans Detection in Ambulatory Environments

2.1. Dataset

For this study, we start from the database assembled in Ref. 22 extending it as showed in 3.1. A signal model that incorporates real TWA into real ECG signals without alternans was used. This model has proven to be robust as it accounts for patient and signal variability.^17,21,35 The dataset consists of ECG segments, each lasting more than 5 minutes, sourced from MIT–BIH Arrhythmia Database ³⁶ (mitdb), the European ST–T Database ³⁷ (edb), and the MIT–BIH Normal Sinus Rhythm Database (nsrdb), all publicaly available in Physionet. ³⁸ We confirmed that all of them were free of TWA using the SM as gold standard. The repository consist of 574 signals of varying lengths from 30 patients (consult^20,22 for further details).

To train our ML models, we randomly select ECG frames consisting of M beats with D beats of overlapping from the 574 signals. Our goal is to develop TWA detectors suitable for ambulatory conditions, so the window size must be as short as possible to minimize the effect of signal variability on the ECG. The selection of these parameter values was thoroughly studied and validated in Ref. 39. Each instance from this set is used as an example for the models. To prevent bias toward patients with longer signals, we ensured a balanced number of instances per signal by limiting the number of instances based on the minimum available across all signals.

The i–th instance is constructed as described in Equation (1), where p cont ( i ) ( t ) , t = 0 , … , L i − 1 , represents a signal frame of M beats from the control ECGs, spanning L _i samples. The coefficients α adjust the alternant voltage for the specific instance i. Setting α = 0,∀k yields the control ECG frame p⁽ⁱ⁾(t).

p ( i ) ( t ) = p cont ( i ) ( t ) + α ( i ) ⋅ θ ( i ) ( t )

(1)

θ ( i ) ( t ) = ∑ k = 1 M 1 + ( − 1 ) k 2 ε ( i ) ( t − t k − t J ) .

(2)

The real alternant waveform θ, provided by J. P. Martínez, is incorporated into the ECG instance, randomly selected from 15 available patient waveforms. ¹² These TWA events are either stationary or sustained, whereas our previous work ³⁹ presents an example of a non-sustained episode introduced into an ECG segment (see Figure 1). In this equation, ɛ⁽ⁱ⁾(t), where t = 0, …, L _ɛ − 1, represents the alternant wave, with L _ɛ denoting the length of the ST–T complex and L _ɛ ≪ L _i . The term t _k is the onset of the ST–T segment for the k-th beat, and t _J is a zero-mean Gaussian random variable with a standard deviation of 20 ms, which introduces uncertainty to the ST–T onset. In this context, TWA occurs in every other beat: for odd k, no TWA is present (θ⁽ⁱ⁾(t) = 0), and for even k, the TWA amplitude is defined by α.OPEN IN VIEWER

2.2. Feature Set

We use a set of predictors composed of informative descriptors extracted from well-known TWA detection methods, namely, the SM, ⁴⁰ the MMA, ¹⁹ the Time Method (TM), ¹⁷ the LLR, ¹² the CM ¹⁸ , and the Complex Demodulation (CD). ⁴¹

All of them extract parameters related to the ventricular repolarization by operating on matrix M ∈ R M × N :

M = m 0 T , m 1 T , … , m M − 1 T

(3)

Therefore, we extracted a total of 14 features from each ECG frame (Equation (1)) to feed the learning-based algorithms and create the detection models. We selected the K score from the SM (K _score ) and the estimated alternant volage from the MMA ( V TWA MMA ) and the TM ( V TWA T M ) . From the LLR method, we took the significance level (T) and the estimated alternant voltage ( V TWA LLR ) . From the CM, the maximum number of zero–crossings ( zcr ¨ ) , and both the mean ( V ¯ TWA C M ) and the maximum ( V ¨ TWA C M ) of the alternant wave. Finally, from the CD method, the mean and max values of the aggregated alternant wave computed as the RMS ( V ¯ r m s C D , V ¨ r m s C D ) and the maximum value ( V ¯ m a x C D , V ¨ m a x C D ) of the demodulated beat series, ⁴¹ as well as from the area under the curve (AUC) ( V ˜ r m s C D , V ˜ m a x C D ). A summary table was provided in Ref. 22 (see Table 1).

2.3. Dimensionality Reduction

Dimensionality reduction has gained significant attention in recent years for its ability to reduce the number of dimensions in data, while uncovering its intrinsic structure with minimal loss of accuracy and information. Often applied in ML tasks such as classification, clustering and regression, dimensionality reduction helps reduce computational complexity and alleviates the curse of dimensionality. Moreover, it facilitates data visualization by projecting high-dimensional data onto two or three dimensions, making it easier to identify patterns and relationships. Feature selection and feature extraction are the main approaches.

Feature extraction, creates new, independent, and informative features from the original data in an unsupervised manner. Its goal is to capture essential information while reducing redundancy and noise. Methods in this domain fall into two main categories: linear and non-linear approaches. Linear techniques, exemplified by PCA, assume that the intrinsic structure of the data can be well-represented in a lower-dimensional linear subspace. By leveraging principles of linear algebra, these methods condense the data, making them particularly effective for datasets with linear relationships among variables. Conversely, non-linear methods, often referred to as MnL techniques, such as Isomap and UMAP, are designed to handle complex data structures with intricate non-linear relationships. These techniques excel in capturing non-linear manifolds and preserving both local and global patterns in reduced space, offering a more flexible and accurate representation of the data intrinsic geometry. ⁴⁴ Additionally, autoencoder-based neural networks (AE-based NN) provide another powerful non-linear approach, wherein a neural network learns a compressed, latent representation of the data. This flexibility in network architecture allows AE-based NNs to adapt to specific data complexities and capture fine-grained patterns while reducing dimensionality. ⁴⁵ We now turn our focus to feature extraction to effectively reduce our dataset dimensionality, thereby enhancing the interpretability of the model behavior.

2.3.1. PCA

PCA, one of the earliest and most widely used techniques in the field, aims to reduce dimensionality by constructing new variables known as principal components, which are linear combinations of the original dataset variables. PCA transforms a high-dimensional input vector into a low-dimensional one by calculating the eigenvectors of the covariance matrix of the centered original inputs. Given the original set of features x = x 1 , x 2 , … , x 14 T , PCA linearly transforms each vector x into a new one y as follows:

y = x U

(4)

Here, U is the 14 × 14 orthogonal matrix whose columns are the eigenvectors of the covariance matrix C of the centered original inputs. The eigenvalue problem is solved as shown in Equation (5):

C = U Λ U T

(5)

where Λ represents the eigenvalues matrix of C. Thus, PCA transforms the original feature space by computing the principal components z as the orthogonal transformation of the centered x as shown in Equation (4). ⁴⁶

The principal components are arranged in descending order of their eigenvalues, with the first component capturing the greatest variance and thus, the most information. Subsequent components account for progressively smaller amounts of variance. By focusing on the first few principal components, one can reduce dimensionality while retaining the most significant information from the dataset. However, despite its widespread use and computational simplicity, PCA has notable limitations. It assumes linear relationships among features, which may not be suitable for datasets with complex non-linear structures, potentially leading to suboptimal dimensionality reduction and loss of crucial information. Moreover, PCA is sensitive to outliers, which can disproportionately affect the principal components and result in biased outcomes. ⁴⁴

2.3.2. UMAP

UMAP, a non-linear technique introduced by McInnes and Healy, ²⁹ involves two main steps: constructing a fuzzy topological representation of the approximated manifold where the data is presumed to lie, and subsequently optimizing this representation in a low-dimensional embedding.

For the initial high-dimensional graph, a KNN graph is built, in which, for each instance x ( i ) = x 1 ( i ) , x 2 ( i ) , … , x 14 ( i ) T , its k nearest neighbors based on Euclidean distance are identified. Subsequently, for the fuzzy-simplicial set representation, the relationship strength between the instance x⁽ⁱ⁾ and each of their selected neighbors, such as x^(j), is determined. To this end, two parameters are computed: ρ⁽ⁱ⁾ and σ⁽ⁱ⁾. The former, defined in Equation (6) as:

ρ ( i ) = min { d ( x ( i ) , x ( j ) ) ∣ d ( x ( i ) , x ( j ) ) > 0 } ,

(6)

defines the smallest positive Euclidean distance from instance x⁽ⁱ⁾ to its nearest neighbor x^(j). The latter, a scaling parameter used to normalize distances between instances and their neighbors while preserving high-dimensional proximities, is computed as shown in Equation (7):

log 2 ( k ) = ∑ j = 1 k exp − max { 0 , d ( x ( i ) , x ( j ) ) − ρ ( i ) } σ ( i ) .

(7)

Through these two parameters, the weight of the edge from instance x⁽ⁱ⁾ to its neighbor x^(j) is computed in Equation (8), forming a weighted graph G. ⁴⁷

w i , j = exp − max { 0 , d ( x ( i ) , x ( j ) ) − ρ ( i ) } σ ( i ) .

(8)

In the final step of UMAP, the high-dimensional graph G is optimized to obtain a low-dimensional layout Y, starting with an initial layout derived from spectral embedding. In this process, w_i,j represents the similarity between the high-dimensional instances x⁽ⁱ⁾ and x^(j), while v_i,j denotes the similarity between their low-dimensional counterparts y⁽ⁱ⁾ and y^(j). The aim is to adjust y⁽ⁱ⁾ to minimize the discrepancy between w_i,j and v_i,j. This is done by minimizing the cross-entropy loss, as shown in Equation (9), using stochastic gradient descent. ⁴⁸

C UMAP = ∑ i , j w i , j ⋅ log v i , j − 1 − w i , j ⋅ log 1 − v i , j

(9)

UMAP excels in preserving both local and global structures in low–dimensional spaces, making it a powerful tool for visualizing and understanding complex data. One of its strengths is the flexibility in parameter fine-tuning, which allows to fit various datasets and analytical needs. However, UMAP is highly sensitive to the choice of hyperparameters, such as the number of neighbors and minimum distance. Therefore, careful and often time-consuming tuning is needed to achieve optimal results. The number of neighbors parameter strikes a balance between capturing fine-grained details and large-scale manifold features. Smaller values focus on preserving detailed local structures, while larger values prioritize global structures, potentially at the expense of losing some local detail. The minimum distance parameter directly influences the resulting embedding by controlling the construction of the fuzzy simplicial set in the low-dimensional space. Essentially, it determines how closely points can be packed together in the embedding. A larger minimum distance value results in a more spread-out embedding, which helps to emphasize global relationships at the cost of local detail. ²⁹

2.3.3. Isomap

Isomap, short for Isometric Mapping, is a widely utilized non-linear dimensionality reduction technique renowned for its ability to preserve geodesic distances rather than merely Euclidean distances. This feature makes Isomap particularly adept at handling data that resides on non-linear manifolds, effectively capturing the underlying geometric structure of complex, high-dimensional datasets. ⁴⁹

Three steps are involved in this algorithm: neighborhood graph construction, shortest paths computation, and low-dimensional embedding construction. The first step calculates the distances between instances using the Euclidean distance, such as d(x⁽ⁱ⁾, x^(j)), to determine the neighborhood relations in the weighted graph denoted as G. Geodesic distances are estimated for this graph in the second step, effectively tracing the manifold curvature rather than traversing the high-dimensional space directly. Lastly, Isomap employs Multidimensional Scaling (MDS) on the distance matrix of G, D _G = {d(g⁽ⁱ⁾, g^(j))}. This allows for the construction of an embedding in a low-dimensional space Y that best preserves the manifold estimated intrinsic geometry. To this end, a cost function that measures the discrepancy between the high-dimensional geodesic distances and the low-dimensional Euclidean distances is minimized, as shown in Equation (10).

E = ‖ τ ( D G ) − τ ( D Y ) ‖ L 2

(10)

where D _Y is the Euclidean distance matrix d(y⁽ⁱ⁾, y^(j)), and ‖ ⋅ ‖ L 2 represents the L² matrix norm ∑ i , j ( A i j ) 2 . The operator τ transforms distances into inner products, which are essential for efficient optimization. The global minimum of this equation is achieved by setting the instances y to correspond to the top d eigenvectors of the τ(D _G ) matrix. ⁵⁰

In summary, Isomap effectively maps high-dimensional data onto lower-dimensional spaces, yet it has several limitations: the choice of neighborhood size can affect the embedding quality, it is computationally intensive for large datasets, and it is sensitive to noise and outliers. Furthermore, Isomap struggles with manifolds that have holes or are not convex, which can result in poor and inaccurate low-dimensional representations.^44,51

2.3.4. Autoencoders

Autoencoders, initially developed as lossy data compressors, have evolved into effective non-linear dimensionality reduction techniques. An autoencoder is a type of neural network consisting of two main components: the encoder and the decoder. The encoder compresses input data into a lower-dimensional representation, known as the latent space, while the decoder reconstructs the data from this compressed form to match the original as closely as possible.

Mathematically, given an input vector x, the encoder function f transforms it into a latent representation z as follows:

z = f ( x ) = σ ( W e x + b e ) ,

(11)

where W _e and b _e are the weights and biases of the encoder, and σ is a non-linear activation function. The decoder function g, acting as a symmetric counterpart to the encoder, reconstructs the original data from the latent representation:

x ^ = g ( z ) = σ ( W d z + b d ) ,

(12)

where W _d and b _d are the weights and biases of the decoder, and x ^ is the reconstructed output.

In this work, we have implemented an AE-based NN, as done in Ref. 52, integrating a two-neuron classification layer into the traditional autoencoder architecture. This design leverages the latent space, allowing the model to utilize its manifold properties while also performing binary classification. Thus, this model is trained to compress the data into the latent space through the encoder layers and classify it based on the compressed representation. Although this architecture is inspired by traditional autoencoders, it does not include a reconstruction objective. The encoder acts as a supervised bottleneck representation that preserves discriminative information for the downstream task.

Figure 1 illustrates the architecture considered, which has been fine-tuned by selecting several parameters such as the number of layers, neurons per layer, and activation functions. Regularization techniques, namely dropout or L2 weight decay, are also employed to prevent overfitting and improve model robustness. Additional key parameters have also been studied. The number of training examples processed in each iteration, known as the minibatch size, affects training efficiency and stability, while the maximum epochs, representing the number of complete passes through the training dataset, influence the duration and thoroughness of the learning process. These parameters are critical for optimizing the model performance and ensuring that it captures the essential patterns in the data while maintaining versatility when applied to new, unseen data.^45,51

2.4. ML Methods

In this stage, the classification process leverages engineered and then reduced features, as detailed in earlier sections, to train learning models. Our goal is to categorize ECG segments from the repository into two categories: no TWA (category 0) and TWA (category 1). We have evaluated multiple methods for this purpose, continuing with methods explored in Ref. 22, namely RF and K-nearest neighbors (KNN). For KNN, similar to the prior study, we optimized the number of neighbors across a range of 2 to 20. For RF, we performed fine-tuning on parameters such as minimum leaf size and number of splits, varying from 15 to 20, and number of trees, ranging from 1 to 15, using a grid search approach. This rigorous parameter optimization aims to identify configurations that achieve the best classification performance for our dataset.

Additionally, we have incorporated MultiLayer Perceptron (MLP) in this study. MLP is a type of artificial neural network that utilizes layers of neurons to establish a nonlinear mapping between input and output vectors. It employs a backpropagation algorithm to optimize weight values based on gradients. Key parameters, including the number of layers and the number of neurons per layer, were carefully optimized to maximize performance. A range of values from 10 to 50 neurons was explored across different layer configurations. ²⁰

3.1. Design Stage

For the model training we feed the 14 features obtained from the feature engineering process into the learning models. TWA is introduced randomly in half of the instances for each patient and consistently across the entire 30-beat window. Additionally, the alternant voltages, ranging from 20μV to 100μV, are evenly distributed within the signals, ensuring the learning models are capable of detecting various episodes effectively. This setup follows the clinically inspired protocol introduced in our previous study, ²² with voltages and durations designed to reflect plausible physiological manifestations of TWA. To mitigate the risk of overfitting to synthetic patterns, we deliberately avoid fixed templates or repetitive insertion points. Instead, TWA episodes are randomized across patients and permutations, ensuring diversity and realism in the training data.

In a supervised classification problem like ours, having a properly diverse and representative dataset is essential for enhancing the model ability to generalize to unseen data. To achieve this, in this work we have expanded our training set by adopting an overlapping approach within the instances in this work. Each window now spans 30 beats, with a 5-beat advancement for the subsequent window, resulting in an overlap of 25 beats. This adjustment allows us to consider 288 windows per patient, determined by the patient with the fewest available windows, compared to the 40 windows considered in our previous study. Consequently, our training dataset now includes a total of 8640 instances, marking an increase of over 7 times from our previous set. This change not only enhances the training of the learning models, making them more robust with a larger number of instances to learn from, but also mirrors the approach used for inline TWA detection in ambulatory recordings. Therefore, the models will experience consistent conditions across both experiments. In essence, the expanded dataset boosts the models capacity to learn, generalize and adapt to different contexts and conditions, ultimately enhancing overall performance and reliability.

In this work, we divide the patients into six uniform groups for a test set permutation, following the same procedure as in Ref. 22 , but increasing the number of instances per group from 200 to 1,440. Each group is used once as the test set and the other five for training. To prevent any window-level leakage, all overlapping windows from each patient remain within the same group, as window generation is performed after patient assignment. This strategy assesses generalization, strengthens statistical validity, and reduces the risk that results arise from random chance or specific data patterns. Within the training groups, we tune model hyperparameters using the F1-score, fitting on four groups and validating on one chosen at random. This yields a distinct model for each permutation, tested on its corresponding test group, and we report the mean and standard deviation across permutations to measure performance consistency.

As discussed in Section 2.3, MnL techniques, including UMAP, Isomap, and AE-based NN, are sensitive to their hyperparameter configurations. To ensure robust performance despite data variability and noise, we conducted comprehensive hyperparameter tuning to identify optimal settings across conditions. In this study, we conducted a hyperparameter tuning process for these three MnL techniques, while PCA was kept at its default configuration, given its simplicity and limited tuning requirements. To systematically evaluate the impact of hyperparameter settings on the performance of these methods, we first optimized the parameters of the ML models, namely KNN, RF, and MLP, using PCA-transformed data. This established a strong baseline configuration for the ML models. Subsequently, we explored a range of hyperparameter values for UMAP and Isomap, evaluating their performance within each of the three ML models. The optimal hyperparameter configuration for both UMAP and Isomap was determined based on their performance across these models. Once the best configurations were identified for each of the ML models, these were re-optimized by fitting them to the data transformed using the selected UMAP and Isomap settings. This two-stage tuning strategy, supported by cross-validation, ensured that the MnL techniques were fine-tuned for the specific data transformations, improving the overall effectiveness of the subsequent ML model evaluations.

To fine-tune the dimensionality reduction methods, we systematically explored the hyperparameter space for each technique. For UMAP, we varied the number of neighbors between 10 and 60 and the minimum distance from 0.1 to 0.9. For Isomap, we tested neighbor values from 10 to 30. For the AE-based NN, we evaluated several architectural configurations before selecting the final design shown in Figure 1. The model consists of a fully connected layer with 50 neurons, followed by a 3-dimensional bottleneck, and a post-bottleneck fully connected layer with 10 neurons feeding a 2-unit softmax classifier. All hidden layers use batch normalization, leaky-ReLU activations, and dropout (0.2). Training is performed end-to-end using a single cross-entropy classification loss (no reconstruction loss), Adam optimization, L2 regularization (λ=0.001), batch size 512, and 1000 epochs.

Finally, to evaluate the performance of the design stage, we use several metrics. Accuracy measures how often the model correctly classifies an ECG frame as either TWA or not. Recall evaluates the proportion of TWA cases that are correctly identified, while precision indicates the correctness of the positive classification results. Finally, the F1-score combines both recall and precision into a single metric to provide a balanced assessment. ²²

3.2. TWA Detection on Ambulatory Recordings

For real-time detection of sporadic TWA episodes in ambulatory settings, we apply a short-term sliding window to the ECG signal to assess the presence of TWA. In this section, we shift focus to the long-term analysis of the 574 ECG signals, denoted as p(t), in contrast to the short-term instances defined in Equation (1), which were previously employed for system design and training. The ECG model incorporating TWA episodes is described in Equation (13), where θ(t) (previously defined in Equation (2)) represents the stationary alternant waveform. However, in this case, instead of iterating over M beats in an instance, we iterate over N _h , which denotes the total number of heartbeats in each signal.

p ( t ) = p cont ( t ) + ψ ( t ) ⋅ θ ( t )

(13)

ψ ( t ) = ∑ j = 1 Q α j ⋅ w j ( t − t j ) ,

(14)

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Figure 2.

Example of inline TWA detection on signal 16265 from nsrdb using the AE-based NN. The model predictions (thin blue line) and the final detections (thick green line) corresponding to the TWA episodes (thick horizontal black line) are illustrated

To make predictions about TWA presence, a sliding square window is applied to the signal, represented as P _w (t, τ) = w(τ)P(t− τ), where the window size M is 30 beats. Signal processing-based methods and ML models generate predictions from this window. However, the former yields continuous-valued predictions, while the latter provides binary decisions. A prediction π(n) is made from the output D of the model M as follows:

π ( n ) = 0 , D M P w ( t , τ ) < u 1 , D M P w ( t , τ ) ≥ u

(15)

Lastly, TWA episodes may appear as sporadic events in long-term ECG signals. However, the learning models were trained under balanced conditions to ensure optimal performance. As a result, the predictions are prone to a high rate of false positives (FP). Thus, when tracking a signal, a positive outcome is considered in π(n) when the prediction is sustained at least the same number of beats M as the window length, which in this case is 30 beats. Equation (16) shows κ(n), the accumulative sum of the predictions belonging to each window. In this detection system, another sliding window is slid across the signal, filtering those predictions that do not accumulate M beats.

κ ( n ) = ∑ n = − M 2 M 2 − 1 w ( τ ) π ( n − τ ) d τ

(16)

δ ( n ) = 0 , κ ( t ) < N 1 , κ ( t ) = N ,

(17)

As shown in Figure 2, from the initial positive predictions made by the model, some were filtered out as false positives (FPs), while four were classified as true positives (TP). For evaluation, we use the same metrics as in the design stage. A correct TWA detection is defined as an intersection between the detection δ(n) and the TWA episode (or extended area), as illustrated, for example, with the second episode in the figure. False negatives (FN) occur when TWA episodes are missed, as with the third episode. No FPs were recorded in this instance, and several predictions, such as the first one, corresponded to true negatives (TN).

4.1. Design Results

In this study, learning-based methods, namely KNN, RF and MLP have been designed and trained for TWA detection. The results feeding the complete set of 14 features to the models versus having as input the transformed sets through the different MnL techniques are included in Table 1. These results are obtained after careful hyperparameter tuning of UMAP, Isomap and the AE-based NN using a cross-validation procedure. Also, the results shown belong to the mean and standard deviation of the test set after the patient permutation procedure. F1-score results are considered, and as it can be seen, there is a small decrease when considering these MnL methods compared to using the complete set of features, caused by the partial loss of information, as only three components are being fed to the models. However, for the AE-based NN, it can be noted that this decrease is not that significant with a 92.1% F1-score, compared to the original 92.5% obtained from the complete set, also with a MLP. In this line of thought, we can also observe that MLP generally outperforms the other two ML methods, across every MnL technique. Also, the improvement in the scores of the original set in comparison to ²² (90% F1-score with RF) is due to the test-bed size increase now that overlap is being considered.

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Table 1.

Test Results for Learning-Based Models Using the Complete and Transformed Feature Sets via Different MnL Techniques. F1-Scores Show the Mean ± Standard Deviation (in %) Over Six Permutations

​	Complete	PCA	UMAP	Isomap	AE-based NN
KNN	91.1 ± 2.7	89.9 ± 2.6	89.5 ± 2.4	90.3 ± 2.4	-
RF	91.5 ± 2.4	88.8 ± 2.5	89.4 ± 2.7	90.0 ± 2.3	-
MLP	92.5 ± 2.5	90.6 ± 2.5	89.7 ± 2.9	90.5 ± 2.5	92.1 ± 2.4

To thoroughly assess the performance of the MLP model, Figure 3 presents a full range of evaluation metrics for two feature set configuration: the complete and the AE-based NN transformed, including training set results. By comparing metrics across training and test sets, we can examine potential overfitting: larger discrepancies between these sets typically indicate reduced generalization capability, as the model may struggle to perform consistently on unseen data. The figure suggests minimal overfitting in the MLP model, as performance metrics remain stable across both sets. This stability is largely attributed to the test permutation procedure, which helps mitigate the potential for overfitting. The AE-based NN stands out by maintaining overall scores comparable to those achieved with the complete feature set, and even exhibiting a slight increase in precision. This suggests that this approach effectively retains essential discriminative features, thereby facilitating robust detection of TN.OPEN IN VIEWER

To complement these observations and statistically validate the performance differences between the complete and reduced feature sets, we conducted paired t-tests and Wilcoxon signed-rank tests across six patient-based permutations. The statistical analysis further confirms that the AE-based NN decrease in F1-score is not significant (t-test: p = 0.7187; Wilcoxon: p = 0.8438), reinforcing its strength in retaining essential discriminative information. In contrast, UMAP, PCA, and Isomap show statistically significant drops in performance (all p < 0.01 in t-tests; p = 0.0312 in Wilcoxon tests), reflecting a consistent degradation in classification capability when using only three components. The Wilcoxon test, being non-parametric and robust to outliers, supports the same conclusion as the t-test, lending robustness to the findings. These results position the AE as the most effective among the explored MnL techniques, offering dimensionality reduction and interpretability with minimal compromise to predictive accuracy.

The use of MnL introduces a new level of explainability to the machine decision process, which was previously obscured by the full set of 14 features. By reducing this space to three dimensions, we can now project the instances and obtain some insight of the classifier decisions. In Figure 4, the predictions made by the MLP on both the train and test sets after manifold application are projected onto this latent space. The displayed decision boundary, established after training, demarcates regions where the classifier considers predictions to be either positive or negative. Moreover, the visualization reveals a clear relationship between prediction accuracy and distance from the decision boundary: true predictions (TPs and TNs) lie farther from the boundary, while misclassifications (FPs and FNs) cluster closer to it, indicating higher uncertainty. This consistent clustering pattern across all MnL approaches for the different categories highlights a strong correlation between classifier confidence and the distance from the decision boundary.OPEN IN VIEWER

The MnL-generated spaces visualization demonstrates clear differentiation between voltage levels in machine predictions as well. Figure 5A focuses exclusively on false predictions, applying UMAP to visualize FNs at extreme voltage levels of 20 μV and 80 μV to heighten contrast. It is important to note that FPs are not associated with a specific voltage value, as they indicate the absence of TWA, corresponding to a voltage of 0 μV. As anticipated, a higher number of undetected episodes occur at lower amplitudes, with only a few missed episodes at 80 μV and even fewer at higher amplitudes. Additionally, mispredictions for lower amplitudes are more widely dispersed in the space, especially for the test set, indicating a greater classification difficulty. In contrast, higher-amplitude misses tend to cluster nearer to the decision boundary, suggesting they were closer to correct classification, which further highlights the relative ease of detecting higher-amplitude alternans.OPEN IN VIEWER

This observation, that most missed events are linked to lower-voltage alternans, aligns with the voltage-wise FN analysis presented in Figure 5B. This figure quantitatively compares the distribution of missed TWA detections between the original model (complete set) and the most competitive one, the AE-based NN. Interestingly, while both models exhibit most errors at low TWA amplitudes, the AE-based model demonstrates slightly fewer FN in this low-voltage range, suggesting improved sensitivity to subtle alternans. However, the original MLP generally outperforms the AE-based model at higher voltages, where it achieves near-complete detection. This trade-off illustrates how the AE-based approach may improve detection in more ambiguous, low-amplitude scenarios, while the complete MLP retains an advantage in clearer, high-amplitude cases. Nonetheless, statistical analysis indicates that their overall performance remains closely comparable.

4.2. TWA Detection on Real Ambulatory Environment

The performance of the trained models for detecting TWA episodes in ambulatory recordings is detailed in this section. As mentioned in Section 3.2, TWA events are now integrated into the signal in a sparse and non-sustained manner, reflecting realistic clinical conditions. This presents a significant challenge for detection compared to sustained events. We also employed the patient permutation procedure to enhance the robustness of our results, allowing us to report mean and standard deviation outcomes. The test results shown reveal the effectiveness of our models in accurately identifying TWA episodes while effectively filtering out FPs through the described post-processing steps.

Specifically, Table 2 presents a comprehensive overview of performance metrics for TWA episode detection under these challenging conditions for the different feature sets: the complete and the transformed through MnL techniques. Consistent with the design phase, the complete feature set delivers better results, also observing a progress compared to. ²² Furthermore, this improvement has further widened the gap between our learning-based models and traditional signal-processing methods for TWA detection under these conditions, since the highest achieved F1-score was 78% with SM. In this ambulatory scenario, the sparse occurrence of TWA episodes, which inherently makes them more challenging to detect, naturally leads to a higher FN rate, as reflected in the recall values. Notably, the combination of Isomap and RF comes closest to matching the performance of the complete feature set, demonstrating particularly high recall rates compared to other methods. While all approaches demonstrate satisfactory overall performance, precision results stand out due to the stringent condition for classifying predictions as positive detections, which effectively filters out FPs. Such a procedure enhances the reliability of predictions, ensuring that the identified TWA episodes are not only numerous but also accurate.

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Table 2.

Performance of TWA Detection in Ambulatory Environments on the Test Set, Evaluated in Terms of Precision, Recall, and F1-Score (in %) for Various Feature Sets Using the Best ML Model for Each Set

​	ML model	Precision	Recall	F1-score
Complete	RF	95.9 ± 3.3	70.9 ± 6.3	81.4 ± 4.5
PCA	KNN	90.2 ± 5.1	65.3 ± 7.6	75.6 ± 5.7
UMAP	KNN	89.6 ± 5.2	63.9 ± 6.6	74.5 ± 5.7
Isomap	RF	88.3 ± 6.7	70.8 ± 7.7	78.5 ± 6.4
AE-NN	MLP	98.4 ± 1.7	63.8 ± 7.8	77.2 ± 5.7

Our analysis now shifts to the interpretability offered by the AE-based NN, with a focus on its decision-making process. This method demonstrates not only a consistently strong F1-score but also the highest precision among all MnL approaches, highlighting its capability in minimizing FPs and enhancing the reliability of the detection mechanism. Figure 2 illustrates an example of TWA detection applied to an ambulatory signal, showing the beat series tracking where the TWA pattern is visible. While the model successfully detects some of the TWA episodes, there are a few false predictions and undetected episodes, the latter being attributed to the consistency constraints imposed on the predictions. Figure 6 visualizes the latent space generated by our model, showing the positions of the instances within this learned space. The decision boundary, established during the model design phase, determines whether an instance is classified as negative (red cross) or positive (blue circle), effectively separating the instances. A critical aspect of this analysis is the post-processing step, where the predictions are refined into detections. As observed, only the green-filled points represent true detections, as they have successfully passed the post-processing test. Interestingly, these detections tend to lie on the far side of the decision boundary, indicating a higher confidence in the model predictions. In contrast, instances closer to the boundary are less likely to be classified as detections, demonstrating the model ability to assess prediction certainty. This thorough examination of the model decision-making process not only bolsters our confidence in its explainability but also validates our FP filtering method, which effectively minimizes incorrect detections.OPEN IN VIEWER