Apnea is one of the deadliest diseases that can be prevented and cured if it is detected in time. In this paper, we propose a precise method for early detection of the obstructive sleep apnea (OSA) disease using the latest feature selection and extraction methods. The feature selection in this paper is based on the Dual tree complex wavelet (DT-CWT) coefficients of the ECG signals of several patients. The feature extraction from these coefficients is done using frequency and time techniques. The Feature selection is done using the spectral regression discriminant analysis (SRDA) algorithm and the classification is performed using the hybrid RBF network. A hybrid RBF neural network is introduced in this paper for detecting apnea that is much less computationally demanding than the previously presented SVM networks. Our findings showed a 3 percent improvement in the detection and at least a 30 percent reduction in the computational complexity in comparison with methods that have been presented recently.

#### Keywords

- Electrocardiogram
- Sleep Apnea
- RBF network
- Wavelet
- DT-CWT
- Feature extraction

Sleeping takes at least a third of the lifetime of every healthy human being and its quality affects the daily actions directly. Many people suffer from the respiration disorders during their sleep. The most alarming case of these disorders is the obstructive sleep apnea (OSA) [1]. The OSA can be described by the respiration cessation during sleep.

List of the used abbreviations.

Obstructive sleep apnea | |

Electrocardiogram | |

ECG-Derived Respiration | |

Apnea-Hypopnea Index | |

Hidden Markov model | |

Random under-sampling Boost | |

Adaptive boost | |

Discrete wavelet transform | |

Tunable Q-factor wavelet transform | |

Linear/Quadratic Discriminant Analysis | |

Sequential forward feature selection | |

Spectral regression discriminant analysis | |

Deep/Convolutional neural network | |

Decision tree classifier | |

Radial basis function | |

Support vector machine | |

Recursive least squares | |

Gram-Schmidt | |

Short-time load forecasting | |

Dual-tree complex wavelet transform |

This problem can cause heart and brain strokes during sleep and many daytime problems. The improvement in detecting the OSA can improve the daily life of many patients and save the lives of many others. The OSA detection has been the investigation topic of many researchers [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. As the ECG signal acquisition is much faster and less computationally demanding, the OSA can be detected from analysis of short durations of the ECG signals and this helps the designing of the home setting of handled devices that can easily be used by the patients. The detection of the OSA with the single lead ECG signals can be performed using various strategies. The main measurement to distinguish between the Apnea and normal ECG signals is the Apnea-Hypopnea Index (AHI). AHI is defined by dividing the total number of apnea events by the total number of minutes of sleep time, multiplied by 60:

Using this index we can mark the apnea ECG signals when

Reference [1] studies the usage of ECG signals in the detection of OSA. In this reference, the method is based on extracting 8 levels of wavelet features from ECG signals and then calculating 12 statistical and entropy-based features from these coefficients. The resulting features are then fed to a family of SVM classifiers (namely the least-square SVM or the Least-squares support vector machine (LS-SVM) and the library for support vector machine (LIB-SVM) which uses the linear kernels) and the results have been very satisfying.

In reference [2] the authors have proposed the Hidden Markov model (HMM) for extracting the correlation feature from the ECG signals and the SVM is used to classify these features.

In [3] the Tunable Q-factor wavelet transform (TQWT) is used instead of the ordinary wavelet transform and the statistical features are extracted from the coefficients of this transform. The RUSBoost classifier has been applied to these features.

The authors of [4] have proposed the usage of several frequency-based features like the Cepstrum, filter bank and Detrended Fluctuation Analysis (DFA) for detecting the OSA. The Logistic Regression (LR), Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) have been used for classification.

The contribution of [5] in OSA detection is the usage of Bootstrap classifier.

The authors in [6] have used the TQWT features and the Adaboost classifier in their method.

In [7] the proposed method is based on the time features of the ECG like the R-R interval and QRS properties and 5 different classifiers have been used for classifying these features.

In reference [8] have used the frequency features like the Spectogram and the statistical analysis to classify these features.

In [9] the ECG-Derived Respiration (EDR) signals along with the RR intervals are extracted from the ECG and the multiple classifiers such as the KNN, SVM, NN and LD-QD have been used to evaluate the results.

Reference [10] is based on cardiopulmonary coupling (CPC) and Respiratory event index (REI) features and statistical analysis for classification.

Reference [11] is based on the feature extraction with TQWT and Random forest classifier. Recently several references have proposed the usage of deep neural networks (DNNs) and convolutional neural networks (CNNs) for the OSA classification. The presented results with these classifiers have been very high, however, the computational complexity of these classifiers makes their usage unpopular.

Reference [12] has used the CNN to classify the R-R interval base features of the ECG signal.

Also, reference [13] has proposed CNN classifier based on the Scalogram features to detect OSA.

In [14] and [15] each has used a modified CNN to classify ECG time features.

Reference [16] has proposed the filter bank based features and their entropies to classify ECG signals with KNN, SVM, Decision tree (DT) classifiers.

Reference [17] is based on the Ensemble, Adaboost and Random forest classifiers.

Reference [18] has used the PCA feature reduction to reduce the DWT extracted features from the ECG and give them to the SVM classifier to detect OSA.

Reference [19] is based on wavelet packet decomposition (WPD), Entropy and R-R interval features and the random forest classifier.

Finally, reference [20] has proposed the feature extraction from ECG signals and in this paper, based on this novelty, we proposed the Dual-tree complex wavelet transform (DT-CWT) extracted features from the ECG to detect the OSA.

The DT-CWT is designed to compute the complex transform of a signal by two individual DWT decompositions. These transforms form two branches as tree

To the best of our knowledge, this is the first time to use DT-CWT for apnea detection purposes. While the DT-CWT extracted features are more promising than those of the DWT, the main hindrance in the usage of the DT-CWT extracted features instead of DWT features, is the computational complexity of the DT-CWT. However, because we wanted to compare our results with [1] and in that reference, the features have been extracted from 8 levels of DWT, we show in this paper that the suitable features with the DT-CWT can be achieved with only 3 levels of this transform and with this we compensate the double computations complexity in comparison with 8 levels of DWT. The overall flowchart of the proposed method in this paper is given in Fig. 1:

We tried to use novel methods in all the parts of the proposed method. In the feature selection part, we used the powerful SRDA algorithm [23] and for the classification, we used the hybrid RBF network using the ‘K-means, RLS’ learning [21,22] that is more powerful than the SVM network. The rest of this paper designed as follows:

In part II, we explain the feature extraction and selection techniques from our databases. Part III is dedicated to the explanation of the hybrid RBF classifier and its differences with the SVM network. Part IV presents our OSA detection results and part V consists of our concluding remarks and the suggestions for the future research.

The database that we implemented our proposed method on is the Physionet apnea ECG data set [24]. The age of subjects in this database is in the range of 27–63 years, and the weights of the subjects are between 35–135 kg. The AHI range in the extracted ECG signals is between 0 and 93.5. There are totally 70 records in this dataset that are clustered into two groups: train (called released-set) and test (called withheld-set). The released-set has 35 records with the indexes of a01-a20, b01-b05 and c01-c10, the withheld-set has 35 records with the indexes of x01-x35.

Signal segmentation with the time duration of 60

After we performed filtering, the weight calculation approach is applied for deleting the noisy segments. In [1] a simple method is proposed for the automatic cancelation of the noisy parts. In this method, a weight (_{st}_{s}_{t}_{s}_{t}_{st}

Feature extraction is a vital part of the computerized disease detection process. This section consists of three parts, in part A, we explain the DT-CWT feature extraction, in part B, we introduce the methods of statistical feature extraction from the DT-CWT coefficients. In part C, the feature reduction or selection method which is the SRDA is explained.

In [20], the usage of DT-CWT in ECG feature extraction is proposed. The main deficiency of DWT based feature extraction in analyzing 1D ECG signals is the lack of shift invariance. It means that the amplitude of the wavelet coefficients varies substantially as the input signal is shifted a little. This happens because of the down sampling operation at each level. A better way of achieving shift invariance is to implement the undecimated form of the dyadic filter tree. However, this method has heavy computation demands and high redundancy in the output.

The DT-CWT tackles this problem with a redundancy factor for 1D signal, which is significantly lower than the undecimated DWT. In [20], the authors have explained the shift invariance property of DT-CWT in detail. The DT-CWT implements two trees of real filters DTCWT of a signal _{1a}, _{01a}, _{001a}, _{000a}, _{1b}, _{01b}, _{001b} and _{000b}.

In Fig. 5 and 6 we depicted the sub band signals for three levels of the tree A and B respectively. It is important to mention that all of these signals are depicted for the same model record of the Fig. 3 of the Physionet database. It is important to mention that for the following figures from Fig. 5 to 8, the horizontal axis depicts the number of signal samples and the vertical axis shows the amplitude of the signal.

The absolute energy of the signal _{000a} is depicted in Fig. 7, and the absolute energy of _{000b} is depicted in Fig. 8.

After extracting the subbands of the DT-CWT from the selected ECG segments, we calculate some non-linear features based on the extracted transform coefficients. In [1] it has been shown that the ApEn, FE, IQR, RP and Poincare plot features make large differences among the two classes (Apnea and Normal). These features are collected in Table 2 and as they are explained in [1], we do not present their theoretical calculations here.

List of non-linear features that are extracted from the DT-CWT coefficients in this paper.

FE | Fuzzy Entropy |

ApEn | Approximate Entropy |

IQR | Interquartile Range |

RP | Recurrence Plot |

SD1, SD2, SD1/SD2 | Poincare Plot |

Using these 7 feature extraction methods and with the 8 DT-CWT coefficients that are explained in part III, we have 56 features for each ECG to be fed to the classifier. However, we used the feature reduction to reduce these features as much as possible.

After the extraction of the final features from the DT-CWT coefficients, it is time to select the most suitable ones to reduce the volume of the features and the amount of computation that is needed for processing them. In [1], the sequential forward feature selection (SFFS) method has been proposed for this task that is based on the detection results. Here we propose a data based feature reduction method. SRDA is one of the most efficient methods for feature reduction. We implemented this technique in our proposed method. To start the SRDA algorithm, suppose we have a set of data points _{1}, ... _{m}^{N} that belong to _{k}

① Let
_{0} = [1,1, … ,1]^{T}represents the vector of ones. The Gram-Schmidt process [23] is utilized for orthogonalization of {_{k}_{0} is in the subspace described by {_{k}

② In this step, a new entry “l” is appended to each _{i}_{i}_{k}

③ The _{k}_{1}, ... , _{Nc}_{−1}], which is a (

We compared the results of our proposed method with that of several classifiers in part IV. Explaining the operation of all these classifiers would increase the volume of the paper inordinately. Therefore, we addressed them accordingly in Table 3 for the interested researchers to find their explanation in the references. Here we only explain the performance of our proposed classifying network:

The comparison of the OSA detection results based on various methods.

ACC% | Sens% | Spec% | |||
---|---|---|---|---|---|

DWT+SFFS | SVM (RBF kernel) | 92.98 | 91.74 | 93.75 | |

HMM | HMM+SVM | 86.2 | 82.6 | 88.4 | |

TQWT | RUSBoost | 88.88 | 87.58 | 91.49 | |

Cepstrum+ Filter bank | QDA | 84.76 | 81.45 | 86.82 | |

Statistical and spectral | Bootstrap aggregating | 85.97 | 84.14 | 86.83 | |

Normal invers Gaussian modeling | AdaBoost | 87.33 | 81.99 | 90.72 | |

QRS features | LS-SVM (RBF kernel) | 83.8 | 79.5 | 88.4 | |

Frequency features | Statistical analysis | 93 | 100 | 81 | |

Time domain feaures+PSD | SVM-KNN-NN-LD-QD | 90.9 | 89.6 | 91.8 | |

Statistical features | Statistical analysis | 87 | 89 | 79 | |

Tunable-Q wavelet transform features | Random Forest | 92.78 | 93.91 | 90.95 | |

RR-intervals | CNN (LeNet-5) | 92.3 | 90.9 | 100 | |

Time-frequency Scalogram features | CNN (AlexNet) | 86.22 | 90 | 100 | |

RR-intervals | CNN | 96 | 96 | 96 | |

RR-intervals | CNN | 97.8 | 100 | 93 | |

Fuzzy-entropy (FUEN) and the Log of signal-energy (LOEN) | KNN-DT-SVM | 90.87 | 92.43 | 88.33 | |

DWT+PCA | Random forest | 92–98 | - | - | |

DWT+PCA | SVM | 94.3 | 92.65 | 92.2 | |

DT-CWT+SRDA | Hybrid “k-means, RLS” RBF |

The SVMs are the most prevalently used classifiers in the field of the disease detection. The RBF networks, on the other hand, are not used as much as SVMs. The hybrid RBF network is the solution for this, because, they can rival the SVMs. The hybrid RBF [21,22] consists of three layers and the middle and the output layers work with the K-means and the RLS algorithms, respectively and for this reason, the hybrid adjective is attributed to them.

In this part, we describe the RBF classifier with hybrid learning that is our proposed classifying tool in this paper. We call the proposed classifier as hybrid RBF because it has a hybrid learning procedure with two stages as follows:

The two-stage design procedure has some desirable features such as low computational complexity and fast convergence.

The RBF network consists of 3 layers as in Fig. 9. Here we describe them briefly [21]:

_{j}

Here we describe learning algorithms of RBF:

K-means is a method that utilizes distances for clustering with two steps [21, 22]:

Adaptive algorithms have been designed to converge to certain weights. These weights in the RBF network are adjusted in the learning phase. The RLS algorithm is one of the most powerful adaptive algorithms. In this section, we explain the role of RLS in the output layer of the RBF network [21]. Let the _{i}_{i}_{i}

Given the training sample

To initialize the algorithm, we have
^{−1}

In [222] a complete analysis was made to show the superiority of hybrid RBF to the SVM classifier both computationally and with respect to accuracy. Also, at least a 30% percent time saving is guaranteed using RBF in comparison with SVM [21]. This is important because we compared the results of our proposed method with that of the reference [1].

The conducted research is not related to either human or animal use.

We mentioned that after feature extraction we get 56 features from each ECG signal. One of the contributions of this paper is the usage of the SRDA feature reduction algorithm that gives the best results for the

As we can see the proposed method can detect the OSA with overcoming results in comparison with the conventional classifiers and can closely rival the results of the computationally complex CNN classifiers. The main purpose of this paper was to improve the results in [1]. By comparing the results, we can see that an average of 31% improvement is achieved in all the performance metrics.

This paper aimed to propose the hybrid RBF classifier along with some novel ECG signal processing techniques to improve the OSA detection. The proposed methods are all selected in order to reduce the computational complexity and the time consumption of the detection process.

For the feature selection, we used 3 levels of the Dual Tree Complex Wavelet Transform (DT-CWT) instead of 8 levels of the DWT features. In addition, the computational complexity of the proposed spectral regression discriminant analysis (SRDA) feature selection algorithm and the hybrid RBF classifier can guarantee at least 30% of complexity reduction plus the improvement of the OSA detection accuracy. The result presented an average of 3% improvement in detection and a 30% of time and complexity reduction when compared to the previously presented methods.

In future works, we will consider the usage of more advanced feature extraction and reduction methods. Also, the usage of DNNs and CNNs based on the features that are extracted in this paper may cause the perfect OSA detection results.

#### List of the used abbreviations.

Obstructive sleep apnea | |

Electrocardiogram | |

ECG-Derived Respiration | |

Apnea-Hypopnea Index | |

Hidden Markov model | |

Random under-sampling Boost | |

Adaptive boost | |

Discrete wavelet transform | |

Tunable Q-factor wavelet transform | |

Linear/Quadratic Discriminant Analysis | |

Sequential forward feature selection | |

Spectral regression discriminant analysis | |

Deep/Convolutional neural network | |

Decision tree classifier | |

Radial basis function | |

Support vector machine | |

Recursive least squares | |

Gram-Schmidt | |

Short-time load forecasting | |

Dual-tree complex wavelet transform |

#### The comparison of the OSA detection results based on various methods.

ACC% | Sens% | Spec% | |||
---|---|---|---|---|---|

DWT+SFFS | SVM (RBF kernel) | 92.98 | 91.74 | 93.75 | |

HMM | HMM+SVM | 86.2 | 82.6 | 88.4 | |

TQWT | RUSBoost | 88.88 | 87.58 | 91.49 | |

Cepstrum+ Filter bank | QDA | 84.76 | 81.45 | 86.82 | |

Statistical and spectral | Bootstrap aggregating | 85.97 | 84.14 | 86.83 | |

Normal invers Gaussian modeling | AdaBoost | 87.33 | 81.99 | 90.72 | |

QRS features | LS-SVM (RBF kernel) | 83.8 | 79.5 | 88.4 | |

Frequency features | Statistical analysis | 93 | 100 | 81 | |

Time domain feaures+PSD | SVM-KNN-NN-LD-QD | 90.9 | 89.6 | 91.8 | |

Statistical features | Statistical analysis | 87 | 89 | 79 | |

Tunable-Q wavelet transform features | Random Forest | 92.78 | 93.91 | 90.95 | |

RR-intervals | CNN (LeNet-5) | 92.3 | 90.9 | 100 | |

Time-frequency Scalogram features | CNN (AlexNet) | 86.22 | 90 | 100 | |

RR-intervals | CNN | 96 | 96 | 96 | |

RR-intervals | CNN | 97.8 | 100 | 93 | |

Fuzzy-entropy (FUEN) and the Log of signal-energy (LOEN) | KNN-DT-SVM | 90.87 | 92.43 | 88.33 | |

DWT+PCA | Random forest | 92–98 | - | - | |

DWT+PCA | SVM | 94.3 | 92.65 | 92.2 | |

DT-CWT+SRDA | Hybrid “k-means, RLS” RBF |

#### List of non-linear features that are extracted from the DT-CWT coefficients in this paper.

FE | Fuzzy Entropy |

ApEn | Approximate Entropy |

IQR | Interquartile Range |

RP | Recurrence Plot |

SD1, SD2, SD1/SD2 | Poincare Plot |

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