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Article

Deep Learning and Recurrence Information Analysis for the Automatic Detection of Obstructive Sleep Apnea

by
Daniele Padovano
1,
Arturo Martinez-Rodrigo
1,*,
José M. Pastor
1,
José J. Rieta
2 and
Raul Alcaraz
1
1
Research Group in Electronic, Biomedical and Telecommunications Engineering, University of Castilla-La Mancha, 16002 Cuenca, Spain
2
BioMIT.org, Electronic Engineering Department, Universitat Politecnica de Valencia, 46022 Valencia, Spain
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(1), 433; https://doi.org/10.3390/app15010433
Submission received: 25 November 2024 / Revised: 29 December 2024 / Accepted: 3 January 2025 / Published: 5 January 2025
(This article belongs to the Special Issue AI-Based Biomedical Signal Processing)
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Abstract

:
Obstructive sleep apnea (OSA) represents a significant health concern. While polysomnography (PSG) remains the gold standard, its resource-intensive nature has encouraged the exploration of further alternative approaches. Most of these were based on the heart rate variability (HRV) analysis, but only a few of them have presented a recurrence-based approach. The present paper addresses this gap by integrating convolutional neural networks (CNNs) with HRV recurrence analysis. Employing three different and publicly available databases from PhysioNet’s official repository (Apnea-ECG, MIT-BIH, and UCD-DB), the presented method was able to expose concealed patterns within the distance matrix of HRV’s phase space, which is discernible at an appropriate level of abstraction through CNNs. Under the challenging context of external validation (MIT-BIH and UCD for training, and Apnea-ECG for testing), the results obtained were comparable to those presented in the state of the art, achieving a peak accuracy of 75%, while maintaining balanced sensitivity and specificity at 74% and 75%, respectively. Moreover, these results obtained by the proposed CNN-based recurrence analysis of HRV also outperformed traditional time–frequency models, which have yielded values of accuracy lower than 65%. Hence, this paper highlights the importance of the proposed method in gaining new insights into OSA’s HRV dynamics, offering a contribution that adds to the existing analytical approaches in the state of the art.

1. Introduction

Obstructive sleep apnea (OSA) is a respiratory disorder of repetitive episodes of breathing arrests during sleep [1]. It has also been associated with increased morbidity and decreased quality of life [1]. OSA sufferers often report daytime somnolence, which can lead to diminished work performance, psychological disturbances, and road accidents in the most severe cases [2]. Moreover, OSA prevalence is estimated to be notably high, affecting between 9% and 38% of general population [3]. However, recent studies highlight a frightening underdiagnosis of this disorder, particularly in individuals with cardiovascular diseases (CVDs), with reported rates exceeding 90% of the surveyed population [4]. Hence, given the substantial comorbidity between OSA and CVDs [5], the early detection of OSA has become a major concern in recent years [6].
Polysomnography (PSG) remains the gold standard for OSA detection but is time consuming and resource-intensive, limiting its availability and delaying diagnosis [7]. It requires placing multiple sensors on the patient, often disrupting sleep quality, and demands overnight monitoring by clinical experts [8,9]. To address these issues, portable technologies for home-based OSA detection, without expert supervision, have been explored by analyzing a limited set of physiological signals from PSG [6]. Among these, heart rate variability (HRV) analysis has shown particular promise [6]. Accordingly, the significance of HRV-based techniques in OSA detection and cardiovascular risk assessment has been underscored by previous research [10]. HRV analysis has gained considerable acclaim for its ability to reflect the autonomic nervous system activity, which is strongly correlated with respiratory control [11]. In this context, the HRV extracted from ECG rather than from other physiological signals (e.g., the photoplethysmogram) has provided more accurate results in identifying arrythmias [12], sleep apnea [13], and other cardiovascular diseases [14].
So far, most of the proposed HRV-based OSA detectors were based on the combination of hand-crafted features through common machine learning (ML) classifiers, such as support vector machine (SVM), k-nearest neighbors (KNN), decision tree (DT), and so forth [7]. For this purpose, common time and frequency HRV features described by the Electrophysiology Task Force of the European Society of Cardiology and the North American Society of Pacing [15] have been widely used [16]. In recent years, other features computed by transforming the HRV signal using wavelet transforms [17,18], Lomb–Scargle periodgrams [19], and complexity planes [20,21] have also been broadly analyzed. In a complementary way and with the aim of improving characterization of the intricate dynamics of OSA episodes, the structural changes and transitions occurring along time in the HRV signal have also been recently considered. Thus, a few works have combined nonlinear features obtained by quantifying recurrence behavior of the HRV signal [22,23,24].
Such analysis primarily relies on the recurrence plot (RP), a graphical tool widely employed in nonlinear dynamics and statistical physics with various applications in pattern analysis and meteorology [25]. This graph results from transforming a time series into a 2D image which represents the times at which a trajectory approximately revisits the same area in the phase space [26]. This plot therefore shows hidden information about the nonlinear dynamics in the time series as well as global information about its recurrence behavior [27]. However, to objectively characterize and compare different types of RP, it is common to quantify the number and duration of recurrences using specific parameters. This process begins by setting a distance threshold to determine if two neighboring data points in the phase space should be considered as recurrence, bringing a binazired image of black and white dots. Later, different indices are computed from that binarized image, such as the percentage of recurrence points (recurrence rate), percentage of points that form vertical lines (laminarity), average length of diagonal lines, and length of the longest diagonal line [27].
This quantitative study of the recurrences in the RP is known as recurrence quantification analysis (RQA) and has provided promising results in a variety of disciplines [28,29]. Previous works have explored RQA and other recurrence-based methods combined with ML for OSA classification, but few have investigated the use of recurrence images from HRV in deep learning (DL) models. Early studies, like those by Acharya et al. [30] and Nguyen et al. [22] used traditional ML techniques such as artificial neural network (ANN) and SVM with RQA features derived from ECG or HRV. More recent works, such as Taghizadegan et al. [18], employed CNNs with RPs from multiple signals including ECG and respiration, showing improved performance. Moreover, Ayatollahi et al. [31] are the only researchers to use CNNs with distance matrices derived from ECG signals. However, while they applied CNNs and RPs to ECGs, this approach may depend on the morphology of the signal, which varies based on the recording system (e.g., conventional, Holter, wearable, etc.). In contrast, HRV signals do not exhibit morphological changes regardless of the recording system, even though this aspect is yet underexplored.
However, RQA strongly depends on the selected threshold for recurrence quantification. Choosing an incorrect threshold can result in recurrence plots dominated by ones or zeros, making it difficult to identify discriminative patterns [32]. Furthermore, recent studies have shown that RQA features provide only a limited representation of the phase space’s characteristics, potentially underestimating important temporal trends and dynamic changes in the original time series [33].
While other nonlinear measures, such as entropy-based indicators, have been explored, they primarily focus on the randomness or complexity of signals and often fail to capture spatial recurrence patterns comprehensively. In contrast, recurrence plots provide unique insights into the spatial organization of recurring states within a signal, offering a richer perspective on the dynamics of physiological processes. This spatial recurrence information has not yet been analyzed in sufficient depth within the context of OSA.
In this context, CNNs present a significant advantage by leveraging recurrence images directly without requiring predefined thresholds or explicit feature engineering. Unlike traditional RQA, CNNs can extract richer spatial and temporal features from recurrence plots, capturing patterns and trends that might otherwise be overlooked. Moreover, CNNs are better suited to generalize across diverse datasets, addressing challenges such as variability in HRV signals or differences in recording conditions. Despite these advantages, none of the previous works explicitly utilized recurrence images derived from HRV signals in combination with CNN architectures. This highlights a clear gap in the literature, where the potential of HRV-based recurrence information combined with deep learning remains largely unexplored.
To this respect, assessing the distances within the phase space (unthresholded RP) instead of focusing on quantitative measures derived from the RP could bring further information on the underlying nonlinear dynamics of HRV. One possible approach can be introducing such unthresholded representations into DL algorithms and letting them automatically extract hidden recurrence patterns to make better extrapolations of OSA episodes. In fact, the global assessment of unthresholded RPs when imputed to different DL-based schemes has revealed more information than RQA, which has been evidenced in different areas of health and engineering, including human activities [34] and heart rate measurement [35].
Accordingly, the aim of the present study is to provide an innovative perspective on OSA detection by exploring the potential of DL algorithms in interpreting HRV’s recurrence information under an image classification approach. Through a detailed and comparative analysis between these approaches and traditional methods based on RQA markers, the intention is not only to demonstrate the effectiveness of this emerging technique but also to foster a broader discussion regarding the optimization and enhancement of OSA detection systems.

2. Methods

The methodology applied in this work is outlined in Figure 1. Initially, the available ECG recordings were processed to eliminate noise and artifacts, and then we extracted the HRV series through their RR intervals. From there, the phase space reconstruction translated the HRV into a higher-dimensional representation, while the interpolation standardized the signal at 4 Hz to ensure time–frequency consistency across all samples. These processes were followed by the construction of a distance matrix and wavelet transforms, respectively, transforming the HRV data into 2D image-like format. These transformed outputs were then used to train and validate various ML and DL models whose operations are depicted in Figure 2. All these steps are detailed in the next subsections.

2.1. Databases

Three widely used and freely available [36] datasets for OSA detection were enrolled in the present study, i.e., the Apnea-ECG Database [37], the MIT-BIH Polysomnographic Database [38], and the University College Dublin Sleep Apnea Database (UCD-DB) [39].

2.1.1. Apnea-ECG Database

This dataset was initially published in the 27th International Conference of Computers in Cardiology 2000, specifically for the challenge of sleep apnea detection from a single-lead ECG [37]. It has been widely regarded as the most appealed database in the state of the art [7,40]. A total of 70 ECG recordings were included in the database, with a duration between 7 and 9 h each, obtained from 30 different subjects, consisting of 25 men and 5 women aged between 27 and 63 years. The ECG recordings were sampled at 100 Hz and quantified at 200 A/D units per mV. For the challenge, the data were divided into a released set (often referred to as the training set) and a withheld set (analogously, the testing set), each containing 35 recordings. Expert-based annotations were provided on a minute-by-minute basis.

2.1.2. MIT-BIH Polysomnographic Database

This dataset was collected at MIT’s Beth Israel Hospital in Boston and includes 18 PSG recordings from 16 male subjects aged between 32 and 56 years [38]. The ECG signal was recorded using a portable holter device, which sampled data at 250 Hz with 12 bits per sample. Expert annotations were provided following the same standardized criteria as those used in the Apnea-ECG database but in segments of 30 s of duration. Specifically, the annotations provided detailed categorizations of different apnea types, such as obstructive, central, and mixed events. Furthermore, the dataset tracks subject movements during sleep, such as leg movements and other motor activity, which could be indicative of sleep disturbances or restlessness.

2.1.3. University College Dublin Sleep Apnea Database

This dataset, obtained from St. Vincent’s University Hospital, consists of 25 PSG recordings with a duration of 6 to 8 h, which were acquired from 21 male and 4 female subjects aged between 28 and 68 years [39]. The ECG signal was sampled at 125 Hz, although the quantification parameters were not explicitly specified. Expert annotations were made following the Rechtschaffen and Kales scoring standard [41], indicating the exact start–stop timestamps of every event in real time. The annotations included various forms of apnea, disordered breathing episodes, and abnormal cardiac rhythms such as bradycardia or tachycardia.

2.2. Data Labeling

The data-labeling process standardized labels across different databases (see Figure 3). In the Apnea-ECG database, labels were based on whether apnea occurred at the start of the minute (Figure 3a) with “A” for apnea and “N” otherwise. In the MIT-BIH database, segments were re-labeled by inheriting the original label, which corresponded to the first episode in the segment (Figure 3b). If the episode was associated with apnea, the label was converted to “A”; otherwise, it was assigned “N”. For the UCD-DB database, the cohesion with the other two was ensured by synchronizing each ECG and its corresponding annotation file to the same time frame (Figure 3c). The recordings were then divided into one-minute segments, which was similar to the other databases. After segmentation, the ECG excerpts were labeled as “A” if an apnea-related episode occurred right at the start of the segment and “N” otherwise. This systematic approach allowed for uniformity in the labeling process across all databases, ensuring a consistent framework for training models.

2.3. Signal Processing

The ECG signals were resampled to 500 Hz solely to improve R-peak detection, since upsampling factors have been widely used in the literature for this purpose [42]. To mitigate high-frequency noise, a second-order Chebyshev filter with a cut-off frequency of 100 Hz was applied. Additionally, a second-order Chebyshev filter with a cut-off frequency of 0.5 Hz was used to reduce low-frequency baseline interference. Both filters were implemented under a zero-phase structure to maintain the original signal’s phase and amplitude characteristics [43]. Next, the Pan–Tompkins algorithm, known for its effectiveness and computational efficiency, was employed for R-peak detection [44]. To account for slightly delayed or missed R-peak locations, a sliding R-peak correction window was applied. Subsequently, the ECG recordings were segmented into 1-min intervals to extract the measure of HRV by calculating the consecutive time differences between R-peaks [15].
Eventually, a manual signal screening process was conducted to discard segments with a high presence of noise or artifacts, such as lead detaching, amplitude saturation, sneezes, and others. As a result, 81% of Apnea-ECG, 87% of MIT-BIH, and 91% of UCD-DB segments were deemed suitable for further analysis. Overall, a total of 40,993 ECG segments were obtained, providing approximately 683 h of valuable information. The distribution of these segments by databases and classes can be found in Table 1.

2.4. RP-Based Representation of the HRV Signal

The RP was introduced by Eckman et al. [27] as an advanced tool of nonlinear data analysis to explore the recurrence features and irregularity properties of time series dynamic information in the phase space [22]. In order to visualize how the trajectory of the time series recurs roughly the same area in the phase space, a multidimensional representation of the series is firstly required. For that purpose, Taken’s time delay theorem has been widely used [45]. Thus, considering the HRV signal as the time series s ( n ) = { s ( 1 ) , s ( 2 ) , … , s ( N ) } of length N samples, it can be embedded into an m-dimensional space as
X → = x → 1 x → 2 . . . x → k = s ( 1 ) s ( 1 + τ ) … s ( 1 + ( m − 1 ) τ ) s ( 2 ) s ( 2 + τ ) … s ( 2 + ( m − 1 ) τ ) . . . . . . . . . . . . s ( k ) s ( k + τ ) … s ( k + ( m − 1 ) τ ) ,
where k represents the k-th point on the trajectory of the time series ( k = 1 , 2 , … , N − ( m − 1 ) τ ), τ is the delay time, and m is the embedding dimension. More precisely, the parameters involved in Equation (1) can be described as follows:
  • X → represents the phase space trajectory matrix.
  • x → i denotes individual state vectors within the phase space.
  • s → i refers to the time series values at different time points.
  • τ is the time delay, determining the temporal separation between consecutive elements in each state vector.
  • m represents the embedding dimension, indicating the number of components in each state vector.
  • k signifies the number of state vectors constructed from the time series.
These parameters collectively define the reconstruction of the phase space from a univariate time series, which is fundamental for the creation of RPs. The matrix structure illustrates how successive time-delayed values are organized to form multidimensional state vectors, capturing the system’s dynamics in a higher-dimensional space.
The optimal selection of both parameters τ and m is a key step to obtain a fully representative RP of the time series recurrence. To this respect, if τ is too large, the points in the trajectory might be disconnected and no recurrences could be observed. Contrarily, if τ is too small, redundant information for the same states of the trajectory could be captured and the reconstructed attractor would be compressed along the identity line [46,47]. Also, if m is too small, the geometry of the phase space is partly folded and, if m is too large, a rounding error due to excessive partitions could contaminate the attractor [48]. Different approaches can be found in the literature to optimize the selection of these two parameters. In the present work, the well-known methods of average mutual information and false-nearest neighbors were used [49], reporting optimal values of m = 3 and τ = 2 , respectively. However, several tests using further values of m and τ have been performed, finding no notable differences respect to the values mentioned before.
Thereafter, the distance between every point x → k and the remaining ones in the phase space must be computed, thus resulting in the squared matrix:
D ( i , j ) = | | x → i − x → j | | ,
where i and j range from i to N − ( m − 1 ) τ × N − ( m − 1 ) τ , and the function | | · | | represents the Euclidean norm. Although different metrics have been used to estimate the distance between pairs of points in the trajectory, such a norm has been widely used in many previous works [50]. This matrix D ( i , j ) is also known as the distance matrix (DM), unthresholded RP or general RP [51], and it provides a global overview of underlying and hidden nonlinear dynamics in the time series [52]. Finally, to easily identify recurrences in the phase space, the DM is converted to an RP by applying a simple binarization approach, so that
R ( i , j ) = 1 if ∥ x i → − x j → ∥   ≤ ϵ , 0 otherwise ,
where i and j range between 1 and N − ( m − 1 ) τ , and ϵ is the threshold distance to consider two points in the trajectory as recurrent [26]. The visual representation of this matrix results in a binary image (i.e., the RP) where, by convention [51], a black dot is represented if the norm is lower than ϵ ( R ( i , j ) = 1 ) and it is a white dot otherwise ( R ( i , j ) = 0 ):
As an example, Figure 4a,b show the overall process for the representation of the DM for two typical normal and apneic episodes, where white zones indicate larger distances between points in the trajectory of the HRV signal and darker zones represent smaller distances. In the same figures, however, the RPs are also represented as thresholded images where recurrence zones are represented in black dots. As can be seen, if the threshold is too large, most points in the RP will be converted to zero, and recurrence information could be blurred. Contrarily, if the threshold is too small, the resulting RP could lose significant information. According to most previous works related to HRV and RP [26,52,53], the selected threshold ϵ was set as 10% of the maximum phase space diameter.

2.5. OSA Detection Based on Deep Learning Techniques

In the DL context, convolutional neural networks (CNNs) are the most extensively employed algorithms for a wide variety of applications, being especially relevant in fields like computer vision [54], medicine [55], and speech recognition, among others [56]. They are generally constituted by an M × M × L input layer followed by one or more convolutional layers, a fully connected layer, and eventually an output layer [57]. Unlike the conventional multi-layer perceptron networks, convolutional layers are typically oriented to make use of full 2-dimensional input data [58]. These layers use a series of filters or kernels that generate abstract representations denominated feature maps, i.e., matrix representations that capture patterns within the input image. These feature maps are obtained as the convolution of an input image with a kernel matrix containing the weights for every corresponding pixel [58].
Kernels can have similar dimensions but different sizes compared to the input layer. These particular filters slide along the input image to generate feature maps employing a determined and quantified displacement measure, usually referred to as stride, which specifies the number of pixels that the kernel has to move along to perform the convolutional operations [58]. Furthermore, for more complex and long-concatenated networks, a pooling layer may also be included at the end of each convolutional layer to downsample the feature maps by aggregating features from local spatial regions [59].
In addition, the process involves mapping both RP and DM representations with specific color codes suitable for input into generic DL-based classifiers. DMs utilize MATLAB’s jet colormap for mapping the distances (Figure 5). On the other side, traditional RPs also employ the same colormap, resulting in red and blue images similar to those depicted in Figure 6. It should be noted that the graphs in Figure 5 and Figure 6 come from the same phase spaces. These representations allow for a distinct visualization of the data, facilitating their use in the CNN models applied in this study. Notice that colorbars follow the same criteria stated in the previous section. All the proposed CNN-based architectures were supplied with identical color images of DMs and RPs. Nevertheless, these images were rescaled to fit the corresponding dimensions of the input layers.
In the current study, in order to discern between normal and apneic episodes, two distinct CNN architectures were employed. Firstly, a customized CNN model (referred to as cuCNN) was designed, as illustrated in Table 2. This architecture incorporated a limited number of layers, starting with three convolutional layers featuring 32, 64, and 128 filters (kernels), each with dimensions of 3 × 3 and a stride of 1 × 1 . Subsequently, the outputs from each convolutional layer underwent max pooling and batch normalization, employing the rectified linear unit (ReLU) activation function [60,61]. Following the last convolutional layer, two fully connected layers were introduced to facilitate the extraction of higher-level features [62]. These high-level features were then processed by an output layer, which determined the classification outcome based on cross-entropy loss and the input weights computed in the preceding layer [63]. To prevent overfitting and enhance the network’s generalization capabilities, a dropout layer with a 50% probability was placed just before the final fully connected layer [64]. Notably, this proposed CNN architecture comprised 25.7 million learnable parameters.
On the other hand, AlexNet is a deep neural network consisting of 56.8 million learnable parameters and several layers [65]. It begins with an input layer of 227 × 227 × 3 pixels, and it incorporates various features such as ReLU activation, local response normalization, overlapping pooling, and dropout regularization [65]. To better illustrate the architecture of the network, Table 3 is provided for a detailed description of the structure.
This latter CNN-based network takes advantage of the widely reported benefits of transfer learning [7]. Transfer learning involves leveraging the knowledge acquired from training a deep neural network on a large-scale dataset, such as ImageNet [66], and applying it to a different task [67]. The use of AlexNet’s pre-trained weights allowed the extraction of meaningful high-level features from the network’s input [68]. Thus, with the aim of providing more robustness to the results, AlexNet was trained with and without the pre-trained weights from ImageNet’s database. Eventually, the training and validation proportion for the suggested DL-based architectures was set to an 80:20% ratio, following the most common practices found in the state of the art [6].

2.6. OSA Detection Based on Machine Learning Techniques

As previously introduced in Section 1, many prior studies addressing OSA detection from RPs have typically combined RQA features with conventional ML classifiers [6]. In these cases, the most commonly computed features from RPs have often included the following [24]:
  • Recurrence rate (REC): percentage of points in the plot that represent recurrences or instances where the system revisits a similar state.
  • Determinism (DET): percentage of recurrence points which form diagonal lines.
  • Shannon entropy (ENTR): Shannon entropy of the probability distribution of the diagonal line lengths.
  • Average diagonal line length (L): average length of all diagonal lines within an RP.
  • Divergence (DIV): inverse of the length of the longest diagonal line, which also corresponds to the sum of the positive Lyapunov exponents [51].
Thus, OSA detection was also tackled by combining the above parameters through the most common ML classifiers, such as support vector machine (SVM), k-nearest neighbor (KNN), decision tree (DT), and two random forest-based ensemble classifiers, i.e., adaptive boosting (ADA) and bootstrap aggregation (BAG). Specific parameters were chosen for each case. More precisely, SVM used a Gaussian radial basis function kernel (kernel scale 1, polynomial order 3). In addition, the KNN algorithm employed the Euclidean distance method with equal weights. DT models were set with a maximum of 2 splits, a minimum leaf size of 1, and a minimum parent size of 10, adhering to the classification and regression trees (CART) predictor [69]. Ultimately, both ensemble models underwent 100 learning cycles using the decision tree learner, differing only in ADA’s learning rate set at 1.

2.7. Other OSA Detectors Based on Time–Frequency Analysis

Other algorithms based on a traditional time–frequency analysis of the HRV were included in the study. First, the two analyzed CNN schemes, i.e., cuCNN and Alexnet, were fed with images obtained by transforming the HRV signal into a bidimensional image using continuous wavelet transform (CWT) [70], resulting in scalograms or graphical representations of the CWT coefficients [71]. In a scalogram, the x-axis typically represents location in time, whereas the y-axis represents scale or frequency, and the color or intensity represents the magnitude of the wavelet coefficients at each location and scale pairs. The employed wavelet was the analytic Morlet wavelet, which was chosen for its effectiveness in capturing the time–frequency components of HRV [72]. Twelve voices per octave (scales) were used based on the approach described by Neto et al. [72], which provided a suitable method for distinguishing subtle differences between apneic and normal episodes. As an example, Figure 7 illustrates some representative wavelet scalograms for apneic (Figure 7a,b) and normal (Figure 7c,d) episodes. Eventually, these images were rescaled to 227 × 227 × 3 pixels to match the input layers of the aforementioned DL algorithms.
It should be noted that to overcome the uneven sampling issue of the RR-interval series, it was resampled with spline interpolation at 4 Hz, which is high enough to satisfy the Nyquist sampling requirements considering that the frequency bands of study for HRV analysis lie between 0.15 and 0.4 Hz [15]. Former works also employed similar sampling frequencies following the same reasoning [73,74].
Several ML-based models were also generated by combining the most common time, frequency, and complexity features proposed to analyzed the HRV signals through the classifiers mentioned in the previous subsection. Specifically, such models were already analyzed in previous works [40] by following a typical ML-based pipeline (signal processing, feature extraction, feature selection, training, classification, and model validation) as well as extracting features from HRV’s time, frequency and complexity domains. Some of these features included statistical maximum, minimum, RR interval counts, the power spectral density in determined frequency bands, and entropy-based measures. Further details of these features can be found in [40] and are fully itemized by the Task Force of The European Society of Cardiology and The North American Society of Pacing and Electrophysiology [15]. Also, the classifiers’ parameters remained consistent with those outlined in Section 2.6.
Ultimately, a variety of feature combinations was used to feed the above ML-based models, coming from the application of two sequential feature selection (SFS) algorithms [75]. Specifically, we applied Sequential Forward Feature Selection (SFFS) and Sequential Backward Feature Selection (SBFS) to identify the most relevant features for the models. The models were initially supplied with the complete set of available features. Then, they were separately fed with two distinct feature sets: one derived from SFFS and the other from SBFS. In SFFS, features were added incrementally, starting from an empty set, and at each step, the feature that contributed the most to improving model performance was selected. Conversely, SBFS started with the full set of features and iteratively removed the least important ones. Due to the large number of results generated, only the models that delivered the best outcomes are presented in the Section 3 out of the three generated (all features, those selected by SFFS, and those chosen by SBFS).

2.8. Training and Testing of the OSA Detectors

In order to ensure the most accurate and unbiased evaluation of a classification model’s performance, it is essential to separate the training and testing procedures using different datasets. This approach is recommended to avoid overly optimistic results that often occur when the same patient data are shared in both stages, as pointed out by the Transparent Reporting of a Multivariate Prediction Model for Individual Prognosis or Diagnosis (TRIPOD) initiative [76]. In the present study, such a recommendation was followed by employing balanced subsets of the MIT-BIH and UCD-DB datasets for training the OSA detection models and leaving Apnea-ECG dataset for testing. During the model testing phase, all the observations from the Apnea-ECG dataset were employed. This choice was made because the Apnea-ECG dataset has been widely used in previous research, allowing to indirectly compare the obtained results with previous works.
Hence, to train all the CNN-based models, provided with DM, RP, and CWT images, the learning rate was established at the initial value of 0.001 following the guidelines of the state of the art [6]. This parameter refers to the step size for updating network weights [77]. The epoch refers to the number of times that the learning algorithm is going to work through the entire training set [78]. In the present work, the generated DL models were trained over 10 epochs. Then, the mini-batch size was established to 128, which is the number of samples sent to the model in each training cycle [77]. Additionally, the adaptive moment estimation (ADAM) optimizer was employed to update model weights during training [79]. While hyper-parameter optimization techniques such as grid search or Bayesian optimization were not employed in this study, the selected hyper-parameter values follow established conventions and were validated through preliminary experiments to ensure robust performance. This approach was chosen to prioritize simplicity and reproducibility.
Eventually, several performance measures were calculated, such as sensitivity (Se), specificity (Sp), accuracy (Ac), positive predictive value (PPV), negative predictive value (NPV), and F 1 -score [75]:
A c = T P + T N T P + T N + F P + F N , S e = T P T P + F N , S p = T N T N + F P , P P V = T P T P + F P , N P V = T N T N + F N , and F 1 = 2 · T P 2 · T P + F P + F N .
where true positive (TP) represents the number of episodes correctly classified as OSA, true negative (TN) corresponds to the number of episodes correctly classified as normal, false positive (FP) corresponds to the number of episodes incorrectly classified as OSA, and false negative (FN) corresponds to the number of episodes incorrectly classified as normal.
All experiments were implemented in MATLAB R.2023a for Linux and the included Deep Learning Toolbox. Whereas the training process was conducted on a cluster of graphical processing units consisting of two NVIDIA GEFORCE RTX (TM) 3080 mounted on an Ubuntu (20.04 LTS) server, the testing stage was performed on an Intel (R) Core (TM) i7-4790 CPU (3.6 GHz) with 16 GB RAM.

3. Results

Table 4 shows the results obtained from DL-based models with different input images. For the DM images, the pre-trained AlexNet model outperforms both cuCNN and the non-pre-trained AlexNet across every performance measure. It consistently achieves the highest values of Ac (74.72%), Se (73.99%), and Sp (75.17%). In the RP images analysis, cuCNN shows relatively good performance across Ac (68.72%), Se (66.52%), Sp (70.07%) Both versions of AlexNet perform similarly: slightly lower than cuCNN in Se and Sp. Regarding CWT images, the cuCNN model displays the lowest overall performance: Ac (64.11%), Se (68.52%), Sp (62.39%). In addition, the non-pre-trained AlexNet model performs better than cuCNN but falls short compared to the pre-trained version, which maintains a slight advantage.
On the other hand, Table 5 shows the results obtained from ML-based models accordingly to the input features. In all cases, the SVM shows higher Sp and lower Se. With five features, the SVM model displays the highest Sp (89.06%) and the lowest Se (21.69%) among the rest. In general, however, as the number of features increases, the performance metrics tend to stabilize with slight fluctuations but no special differences between them.

4. Discussion

First of all, it is important to clarify that a 1-min signal length was selected for HRV analysis because most studies have based their classifiers on this timeframe [7,80]. This is primarily because the most widely used database in the literature, APNEA-ECG, provides annotations in 1-min intervals. Although the Task Force established that the minimum required for HRV analysis was 5 min of ECG recordings, trends have evolved over the decades, showing that analysis can be effectively reduced to shorter intervals without compromising classifier performance, especially when it comes to detect OSA episodes, which generally last from 15 to 30 s [3]. This has been supported in other studies with ultra-short ECG recordings, considering intervals as brief as 15 s [81].
The results clearly show that DL models outperform ML models, underscoring the limited value of RQA features in ML compared to the richer, unthresholded RP representation (i.e., DM). This aligns with findings in other research fields [32,33], where RQA can introduce information leakage by oversimplifying changes in the phase space. As seen in Table 5, ML models based solely on RQA features delivered poor results, while significant improvements occurred with image-based features and DL models. This suggests that recurrence analysis, at an adequate level of abstraction, enhances classification performance. Conversely, this pattern does not reproduce for time–frequency analysis. Traditional ML models trained on discrete time–frequency features showed no substantial performance gains when compared to their DL counterparts using CWT and CNNs. Therefore, recurrence analysis offers deeper insights into HRV dynamics for OSA detection than conventional time–frequency transformations, such as CWT.
Furthermore, the significance of pre-training becomes evident in the final performance of the models. As demonstrated in the results in Table 4, the pre-trained version of AlexNet with DMs outperformed the rest of the DL models. The prior exposure to a diverse range of colors and shapes from ImageNet may have provided the network with additional levels of abstraction, enhancing its ability to distinguish between apneic and normal episodes. However, this effect was not replicated in subsequent experiments involving RP (thresholded DM) and CWT. This missing improvement may be attributed to the information leakage inherent in RP and CWT representations, making DM images more effective for this task.
The optimal outcomes in our study, around 75% Ac, may appear lower compared to previously reported state-of-the-art results. However, direct comparisons are difficult due to differences in experimental contexts. Many prior studies reporting Ac above 90% often rely on training and validating their models with a single dataset, which has been shown to artificially inflate results, as demonstrated in previous works [40,82,83,84,85]. This discrepancy arises because, in the case of a single dataset for both training and testing, samples from the same patients are mixed in both the training and testing sets. Consequently, the algorithms tend to memorize the data, resulting in inflated classification metrics, failing to demonstrate the model’s ability to generalize to new, unseen data, which is crucial for assessing the model’s true performance. This effect is particularly crucial to consider when using cross-validation. Most studies classifying OSA episodes have not mentioned or specified implementing a patient hold-out strategy, which is essential to avoid potential bias in cross-validated tests [85] (see Table 6).
In order to provide a more realistic assessment of the model performance, it is imperative to use an external validation framework, which is advocated by international guidelines such as the TRIPOD statement [76]. In this study, distinct datasets have been employed with variations in recording times, patient demographics, and acquisition systems for training and testing, offering a less biased representation of performance in conditions more similar to clinical practice. Indeed, as previously published in an earlier work [40], when the same ML models are tested with 10-fold cross-validation, Ac, Se, and Sp are, on average, up to 15% higher than those obtained through external validation regardless of the feature set used to train the models.
The datasets used in this study (Apnea-ECG, MIT-BIH, and UCD-DB) were collected in diverse clinical contexts, including healthy individuals and patients with cardiac conditions such as arrhythmias. While these datasets differ in demographics and technical characteristics such as age ranges, gender representation, and equipment specifications, our HRV-based methodology is robust to these variations. Unlike methods reliant on raw ECG signals, which are sensitive to factors like electrode placement and sampling frequency, HRV analysis ensures greater adaptability across different acquisition systems. However, the limited demographic diversity highlights the need for future studies with more representative datasets to further validate and generalize the findings.
The analysis of false positives and false negatives may provide valuable information. False positives are often linked to subtle signal artifacts or transient HRV fluctuations that, despite noise filtering, may affect the classifier’s belief. This suggests that refining artifact detection criteria, particularly for borderline cases such as bradycardia or transient autonomic changes, could improve accuracy [15]. Conversely, false negatives might indicate an underrepresentation of certain apnea patterns or demographic subgroups in the training data. If this is the case, expanding the diversity of datasets and incorporating augmentation techniques could help the model generalize better [76]. These considerations point to the importance of balancing preprocessing rigor with representativeness in training.
When comparing our findings with those of Nguyen et al. [22], who also validated an ML model based on RQA features extracted from HRV using a three-fold cross-validation on a single database (the Physionet Apnea-ECG database), our results align with theirs, demonstrating more moderate performance compared to inflated results from cross-validation alone (Table 6). This reinforces the robustness of our model under more strict evaluation conditions. Other works not solely based on RQA but also concerning OSA detection using HRV, such as Varon et al. [86] and Martín-Gonzalez et al. [87], reported similarly moderate results (around 80–85%) when using external databases with segments of one-minute length of ECG. This consistency underscores the importance of rigorous validation practices.
Moreover, the present study has faced common limitations related to data scarcity and the computational demands of the proposed models, especially for the DL ones. These challenges are common in the field, requiring larger and more diverse datasets. In view of this, it is also important to highlight the value of employing public databases, since this allows the reproducibility of experiments by other researchers and facilitates direct comparisons (provided the same experimental setup).
Also, while RQA systematically calculates specific recurrent patterns, combining it with other techniques like entropy and fractal analysis could provide complementary insights and enhance the characterization of nonlinear dynamics in OSA events. These methods can generate additional images, which, when combined with recurrence-based images, can be fed into DL models. Since DL has shown superior performance compared to traditional machine learning approaches, future research should explore this fusion of diverse visual representations to potentially improve the accuracy and comprehensiveness of OSA diagnostic models, ultimately benefiting clinical practice.

Future Work

Future work can explore advanced feature engineering techniques, such as higher-order statistical measures or nonlinear dynamics, to capture subtle physiological variations beyond standard HRV features, aligning with Quin et al.’s 2021 insights [88]. Integrating multimodal data (e.g., EEG, PSG) offers potential to enhance the detection of subtle changes and broaden understanding of conditions like sleep apnea. Additionally, adopting deep learning architectures like attention mechanisms or transformers could improve the modeling of complex time-series dependencies. Efforts should also prioritize larger, more diverse datasets and robust preprocessing techniques to handle noise or artifacts, further enhancing model generalization and applicability in clinical and research contexts.
Moreover, one of the challenges in DL-based approaches is the phenomenon of model degradation over extended periods of use. This issue arises due to changes in data distributions, sensor drift, or evolving application scenarios, which can lead to a decline in model performance. Even though the proposed method was developed and validated under the assumption of stable data characteristics exposed to CNN-based structures with no recurrent connections within the network, the proposed method is not completely exempt from this limitation. Thus, a potential solution to address this issue is the periodic re-training of the model with updated data, as suggested in related works. For instance, Wang et al. explore re-training as a strategy to maintain model Ac over time [89].
In the context of our work, integrating such re-training strategies could improve the robustness and long-term applicability of our method, particularly in scenarios where signal properties may evolve or where datasets are expanded with new populations. Future studies could explore combining our synchronization framework with adaptive learning mechanisms, such as transfer learning or domain adaptation, to counteract the effects of model degradation. This would not only enhance performance but also ensure the reliability of the system in dynamic environments.
Table 6. Previous works on apnea detection based on recurrence information analysis and ECG.
Table 6. Previous works on apnea detection based on recurrence information analysis and ECG.
Ref.YearAuthorsDatabasesMethodologyClassifiersValidationAc (%)Se (%)Sp (%)
[30]2011Acharya et al.UCD-DBNonlinear features from ECG: ApEn, fractal dimension, correlation dimension, Lyapunov exponents, Hurst exponentsANN3-fold cross-validation89.1100.095.0
[22]2014Nguyen et al.Apnea-ECG
(released set)		Recurrence Quantificantion Analysis (RQA) from HRV with Fixed Amount of Neighbor thresholdingSVM, ANN3-fold cross-validation85.2686.3783.47
[90]2016Cheng et al.Apnea-ECG
(released set)		Heterogeneous Recurrence Analysis on HRV series with PCALRAverage of 100 iterations of randomly selected training and testing datasets85.083.082.0
[23]2016Le and BukkapatnamApnea-ECG
(released set), UCD-DB, Custom recorded		Characterization of the HRV state space with RP (RQA)SVMTested on Apnea-ECG and custom dataset83.6--
[87]2017Martín-Gonzalez et al.Apnea-ECG, HuGCDN2014Filterbank, Cepstrum, DFA, and QDA on HRVLDA, QDA, LRApnea-ECG as Training set, HuGCDN2014 as Testing set84.7681.4586.82
[24]2018Martín-Gonzalez et al.Apnea-ECG, HuGCDN2014Recurrence Quantification Analysis (RQA) based on HRV obtained with Fixed Amount of Neighbors (FAN) algorithm (5%)LDATrain with Apnea-ECG, test with HuGCDN201486.33--
[18]2021Taghizadegan et al.MIT-BIH, UCD-DBReproduce RP from ECG, EEG, and respiration signals. Transfer learning with fine-tuning and Weighted Majority Voting (WMV)CNN10-fold cross-validation on MIT-BIH90.7289.6189.29
[91]2021Mukherjee et al.Apnea-ECGThree different CNN models: Wang, Sharan and Almutairi’s models. All adapted to input 1-D ECG signalCNNUsed original training (released) and testing (withheld) proportion85.5888.26-
[31]2022Ayatollahi et al.Apnea-ECGCustom CNN, ECG’s distance matrix as inputCNN5-fold cross-validation93.33-93.6
-2024Padovano et al.Apnea-ECG, MIT-BIH, UCD-DBCustom CNN, HRV’s DM as inputCNNExternal validation74.7273.9975.17

5. Conclusions

The recurrence analysis of the distance matrix extracted from HRV’s phase space, when applied at the adequate level of abstraction provided by a pre-trained convolutional neural network, significantly enhances apnea detection compared to previous models based on time–frequency analysis and traditional machine learning techniques. The moderate results in our study reflect a more realistic evaluation, increasing the reliability of the findings over those inflated by single-dataset analyses. The external validation framework shows that valuable information can be extracted from the HRV recurrence dynamics without thresholding recurence plots, offering new insights into apnea detection that are more predictive than traditional methods like continuous wavelet transforms and recurrence quantification analysis. Thus, whilst this paper did not aim to propose a superior predictive method, it illustrates that meaningful insights could emerge from appropriately combining recurrence information with deep learning techniques.

Author Contributions

Conceptualization, D.P., A.M.-R. and R.A.; methodology, D.P.; software, D.P.; validation, D.P., A.M.-R. and R.A.; formal analysis, D.P., A.M.-R. and R.A.; investigation, D.P., A.M.-R. and R.A.; resources, A.M.-R., R.A., J.M.P. and J.J.R.; data curation, D.P.; writing—original draft preparation, D.P.; writing—review and editing, D.P., A.M.-R. and R.A.; visualization, D.P., A.M.-R. and R.A.; supervision, A.M.-R. and R.A.; project administration, A.M.-R. and R.A.; funding acquisition, A.M.-R., R.A, J.M.P. and J.J.R. All authors have read and agreed to the published version of the manuscript.

Funding

This research has received financial support from public grants PID2021-128525OB-I00 and PID2021-123804OB-I00 of the Spanish Government 10.13039/501100011033 jointly with the European Regional Development Fund (EU), SBPLY/21/180501/000186 from Junta de Comunidades de Castilla-La Mancha, TED2021-130935B-I00, funded by the Spanish Government in conjunction with the European Regional Development Fund (EU), and AICO/2021/286 from Generalitat Valenciana. Moreover, Daniele Padovano holds a predoctoral scholarship 2022-PRED-20642, which is co-financed by the operating program of European Social Fund (ESF) 2014-2020 of Castilla-La Mancha.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available in the article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Schematic representation of the proposed methodology.
Figure 1. Schematic representation of the proposed methodology.
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Figure 2. Illustrative summary of ML and DL operations.
Figure 2. Illustrative summary of ML and DL operations.
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Figure 3. Adaptation of the labeling system across three different databases: (a) the Apnea-ECG database uses an original labeling system, (b) the MIT-BIH database labels with inheritance every 30 s, and (c) the UCD-DB database employs real-time sampled inheritance. Each dashed block represents a one-minute segment. Respiratory episodes are labeled as: normal (N), apnea (A), obstructive apnea (O), central apnea (C), and hypopnea (H).
Figure 3. Adaptation of the labeling system across three different databases: (a) the Apnea-ECG database uses an original labeling system, (b) the MIT-BIH database labels with inheritance every 30 s, and (c) the UCD-DB database employs real-time sampled inheritance. Each dashed block represents a one-minute segment. Respiratory episodes are labeled as: normal (N), apnea (A), obstructive apnea (O), central apnea (C), and hypopnea (H).
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Figure 4. Generation of DM and RP images from HRV series: (a) illustrates an apneic episode, while (b) presents a normal episode. Both show how HRV data are transformed into corresponding DM and RP images for further analysis.
Figure 4. Generation of DM and RP images from HRV series: (a) illustrates an apneic episode, while (b) presents a normal episode. Both show how HRV data are transformed into corresponding DM and RP images for further analysis.
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Figure 5. Visual comparison of DMs for apneic and normal episodes: (a,b) represent apneic episodes, whereas (c,d) represent normal episodes.
Figure 5. Visual comparison of DMs for apneic and normal episodes: (a,b) represent apneic episodes, whereas (c,d) represent normal episodes.
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Figure 6. Visual comparison of RPs: (a,b) represent apneic episodes, whereas (c,d) represent normal episodes.
Figure 6. Visual comparison of RPs: (a,b) represent apneic episodes, whereas (c,d) represent normal episodes.
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Figure 7. Visual comparison between apneic and normal scalograms: (a,b) represent apneic episodes, whereas (c,d) represent normal episodes.
Figure 7. Visual comparison between apneic and normal scalograms: (a,b) represent apneic episodes, whereas (c,d) represent normal episodes.
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Table 1. Distribution per class and database (one minute-length recordings).
Table 1. Distribution per class and database (one minute-length recordings).
Class/DBApnea-ECGMIT-BIHUCD-DB
Apnea10,37328413977
Normal15,97114726359
Total26,344431310,336
Table 2. Layer breakdown of cuCNN.
Table 2. Layer breakdown of cuCNN.
LayerTypeInput SizeOutput Size
1Input227 × 227 × 3227 × 227 × 3
2Convolutional227 × 227 × 3227 × 227 × 32
3Max Pooling227 × 227 × 32114 × 114 × 32
4Convolutional (ReLU)114 × 114 × 32114 × 114 × 64
5Max Pooling114 × 114 × 6457 × 57 × 64
6Convolutional (ReLU)57 × 57 × 6457 × 57 × 128
7Max Pooling57 × 57 × 12828 × 28 × 128
8Fully Conn. (ReLU)28 × 28 × 128256
9Fully Conn. (ReLU)2562
10Fully Conn. (Softmax)22
Table 3. Layer breakdown of AlexNet (modified for OSA detection).
Table 3. Layer breakdown of AlexNet (modified for OSA detection).
LType (Activation)Input SizeOutput Size
1Input227 × 227 × 3227 × 227 × 3
2Convolutional (ReLU)227 × 227 × 355 × 55 × 96
3Max Pooling55 × 55 × 9627 × 27 × 96
4Convolutional (ReLU)27 × 27 × 9627 × 27 × 256
5Max Pooling27 × 27 × 25613 × 13 × 256
6Convolutional (ReLU)13 × 13 × 25613 × 13 × 384
7Convolutional (ReLU)13 × 13 × 38413 × 13 × 384
8Convolutional (ReLU)13 × 13 × 38413 × 13 × 256
9Max Pooling13 × 13 × 2566 × 6 × 256
10Fully Conn. (ReLU)6 × 6 × 2564096
11Fully Conn. (ReLU)40964096
12Fully Conn. (Softmax)40962
Table 4. Table of DL results with DM, RP, and CWT images. Models trained with MIT-BIH + UCD-DB, and tested with Apnea-ECG.
Table 4. Table of DL results with DM, RP, and CWT images. Models trained with MIT-BIH + UCD-DB, and tested with Apnea-ECG.
InputModelAc (%)Se (%)Sp (%)PPV (%)NPV (%)F1 (%)
DM imagescuCNN68.1166.4469.1457.0576.9661.39
AlexNet64.8668.2962.7453.0676.2359.72
AlexNet (pre-trained)74.7273.9975.1765.0282.4169.40
RP imagescuCNN68.7266.5270.0757.8277.2361.87
AlexNet68.9762.9572.6958.7176.0860.75
AlexNet (pre-trained)67.6562.5470.8056.9275.3959.60
CWT imagescuCNN64.1168.5262.3952.2640.7859.30
AlexNet60.9481.5048.2549.2880.8761.42
AlexNet (pre-trained)64.1460.4866.3952.6135.9856.27
Table 5. Table of results from other OSA detectors based on traditional ML. Models trained with MIT-BIH + UCD-DB, and tested with Apnea-ECG.
Table 5. Table of results from other OSA detectors based on traditional ML. Models trained with MIT-BIH + UCD-DB, and tested with Apnea-ECG.
Input# FeaturesModelAc (%)Se (%)Sp (%)PPV (%)NPV (%)F1 (%)
5SVM68.4121.6989.0646.7072.0129.62
5KNN62.3533.3275.1837.2471.8435.17
RQA features5DT59.3841.2667.3935.8772.1938.37
5BAG62.7632.1876.2837.4871.7934.63
5ADA66.4527.8483.5242.7572.3733.72
Time,4SVM63.8259.6570.4276.1352.4555.82
frequency,11KNN61.8162.2359.5871.2250.6056.21
and complexity5DT59.7963.6553.6968.4948.2854.91
features8BAG63.3962.4764.8673.7752.2156.88
9ADA65.8968.4261.9173.9755.3461.18
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Padovano, D.; Martinez-Rodrigo, A.; Pastor, J.M.; Rieta, J.J.; Alcaraz, R. Deep Learning and Recurrence Information Analysis for the Automatic Detection of Obstructive Sleep Apnea. Appl. Sci. 2025, 15, 433. https://doi.org/10.3390/app15010433

AMA Style

Padovano D, Martinez-Rodrigo A, Pastor JM, Rieta JJ, Alcaraz R. Deep Learning and Recurrence Information Analysis for the Automatic Detection of Obstructive Sleep Apnea. Applied Sciences. 2025; 15(1):433. https://doi.org/10.3390/app15010433

Chicago/Turabian Style

Padovano, Daniele, Arturo Martinez-Rodrigo, José M. Pastor, José J. Rieta, and Raul Alcaraz. 2025. "Deep Learning and Recurrence Information Analysis for the Automatic Detection of Obstructive Sleep Apnea" Applied Sciences 15, no. 1: 433. https://doi.org/10.3390/app15010433

APA Style

Padovano, D., Martinez-Rodrigo, A., Pastor, J. M., Rieta, J. J., & Alcaraz, R. (2025). Deep Learning and Recurrence Information Analysis for the Automatic Detection of Obstructive Sleep Apnea. Applied Sciences, 15(1), 433. https://doi.org/10.3390/app15010433

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