A new method for sleep apnea classification using wavelets and feedforward neural networks

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1 Artificial Intelligence in Medicine (2005) 34, A new method for sleep apnea classification using wavelets and feedforward neural networks Oscar Fontenla-Romero, Bertha Guijarro-Berdiñas, Amparo Alonso-Betanzos, Vicente Moret-Bonillo Department of Computer Science, Faculty of Informatics, University of A Coruña, Campus de Elviña s/n, A Coruña, Spain Received 17 March 2004; received in revised form 15 July 2004; accepted 22 July 2004 KEYWORDS Sleep apnea syndrome; Detection and classification of apneas; Supervised neural networks; Discrete wavelet transformation Summary Objectives: This paper presents a novel approach for sleep apnea classification. The goal is to classify each apnea in one of three basic types: obstructive, central and mixed. Materials and methods: Three different supervised learning methods using a neural network were tested. The inputs of the neural network are the first level-5-detail coefficients obtained from a discrete wavelet transformation of the samples (previously detected as apnea) in the thoracic effort signal. In order to train and test the systems, 120 events from six different patients were used. The true error rate was estimated using a 10-fold cross validation. The results presented in this work were averaged over 100 different simulations and a multiple comparison procedure was used for model selection. Results: The method finally selected is based on a feedforward neural network trained using the Bayesian framework and a cross-entropy error function. The mean classification accuracy, obtained over the test set was 83:78 1:90%. Conclusion: The proposed classifier surpasses, up to the author s knowledge, other previous results. Finally, a scheme to maintain and improve this system during its clinical use is also proposed. # 2004 Elsevier B.V. All rights reserved. 1. Introduction Corresponding author. Tel.: x1322; fax: addresses: oscarfon@udc.es (O. Fontenla-Romero), cibertha@udc.es (B. Guijarro-Berdiñas), ciamparo@udc.es (A. Alonso-Betanzos), civmoret@udc.es (V. Moret-Bonillo). The sleep apnea syndrome (SAS) is a respiratory disorder suffered by people who stop breathing during their sleep. The number of apneic events per hour in order to diagnose the syndrome is age dependent. For example, for patients between 20 and 40 years old, the minimum number of apneas /$ see front matter # 2004 Elsevier B.V. All rights reserved. doi: /j.artmed

2 66 O. Fontenla-Romero et al. per hour is five. The apneic events can be characterized as either apneas, defined by respiratory pauses with cessation of airflow lasting at least 10 s, or hypoapneas, defined as reductions in airflow accompanied by desaturations or arousals or both. A patient with SAS can suffer until 200 apneic episodes by night, usually with intermittent snoring; respiratory pauses of s in duration, or even more, with intense inspiration noises at the end of the apnea; and diurnal tiredness due to a scarce repairing nighttime sleep. Besides, it has been proved that SAS is associated with cardiovascular problems such as systemic and pulmonar hypertension, arrythmias and ischemic cardiac illness [1,2]. The most common method for the diagnosis of the SAS is based on nocturnal polysomnography. It consists of a polygraphic recording during sleep of the electrophysiological and pneumological signals. Thus, this method uses the electroencephalogram (EEG), electrocardiogram (ECG), electro-oculogram (EOG), electromyogram (EMG), airflow, thoracic breathing movements, the position of the body during sleep, and arterial oxygen saturation signals [3,4]. Typically, the diagnostic process comprises the detection of possible apneic events, their confirmation and later classification in three basic types of respiratory disfunctions: Obstructive apneas (OA): This is the more frequent pattern, characterized by the presence of thoracic effort for continuing breathing while air flow completely stops. Central apneas (CA): These are characterized by a complete cessation of both respiratory movements and airflow during, at least, 10 s. Mixed apneas (MA): This pattern is a combination of the previous two, defined by a central respiratory pause followed, in a relatively short interval of time, by an obstructive ventilatory effort. Following conventional clinical criteria, the a- pneic episodes are detected in the airflow signal, the thoracic effort is used for classification, and the information derived from electrophysiological and oxygen saturation signals is used as context for interpretation [5]. Fig. 1 showsexamplesofsleep apneas together with the two signals employed in the detection and classification tasks. In this respect, and strictly from a clinical point of view, it is specially important to be able to distinguish correctly between OAs and CAs, because the appropriate therapy will depend on that [6]. As already mentioned, the analysis of a nocturnal polysomnography, implies the study of a considerable number of physiological variables during a prolonged lapse of time. For this reason, computational systems are almost indispensable in order to facilitate the evaluation process of the polysomnographic records. Several approaches can be found regarding these systems. Thus, Rauscher et al. proposed a method to detect apneas and hypopneas during sleep investigating rapid resaturations from the oxygen saturation signal [7]. Macey et al. proposed and implemented an algorithm for apnea s detection that analyzes the statistical properties of the respiratory effort signal with the aim of finding respiratory pauses [8]. Recently, some approaches based on neural networks have been proposed for the detection and classification of apneas [9 12]. Also, Daniels et al. presented a decision-support knowledge-based system for the differential diagnosis of OA [13]. Other valuable contributions to this field can be found in [11,12,14,15]. Figure 1 (a) Airflow and (b) thoracic effort signals.

3 A new method for sleep apnea classification using wavelets and feedforward neural networks 67 Our contribution in the field of computerized diagnosis of SAS is the intelligent monitoring system SAMOA [16,17]. SAMOA is an integrated decisionsupport system that is able to interpret apneic episodes in the context of the sleep phase of the patient, and later to explain the transitions in the sleep phases of the patient in the context of the respiratory anomalies encountered. The complete process follows the protocol below: (1) detection of apneic events; (2) classification of the events detected in the previous phase; (3) contextual and temporal analysis of the available information; and (4) interpretation and diagnostic. For the SAMOA system, several different approaches have been tried in order to detect and adequately classify the different apneic events registered in the polysomnographic records, as this was one of the aspects clearly improvable in the first version of our intelligent system. In this paper, a new method for classifying sleep apneas in one of the three basic types (OA, CA or MA) that considerably improves previous results is presented. This new approach uses wavelets for the feature extraction from the raw samples of the thoracic signal, and a Bayesian neural network for the subsequent classification stage. Steps 3 and 4 (described above) of the process are adequately addressed in [16,17]. 2. Development of the sleep apnea detection and classification modules The global scheme of the automatic apnea classifier presented in this paper is composed of three stages as shown in Fig. 2. First, a detection module receives the airflow signal and returns the location of each apnea. Subsequently, a sample selector module selected the corresponding samples of the apneas but in the thoracic effort signal. Afterwards, a pre-processing stage receives this raw samples and extracts the features that will serve as inputs to the classifier. Finally, the classification module will label the detected apnea as central, obstructive or mixed Detection stage As previously defined, an apnea is a cessation of airflow lasting at least 10 s. The airflow signal recorded during nocturnal polysomnography shows the respiration of the patient and reflects all the changes in the respiratory airflow. Each time that an apnea appears, there is a reduction in the amplitude of the airflow signal with respect to the normal amplitude (see Fig. 1(a)). For this reason, usually the algorithms for the detection of apneas look for the intervals in which the airflow signal suffers a reduction in its amplitude [11]. The main idea of our algorithm is to follow the airflow signal, marking those samples that have an amplitude below a certain threshold. After that, the signal must be processed again in order to find sequences of at least 125 consecutive marked samples (the signal has a frequency of 12.5 Hz and by definition an apnea must last at least 10 s). However, detection is not so simple as the amplitude of the signal varies with time depending on sleep stage. Thus, on one hand when the amplitude decreases several false apneas could be detected. On the other hand, when the averaged amplitude of the signal is high, some apneas could be not detected. To overcome these two problems, first Figure 2 Structure of the proposed classification method.

4 68 O. Fontenla-Romero et al. is variable for each event while the number of inputs to the classification system must be fixed. Usually, due to the sampling frequency, the number of sleep apnea s samples varies from 125 to 750. Clearly, this number of inputs is very high and so a pre-processing technique is required to reduce the number of them. For this reason, the classification stage has two different modules, as it is shown in Fig. 2. Figure 3 Sample windows used for determining the detection threshold. the original airflow signal is preprocessed. Each sample of this pre-processed signal (S) is the difference, in absolute value, between the original airflow signal and the average airflow signal, calculated using a sliding window (W 0 ) taken from the present sample. In this way, we take into account the possible differences in the maximum amplitude of the signal corresponding to different sleep stages. Second, an adaptive threshold that varies with the changes in the respiratory flow of the patient is applied over S to detect the apneas. To determine the value of the threshold (g) for a specific sample (i) two windows W 1 and W 2 of previous and posterior samples, respectively, are considered (see Fig. 3). Specifically, the detection threshold is calculated as: g i ¼ g 0 1 max ðw 1Þ meanðw 2 Þ max ðw 1 Þ (1) where g 0 is the initial threshold. The values of g 0 and the sizes of W 0, W 1 and W 2 were empirically determined as 55, 750, 25 and 100, respectively. Using this algorithm and a set of six patients, whose airflow signal has been reviewed by an expert in the field, an average sensibility of 0.91 and average Predictive Positive Value of were obtained. The results improve significantly those previously obtained in [11] Classification stage After the detection module, the raw samples of the apneas in the thoracic effort are fed to the classification stage. However, there are two main reasons for which the raw samples of the signal cannot be directly used as inputs to the classifier: Each apnea has different duration (from 10 s to 1 min, or even more), thus the number of samples Pre-processing module A discrete wavelet transformation [18] was used as a pre-processing phase to reduce and fix the number of inputs of the classifier. The wavelet transformation provides a decomposition of a given signal into a set of approximation (a i ) and detail (d i ) coefficients of level i. The decomposition process can be iterated, with successive approximations being decomposed in turn, so that a signal is broken down into many lower-resolution components (see Fig. 4). Thus, in this case the samples of the sleep apnea event, in the thoracic effort signal, are processed to obtain a level-1 transformation (a 1 and d 1 coefficients). Subsequently, each set of a i coefficients is decomposed into a set of approximation a iþ1 and detail d iþ1 coefficients. Also, to obtain this decomposition some different types of wavelets functions can be used. Experimentally, for this work it was determined that the absolute value of the level-5- detail coefficients, d 5, are the set of inputs that obtains the best apnea classification results. Several experiments were carried out using coefficients from the lowest level of detail to the highest possible (log 2 L, where L is the number of samples of the detected apnea) but the results were significantly worse. Also, in order to make the decomposition, the symlet wavelet family [19] was used with a length of the filter equal to 14 (symlet of order: O ¼ 7). This wavelet family was chosen after performing some other experiments with other wavelet families, specifically, the Haar, Daubechies, Coiflets, Biorthogonal, Reverse Biorthogonal and the discrete approach of the Meyer wavelet. The number of coefficients supplied by the wavelet transformation depends on the number of samples of the detected pattern. In this case, the minimum number of samples is 125 (as it was mentioned in the detection stage section), therefore, the number of corresponding wavelet coefficients in level-5-detail is 16. As the number of inputs to the classification module must be fixed, the maximum number of coefficients that could be used is 16. For those patterns in which the duration is the minimum (10 s) all the coefficients (16) were used. For those other patterns with a duration greater

5 A new method for sleep apnea classification using wavelets and feedforward neural networks 69 Figure 4 Wavelet decomposition tree. than 10 s (for which more than 16 coefficients could be obtained) two different approaches were tried: The first 16 coefficients were used as inputs to the classifier. Over the total number of obtained coefficients, 16 coefficients, equally distributed, were used. To determine the best approach, several experiments were carried out. In all cases, the first option achieved considerably better results. Therefore, it was the one implemented in the pre-processing stage. Fig. 5 shows, for each class of apnea, an example of the airflow and thoracic effort signals and its corresponding first 16 coefficients in absolute value. These coefficients will be the inputs to the classification module described in the next subsection Classification module For the classification module, the employed system was a feedforward artificial neural network with one hidden layer, as it has been demonstrated that, with appropriate number of hidden neurons, one hidden layer is enough to model any function [20]. The input of the network is formed by the vector x ¼ðx 1 ;...; x I Þ T, where I is the number of input variables. In this case, x is a vector composed by the first I coefficients of the d 5 decomposition of the wavelet transformation of the samples of the apnea in the thoracic effort signal. This input of the network was normalized to have zero mean and standard deviation equal to one. The output k of the network, y k,isdefined by the following equations: y k ¼ f ð2þ ða k Þ; h j ¼ f ð1þ X I i¼1 a k ¼ XH j¼1 w ð1þ ji x i þ w ð1þ j0 w ð2þ kj h j þ w ð2þ k0 ;! ; j ¼ 1;...; H k ¼ 1;...; C (2) where C is the number of outputs, H the number of hidden neurons, the superindex indicates the number of the layer, w are the weights of the neural network, and f ð1þ and f ð2þ are, respectively, the activation functions of the neurons of the hidden

6 70 O. Fontenla-Romero et al. Figure 5 Example of the three types of sleep apnea and the corresponding level-5-detail coefficients in absolute value. and output layers. In this work, we have used the hyperbolic tangent function for f ð1þ. With the aim of obtaining the optimal set of values for the network weights that minimize the error function, several topologies and three different approaches using supervised learning were employed. The first approach employs the scaled conjugate gradient (SCG) learning algorithm [21] and the mean squared error (MSE) as cost function, E MSE ðwþ. The SCG was selected as learning algorithm for the network due to its fast convergence speed and low memory requirements. The second approach is analogous to the first one, but using as cost function the MSE with a regularization term called weight decay [22]: EðwÞ ¼bE MSE ðwþþð1 bþe W ðwþ; (3) where all the weights of the network were compactly represented by the vector w for a simplicity of notation and b is a fixed regularization parameter. The second term in equation (3), E W ðwþ, is a regularization function, called weight decay, defined as: E W ðwþ ¼ 1 2 X N W j¼1 w 2 j (4) where N W is the number of weights of the neural network and w j the jth component of w. The use of this term avoids the overfitting problem and thus it enhances the network generalization [22,23]. In these two approaches, the lineal function was employed as f ð2þ. Finally, the third approach used is a Bayesian neural network [24,25]. In this last case, the softmax activation function was used for f ð2þ, because this makes possible to interpret the outputs as probabilities [26] and it is defined as: f ð2þ ða k Þ¼ e a k P Ck0 ¼1 ea k 0 : (5) In this third supervised learning method the following cost function is employed: EðwÞ ¼E D ðwþþae W ðwþ; (6) Also, in Eq. (6) the E D ðwþ term measures the error obtained when the output of the network is compared with the expected output. In this work, the cross-entropy error function has been used as it is the more suitable for classification problems [23]. Therefore, E D ðwþ is defined as: E D ðwþ ¼ XN D X C n¼1 i¼1 t ðnþ i ln ðy i ðw; x ðnþ ÞÞ (7) where N D is the number of training data, C the number of classes, fðx ðnþ ; t ðnþ Þg is the set of training

7 A new method for sleep apnea classification using wavelets and feedforward neural networks 71 input output pairs and t ðnþ, the expected output, is given by: t ðnþ k ¼ 1 ifxðnþ 2C k (8) 0 otherwise where k ¼ 1;...; C and C k is the set of patterns in the class k. The second term in Eq. (6), E W ðwþ, is the same regularization function defined in Eq. (4). Moreover, in this case, the a parameter in Eq. (6) is called the adaptive regularization hyperparameter and it is automatically updated each time the weights have converged. After that, the learning process is repeated until the hyperparameter also converges. For the adaptation of a the equation in [24] was used: a new ¼ N W a old TraceðA 1 Þ 2E W ðw (9) Þ where A is the Gauss Newton approximation to the Hessian matrix and w is the optimum weight vector. To obtain w, it was employed the UCMINF method [27] that is a Quasi-Newton optimization algorithm with a soft line search and a BFGS (Broyden, Fletcher, Goldfarb, Shanno) updating on the inverse Hessian. 3. Experimental results To obtain the training set, six different recordings from six patients were available. The signals were sampled with a frequency of 12.5 Hz. The apneas contained in these recordings were classified by an expert in the field (217 obstructive apneas, 40 central apneas and 82 mixed apneas). To obtain a balanced training set, 120 apneas were selected (40 of each class), thus N D ¼ 120. All the central patterns were used while the other 40 events of each class were randomly selected. Due to the small size of the training set, in order to estimate the true error rate of the classifier, a 10-fold cross validation was used. To choose the best network the following model selection method was employed, where M is the number of different models: (1) for m ¼ 1toM (1.1) Take the whole data set and generate N different 10-fold cross validation sets in order to have disjoint and different partitions (randomly selected) of the training set. Also, in each simulation, employ different initial conditions of the model (weights of the neural network). (1.2) Train a model (neural network) with a certain degree of complexity (number of hidden neurons and number of inputs) and obtain N accuracy measures over the test set: T m ¼ T m1 ;...; T mn. (2) end. (3) Apply a Kruskal Wallis test [28], a nonparametric version of the classical one-way analysis of variance (ANOVA), to check if there are significant differences among the means of the M models for a level of significance g. (4) If there are differences among the means, then apply a Multiple Comparison Procedure (MCP) [29] to find the set of models whose errors are not significantly different from that corresponding to the model with the maximum mean accuracy rate. From this set select the simplest model (lowest complexity). In this work, a Tukey s honestly signicant criterion [29] was used as multiple comparison test. Following the previous steps, with N ¼ 100, several neural networks were trained using from 12 to 16 coefficients of the wavelet transformation (inputs of the network) and from 4 to 14 neurons in the hidden layer. Figs. 6 8 show the obtained results, using a 10-fold cross validation, for the test set and the three approaches previously described. These figures show the box whiskers plots for each network topology. The box corresponds to the interquartile range, the bar represents the median, and the whiskers extend to the minimum and maximum values. Outliers are data with values beyond the ends of the whiskers and they are represented by the plus sign. In these figures, x-axis represents the classification accuracy and y-axis is formed by a pair indicating the number of coefficients used as inputs in the network and the number of hidden neurons. In these figures, it can be seen that the results obtained using from 13 to 16 coefficients are similar and always better than using 12. Employing the step 4 of the selection model criteria described above, the simplest model corresponds to the one with 13 c- oefficients in all the described methods. Fig. 9 shows the comparison of the three approaches using 13 coefficients. In this figure can be observed that the topology, for the Bayesian method, obtains the best median accuracy. In order to rigorously select the final topology, the Kruskal Wallis test was applied to check if there are statistically differences among the mean test accuracies. The p-value obtained was 0 for a significance level of 95%. Therefore, the null hypothesis (all means are equal) can clearly be rejected. Afterwards, the multiple comparison procedure was performed to make all-pairwise comparisons among each model. Fig. 10 graphically represents the comparison for those topologies whose mean accuracy are significantly different from the best (13 inputs and six

8 72 O. Fontenla-Romero et al. Figure 6 Bayesian learning: box whiskers plots for the test data using a 10-fold cross validation and 100 different experiments. hidden neurons trained with the Bayesian framework). Those topologies whose interval is not crossing the dashed line are significantly different from the best topology, therefore, can be discarded, i.e. all models trained with SCG or regularized SCG. Among the other topologies whose interval is crossing the dashed line, the simplest must be chosen. Therefore, the topology, trained with the Figure 7 SCG learning: box whiskers plots for the test data using a 10-fold cross validation and 100 different experiments.

9 A new method for sleep apnea classification using wavelets and feedforward neural networks 73 Figure 8 SCG learning with regularization: box whiskers plots for the test data using a 10-fold cross validation and 100 different experiments. Bayesian framework, was selected as the model to use as sleep apnea classifier. The mean test accuracy obtained for the selected topology (13-4-3) in 100 different 10-fold cross validations was 83:78 1:90%. Also, the mean accuracy and the confidence interval obtained for each one of the classes was 80:90 2:53% (obstructive), 80:48 3:65% (mixed) and 89:95 2:71% (central). Figure 9 Box whiskers plots for the test set for the three methods using 13 coefficients.

10 74 O. Fontenla-Romero et al. Figure 10 Plot for the multiple comparison procedure. Table 1 Real Confusion matrix Neural network s output Obstructive Mixed Central Obstructive 32:36 1:01 6:10 0:88 1:54 0:70 Mixed 2:91 0:93 32:19 1:46 4:90 1:07 Central 1:40 0:83 2:62 0:63 35:98 1:08 The corresponding confusion matrix is shown in Table 1. As can be seen, the main discrepancies appear between the obstructive and mixed class and between the central and mixed class. This is a logical result due to the fact that the mixed class is a mixture of the other two classes. Finally, we also validate the selected network using the other available 219 apneas not used for the learning/test process. In this case, 177 examples are obstructive apneas and 42 are mixed apneas, thus there are not any examples of the central type. Table 2 shows the confusion matrix for this validation set for which the global accuracy obtained was 73:99 0:24%. As can be seen, this accuracy is Table 2 Real The confusion matrix for the validation set Neural network s output Obstructive Mixed Central Obstructive 133:83 2:70 23:24 2:25 19:93 1:47 Mixed 4:53 0:94 28:20 1:66 9:26 1:32 significantly smaller than the one achieved in the test set. This can be partially explained by the fact that the central class, which is the best predicted by the network in the training/test set, is the missing class in this validation set. 4. Conclusions In this paper, a new method for sleep apnea classification has been proposed. Three different supervised learning methods were tried for a feedforward neural network: scaled conjugated gradient, regularized scaled conjugated gradient and a Bayesian approach. The best results were achieved using the Bayesian framework and a regularized cross-entropy function. The input of the neural network is formed by the coefficients of a discrete wavelet decomposition applied to the raw samples of the apnea in the thoracic effort signal. The obtained experimental results, using 120 apneas from six different patients, have demostrated the validity of the proposed method. Most of the computational systems proposed in the field of sleep apnea deal with the detection problem. Up to the authors knowledge, not many previous methods were proposed for apnea classification. First applications of neural networks to this problem have been reported in [9,10]. In these cases a backpropagation method was employed, however,

11 A new method for sleep apnea classification using wavelets and feedforward neural networks 75 the classification rates did not exceed 60%. More recently, in [12], Zemen et al. applied a radial basis function neural network for an integrated detection-classification task obtaining an accuracy of 64 3:4% for adults and 62:6 3:4% for infants. Therefore, the results obtained in our work surpasses these previous ones. However, both results are not fairly comparable as there are the following differences: Only two types of apnea are consired: OA and CA. In the case of the infants another type is considered: signal (SI). They used a set of features extracted from three different sources: electric field plethymography, blood oxygen saturation and heart rate signals. In our work, only one signal is considered for classification: the thoracic effort signal. Finally, in [11] a neural system for the sleep apnea classification was proposed, which uses the raw samples of the thoracic signal as inputs. The accuracy obtained, over the test set, was 75:32%, which again is improved in the approach proposed in this paper. To conclude, it is relevant to establish a method to maintain this system during its clinical use which is based on a procedure already implemented for another clinical software system [30]. The selected Bayesian network has the advantage that all the learning parameters are auto-adaptive and no external-human action is needed. However, this is a supervised approach and therefore a classification criterion must be provided. To obtain such a reliable criterion a training shell is built in charge of automatically controlling the learning process. Thus, every time a new pattern is found, clinicians will be asked to classify this pattern at different moments, at least three times. The kappa measure [31] will be used to determine when the agreement between an expert and him/herself is in range of good agreement [32] to establish his/her final classification for a pattern. This measure will be also calculated among clinicians. This way, the inter- and intra-expert variability in classification is reduced. The retraining process of the neural network will take place whenever a good agreement is obtained, among the criteria provided by the clinicians, for a set of equally distributed patterns. Several topologies will be trained starting from the current topology and adding some hidden neurons up to 2I þ 1, where I is the number of inputs of the network [33]. After that, to select the best topology, the model selection method described in Section 3 will be applied. To prevent a degradation of the system if the retrained network gives worst results than the original one, an alarm will be sent by to the system s maintainer. On the other hand, if a better performance is obtained the new network will become the standard of comparison for future significance tests. Acknowledgements This research has been supported by the Xunta de Galicia (Project PGIDT-01PXI10503PR). We are very grateful to Maite Martín-Egaña, Héctor Verea-Hernando and to the Juan Canalejo Hospital for their clinical assistance. Also, we would like to thank the Supercomputing Center of Galicia (CESGA) for allowing the use of the high performance computing servers. References [1] Thorpy M. Handbook of Sleep Disorders. New York: Marcel Dekker Inc.; [2] Schochat T, Hadas N, Kerkhofs M, Herchuelz A, Penzel T, Peter J, Lavie P. The sleepstrip: an apnoea screener for the early detection of sleep apnoea syndrome. Eur Respir J 2002;22: [3] Penze T, McNames J, de Chazal P, Raymond B, Murray A, Moody G. Systematic comparison of different algorithms of apnoea detection based on electrocardiogram recordings. Med Biol Eng Comput 2002;40: [4] American Academy of Sleep Medicine Task Force. Sleeprelated breathing disorders in adults: Recommendations for syndrome definition and measurement techniques in clinical research. Sleep 1999;22: [5] Varady P, Micsik T, Benedek S, Benyo Z. A novel method for the detection of apnea and hypopnea events in respiration signals. IEEE Trans Biomed Eng 2002;49(9): [6] Steltner H, Staats R, Timmer J, Vogel M, Guttmann J, Matthys H, Virchow J. Diagnosis of sleep apnea by automatic analysis of nasal pressure and forced oscillation impedance. Am J Respir Crit Care Med 2002;165: [7] Rauscher H, Popp W, Zwick H. Computerized detection of respiratory events during sleep from rapid increases in oxyhemoglobin saturation. Lung 1991;169(6): [8] Macey P, Ford R, Brown P, Larkin J, Fright W, Garden K. Apnoea detection: human performance and reliability of a computer algorithm. Acta Pediatr 1995;84: [9] Clabian M, Nussbaum C, Pfützner H. Artificial neural networks for apnea detection. Proc EANN 1996; [10] Clabian M, Pfiitzner H. Determination of decisive inputs of a neural network for sleep apnea classification. Proc EANN 1997; [11] Hernandez-Pereira E, Carrillo-Rozas N, Cabrero-Canosa M, Moret-Bonillo V. Deteccion y clasificacion de apneas de sueno mediante wavelets y redes de neuronas artificiales. In: Lasaosa PL, Gassó SO, Gascón GM, Cortes JPM, editors. Proceedings of the XXth Congreso Anual de la Sociedad Espanola de Ingenieria Biomedica; p [12] Zemen T, Clabian M, Pfützner H. Classification of sleep apnea events by means of radial basis function networks. In:

12 76 O. Fontenla-Romero et al. International ICSC/IFAC Symposium on Neural Computation (NC98); p [13] Daniels J, Cayton R, Chappel M, Tjahjadi T. CADOSA: a fuzzy expert system for differential diagnosis of obstructive sleep apnoea and related conditions. Expert Syst Appl 1997;12(2): [14] Kermit M, Eide A, Lindblad T, Waldemark K. Treatment of obstructive sleep apnea syndrome by monitoring patient airflow signals. Pattern Recog Lett 2000;21: [15] Stradling J. New approaches to monitoring sleep-related breathing disorders. Sleep 1996;18(3): [16] Cabrero-Canosa M, Castro-Pereiro M, Graña-Ramos M, Hernández-Pereira E, Moret-Bonillo V, Martín-Egana M, Verea- Hernando H. An intelligent system for the detection and interpretation of sleep apneas. Expert Syst Appl 2003;24(4): [17] Cabrero-Canosa M, Hernández-Pereira E, Moret-Bonillo V. Intelligent diagnosis of sleep apnea syndrome. IEEE Eng Med Biol Mag 2004;23(2): [18] Rao RM, Bopardikar AS. Wavelet Transformations. Introduction to Theory and Applications. Reading (MA): Addison Wesley; [19] Daubechies I. Ten lectures on wavelets, vol. 61. Cbms-Nsf Regional Conference Series in Applied Mathematics. Society for Industrial & Applied Mathematics; [20] Hornik K, Stinchcombe M, White H. Multilayer feedforward networks are universal approximators. Neural Networks 1989;2(5): [21] Moller MF. A scaled conjugate gradient algorithm for fast supervised learning. Neural Networks 1993;6: [22] Hinton GE. Learning translation invariant recognition in massively parallel networks. In: Nijman AJ, de Bakker J, Treleaven PC, editors. PARLE Conference on Parallel Architectures and Languages Europe. Berlin: Springer; [23] Bishop CM. Neural Networks for Pattern Recognition. New York: Oxford University Press; [24] MacKay DJC. A practical Bayesian framework for backprop networks. Neural Comput 1992;4(3): [25] MacKay DJC. The evidence framework applied to classification networks. Neural Comput 1992;4(5): [26] Bridle J. Probabilistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition. In: Fogelman-Soulie F, Herault J, editors. Neurocomputing: Algorithms, Architectures and Applications. New York: Springer Verlag; p [27] H. Nielsen, UCMINF An algorithm for unconstrained, nonlinear optimization. Tech. Re IMM-REP , Department of Mathematical Modelling. Technical University of Denmark; [28] Hollander M, Wolfe DA. Nonparametric Statistical Methods. New York: John Wiley & Sons; [29] Hsu JC. Multiple Comparisons. Theory and Methods. Boca Raton (FL): Chapman & Hall/CRC; [30] Guijarro-Berdiñas B, Alonso-Betanzos A, Fontenla-Romero O, García-Dans O, Sánchez Maroño N. An auto-learning system for the classification of fetal heart rate decelerative patterns. In: Mira J, Prieto A, editors. Lecture Notes in Computer Science Bio-Inspired Applications of Connectionism, Heidelberg (Germany): Springer Verlag; p [31] Fleiss J. Statistical Methods for Rates and Proportions. New York: John Wiley & Sons; [32] Landis JR, Koch GG. The measurement of observer agreement for categorical data. Biometrics 1977;33: [33] Kurkova V. Kolmogorov s theorem is relevant. Neural Comput 1991;2(4):