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Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2013 Article ID 238937 13 pageshttpdxdoiorg1011552013238937

Research ArticleComparison of SVM and ANFIS for Snore RelatedSounds Classification by Using the Largest LyapunovExponent and Entropy

Haydar AnkJGhan1 and Derya YJlmaz2

1 Department of Biomedical Equipment Technology Vocational School of Technology Baskent University 06810 Ankara Turkey2Department of Electrical and Electronic Engineering Faculty of Engineering Baskent University 06810 Ankara Turkey

Correspondence should be addressed to Derya Yılmaz deryabaskentedutr

Received 28 May 2013 Revised 13 August 2013 Accepted 15 August 2013

Academic Editor Ricardo Femat

Copyright copy 2013 H Ankıshan and D Yılmaz This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Snoring which may be decisive for many diseases is an important indicator especially for sleep disorders In recent yearsmany studies have been performed on the snore related sounds (SRSs) due to producing useful results for detection of sleepapneahypopnea syndrome (SAHS) The first important step of these studies is the detection of snore from SRSs by using differenttime and frequency domain features The SRSs have a complex nature that is originated from several physiological and physicalconditionsThe nonlinear characteristics of SRSs can be examined with chaos theorymethods which are widely used to evaluate thebiomedical signals and systems recently The aim of this study is to classify the SRSs as snorebreathingsilence by using the largestLyapunov exponent (LLE) and entropy with multiclass support vector machines (SVMs) and adaptive network fuzzy inferencesystem (ANFIS) Two different experiments were performed for different training and test data sets Experimental results show thatthe multiclass SVMs can produce the better classification results than ANFIS with used nonlinear quantities Additionally thesenonlinear features are carrying meaningful information for classifying SRSs and are able to be used for diagnosis of sleep disorderssuch as SAHS

1 Introduction

Sleep apneahypopnea syndrome (SAHS) is a sleep disorderwhich is defined by instances of low-level breathing orpauses in breathing during sleep SAHS is diagnosed bypolysomnography (PSG) However PSG is highly trouble-some test owing to the patients sleeping for an overnightin the hospital Researchers indicate that there is a seriousrequirement to simplified systems instead of PSG for diag-nosing SAHS [1] For this purpose some approaches havebeen developed by using several physiological signals such aselectrocardiography (ECG) electroencephalography (EEG)and snore related sounds (SRSs) Recently there are manystudies available for diagnosing SAHS working with the SRSs[2ndash9]

The snoring is one of the SAHSrsquos symptoms and it may beinterpreted as an indicator for many different diseases suchas cardiovascular and sleep disorders [10] It is stated that

snoring is associated with physical and functional defects ofupper airway responses and generally occurring in patientshaving narrower upper airway than the normal ones [3 4 611] Hence the knowledge about physiology and functions ofupper airway can be obtained fromSRSs [4] Because SAHS isconcernedwith partial or full collapse of upper airwaysmanystudies using different linear techniques have been performedfor SRSs analysis [5 7 12ndash16] The results of these studiesindicate that SRSs carry significant information on SAHS

Recently some studies have been shown to classify SRSsthat is a first task for detecting snoring and SAHS [17ndash20]Duckitt et al [17] presented a method which provides theautomaticmonitoring of snoring characteristic depending onintensity and frequency of data They used mel-frequencycepstral coefficients (MFCCs) with hidden Markov model(HMM) Their system obtained 82ndash89 accuracy in spec-ifying snores Cavusoglu et al [18] estimated energy andzero-crossing rates of SRSs and used linear regressionmethod

2 Computational and Mathematical Methods in Medicine

for classifying SRSsrsquo segments as snorenonsnore Theyobtained 868 accuracy for obstructive sleep apnea (OSA)patients Karunajeewa et al [19] calculated zero-crossingrates normalized autocorrelation coefficients energy andfirst predictor coefficient of linear predictive coding (LPC)analysis as features for classification of SRSs into snoringbreathing and silence They also used three noise reductiontechniques and compared their performanceWhile they hadan overall classification accuracy of 9074 their accuracyis up to 9678 with noise reduction techniques and aproper choice of features Yadollahi and Moussavi [20] triedto classify breath and snore sounds by using Fisher lineardiscriminant (FLD) based on zero-crossing rates energyand first formant of the SRSs that are recorded by twomicrophones (tracheal and ambient) They investigated thebody and neck positionsrsquo effects on the classification resultsThe overall accuracies were found as 957 and 932for tracheal and ambient recordings regardless of the neckposition respectively [20]

It is seen that these studies have focused on examiningsnoring sounds by linear features analysis such as Fouriertransform LPC but the nonlinear characteristics of SRSs forclassifications have not yet been evaluated so far SRSs areknown to have nonstationary and complex behaviours [2122] Some parts of SRSs have nonlinear acoustic vibrationsdepending on out- and in-factors such as the respiratoryairflow strength vibrations on the soft palate the shapeand differences of upper airway and the airway obstructiondue to tongue subsidence [22 23] These make it difficultto solve the identification of SRSs depending on traditionallinear frequency and time domain based methods In thesecases the nonlinear analysis can be performed to revealthe undefined characteristics of the signal It is possible touse the linear and nonlinear analyses together since theseapproximations can produce the meaningful results whichsupport each other For example a wideband spectrum maybe indicator of chaos but it cannot only identify definition ofchaos However spectral analysis may give some informationfor examining the source of variations in the signals

From the biomedical perspective nonlinear analysesmethods coming from chaos theory have been used to evalu-ate the states of biological systems and signals from systemiclevel to the cellular scale [24ndash28] The behaviours of dynam-ical biological systems are interpreted by evaluating thechaotic indicators such as Lyapunov exponents correlationdimension Poincare section and entropy While some sys-tems show a chaotic behaviour under the normal operatingconditions at the pathological conditions a degree of systemsrsquochaotic behaviour may be reduced or increased or systembehaviour can turn to a regular state [23ndash28] Hence somecontributions related to commentating of system functionscan be provided by evaluating the effects of pathological ornormal conditions on the system behaviour There are a fewstudies which investigated the nonlinear properties of SRSsin the literature [29ndash33] Sakakura [29] used Poincare sectionand the largest Lyapunov exponent (LLE) for indicatingthe chaotic characteristics of snoring sounds Mikami [30]performed surrogate analysis by using correlation integraland showed that snoring sounds have nonlinear properties

Yılmaz and Ankıshan [31] calculated the LLE values for snoresegments obtained from apneahypopnea patients and simplesnorers Their results showed that the LLE of simple snorergroup was significantly higher than apneahypopnea group[31] Ankıshan and Arı [32] showed from their experimentalresults that SRSs have chaotic behaviour and carry meaning-ful information so the LLE can be used for classification ofSRSs Moreover they also showed that entropy can be usedin classification of SRSs with time domain features [33]Thesestudies have shown that nonlinearmeasures can bring to lightsignificant outcomes for SRSs

The LLE quantifies the dynamic stability of a system andgives information about the predictability of a system [34 35]The positive value of the LLE is accepted as a key indica-tor of chaotic behaviour Entropy which has also multipledefinitions may be interpreted as the average amount ofnew information obtained by making the measurement ininformation theory sense [35] In previous studies it wasreported that these features are the quantitative measures ofchaos and frequently used in the nonlinear analysis of theexperimental time series [23ndash33] So the aims of this workare to extractmeaningful information from SRSs related to itsnonlinear characteristics to investigate the variability of thesechaotic measures for different SRSs segments and to test theavailability of these quantities for classifying SRSs For thispurpose SRSs were analysed by using entropy and the LLEand classified as snorebreathingsilence with support vectormachines (SVMs) and adaptive network fuzzy inferencesystem (ANFIS)

There have been several methods which are used forclassification of biological data Two of them are ANFISand SVMs which are effective methods for classification andmachine learning systems such as face detection speechrecognition pattern recognition and lots of biomedicalapplications [36ndash41] Recently multiclass SVMs have beenvery popular and successful for different classification issues[42 43] In previous studies for classifying SRSs someclassification methods such as the linear regression LPCHMM and FLD have been used [17ndash20] Unlike the previousones in this study it has been taken into consideration thesuccessfulness of SVMs and ANFIS in biomedical appli-cations the multiclass SVMs and ANFIS were chosen asclassifiers

2 Material and Methods

21 Data In this study Cavusoglu et alrsquos [18] data setobtained from Gulhane Military Medical Science Sleep Lab-oratory was used While recording data a Sennheiser ME64 condenser microphone with a 40Hzndash20 kHz plusmn 25 dBfrequency response was used and placed 15 cm over thepatientrsquos head So a BNC cable UA-1000model multichanneldata acquisition system and a personal computer were usedfor obtaining the data The computer was placed out of theroom for avoiding its noise Signal records were made at16 kHz sampling frequency and 16-bit resolution and storedwith patient information The details about this database arereferred to in Cavusoglu et alrsquos study [18] 12 patientsrsquo data

Computational and Mathematical Methods in Medicine 3

Table 1 Information of patients

Subject no AHI BMI Age Gender1 127 2603 39 F2 92 2728 51 M3 143 2438 40 M4 147 2736 42 M5 177 2746 44 M6 19 3247 55 F7 203 2841 36 M8 22 2625 55 M9 24 2678 25 M10 246 3331 59 F11 247 261 67 M12 2986 2967 48 M

were used in the experiments of this study The informationof related patients is given in Table 1

22 Entropy Entropy is defined in terms of a random vari-ablersquos probability distribution and generally interpreted as ameasure of uncertainty The concept of entropy is used invery large area from physic to information theory [35] Theamount of entropy is often thought of as the amount of infor-mation used to define the systemrsquos state [35] Shannon givesthe definition of entropy which states the content of expectedinformation or uncertainty of a probability distribution [44]In this work with the considering successfulness about theshort signal entropy estimation Shannon entropy algorithmwas used to evaluate the average amount of new informationobtained from segments of SRSs [44] Shannon proposeda quantity called self-information which is a logarithmicfunction on the interval (0 1] and related to the probabilityof event 119883 = 119909

119894 (119894 = 1 2 119899) Self-information ℎ(119901

119894) is

given by

ℎ (119901119894) = log

2(

1

119901119894

) (1)

Average self-information or entropy is derived by weighingthe 119899 numbers of self-information values ℎ(119901

119894) by their

individual probabilities [44]

119867119896=

119899

sum

119894=1

119901119894log2(

1

119901119894

) (2)

23 Phase Space Reconstruction The concepts coming fromnonlinear dynamic theory are applied to biomedical timeseries by using some methods proposed for calculating thechaotic measures (Lyapunov exponents correlation dimen-sion etc) For estimation of these measures the first step isthe reconstruction of systemrsquos attractor (phase space recon-struction) from the scalar time series data [34 35] Eventhough the dynamical systemmight have many variables theobtaining of one variable from the system is sufficient forreconstructing the phase space of the system [35] The time-delay technique is easy systematic and the most popular

approach to reconstruct the attractor [34 35] In this studyTakensrsquo time-delay embedding method [45] was used for thereconstruction of the attractor from SRSs segment parts inthe phase space According to embedding theorem of Takens[45] 119898-dimensional time-delay vectors are reconstructedfrom SRS segment parts (119909(119899) = 119909(119899Δ119905) 119899 = 1 2 119873)as follows

119883119894= (119909119894 119909119894+120591

119909119894+2120591

119909119894+3120591

119909119894+(119898minus1)120591

) (3)

where 119909(119894) is the 119894th value of the sound segment part119883119894is the

119894th point on the attractor (119894 = 119873minus(119898minus1)120591)119898 is the dimensionof the phase space (embedding dimension) and 120591 is the lagor time delay [45] In this theorem selection criterion is119898 ge

2119863 + 1 for embedding dimension herein 119863 is the attractordimension According to Abarbanel [34] 119898 gt 119863 wouldbe sufficient The chosen embedding dimension and time-delay parameters are important and determined from timeseries data since the optimal values of them are not knownin advance There are many proposed methods for choosingtheir values [35] In this paper the false nearest neighbours(FNN) method was applied to select the embedding dimen-sion [46] The suitable embedding dimension is determinedas the phase space dimension for the zero percentage value ofFNN where the number of FNN is below a threshold valueThe average mutual information (AMI) that is a nonlinearautocorrelation function was used for finding the time delay[34 47] In this study the proper value of time delay isselected as the first minimum value of AMI

24 The Largest Lyapunov Exponent The Lyapunov expo-nents or characteristic exponents specify the sensitivity toinitial conditions of a dynamical system and measure theaverage rate of convergence or divergence of nearby trajecto-ries on the attractor [34 35 48] For detection of the chaoticbehaviour the calculation of the LLE is sufficient since apositive LLE can be accepted as good evidence for a chaoticsystem [34 35 48] In this study the LLE measure was usedin the determination of the complexity of the SRS segments

Several methods estimating the LLE or Lyapunov expo-nent spectrumhave been proposed [48ndash51] A simplemethodwhich calculates only the LLE is Rosenstein et alrsquos algorithm[51] and this algorithm is suitable especially for small noisydatasets In this paper Rosenstein et alrsquos algorithm [51]was chosen to calculate the LLE of snore episodes It wasstated that this algorithm is a suitable method for embeddingdimension is smaller than Takensrsquo selection criterion and fora wide range of time delays [51]

According to Rosenstein et alrsquos algorithm [51] after re-constructing the time-delay vectors the nearest neighboursof each state on the phase space trajectory are searched It isopined that the 119895th nearest neighboursrsquo pair diverges nearlyat a rate dedicated by the LLE (120582

1) [51]

119889119895 (119894) asymp 119862

1198951198901205821(119894Δ119905)

(4)

where 119862119895is the initial separation Δ119905 is the sampling period

and 119889119895(119894) is the distance between the 119895th pair of nearest


neighbours after (119894 times Δ119905) seconds Equation (5) is obtainedby taking the logarithm of both sides of (4)

ln 119889119895 (119894) asymp ln119862

119895+ (119894 sdot Δ119905) (5)

This equation gives a set of approximately parallel lines (for119895 = 1 2 119872) each with a slope roughly proportional to1205821 The LLE values of sound segment parts are computed by

using a least squares fit to the averaging line defined by

119910 (119894) =1

Δ119905

⟨ln 119889119895 (119894)⟩ (6)

where ⟨sdot sdot sdot ⟩ represents the average of all 119895 values [51]

25 Support Vector Machines Support vector machines(SVMs) is a tool used in machine learning It was proposedby Cortes and Vapnik in 1995 [52] SVMs that motivate min-imizing Vapnik-Chervonenkis (VC) dimension have provedto be very successful in classification learning [52ndash54] In thisalgorithm it is easy to formulate the decision functions interms of a symmetric positive definite and square integrablefunction 119896(sdot sdot) referred to as a kernelThe class of the decisionfunctions also known as kernel classifiers [55] is then given by

119891 (119909) = sign(

119897

sum

119894=1

120572119894119910119894119896 (119909119894 119909)) 120572 ge 0 (7)

where training data 119909119894isin 119877119889 and labels 119910

119894isin plusmn1

251 Multiclass Support Vector Machines SVM has beenused in numerous studies of interest in different areas WhenSVMs are performed for multiclass problems the generallyused technique is to solve the problem as a collection of sometwo-class classifications that can be solved by binary SVMs[54]

According to Vapnik [54] some information is stated asfollows suppose that we have a set of training data ((119909

119894 119910119894)

for 119894 = 1 119899 and 119909119894isin 119877119889 and 119910

119894isin plusmn1) and a nonlinear

transformation to a higher dimensional space the featurespace (Φ(sdot sdot) 119877

119889Φ(sdotsdot)

997888997888997888997888rarr 119877119867) the SVMs solves

Minimize(119908120577119894 119887)

1

21199082+ 119862sum

119894

120577119894 (8)

Subject to 119910119894(120601119879(119909119894) 119908 + 119887) ge 1 minus 120577

119894

forall119894= 1 119899 120577

119894ge 0

(9)

where (119908 119887) defines the linear classifier in the feature spaceThe SVMs try to enforce positive samples to present anoutput greater than +1 and the negative samples present anoutput less than minus1 for two classes Those samples are notfulfilling this condition and need a nonzero 120577

119894in (9) so they

will introduce a penalty in the objective function (8) Theinclusion of the norm of119908 in (8) checks whether the solutionis maximummargin [54]

The purpose of 119862sum119894120577119894is to control the number of mis-

classified samplesThe usage of a larger value of parameter119862

which is chosen by the user corresponds to assigning a higherpenalty to errors When application of this optimizationfor solving problems generally suffering the balance of thesamples between the classes and the unequal density of theclusters in the feature space [56] In multiclass support vectormachines the binary SVMs that is using a vector of differentweight and bias for each class (119908119895 and 119887

119895 for 119895 isin 1 2 119896)are applied The classifier function of SVMs is given as

119891 (119909) = arg sdotmax (120601119879 (119909) 119908119895 + 119887119895) 119895 isin 1 119896 (10)

Accordingly we can impose (9) for each class it does notbelong to as suggested in [54 57] leading to

Minimize(119908119895119887119895120577119895119898

119894)

1

2

119896

sum

119895=1

1003817100381710038171003817100381711990811989510038171003817100381710038171003817

2

+ 119862

119896

sum

119895=1

119896

sum

119898=1

119898 = 119895

119899119895

sum

119894=1

120577119895119898

119894

Subject to (120601119879(119909119895

119894)119908119895+ 119887119895) minus (120601

119879(119909119895

119894)119908119898

+ 119887119898)

ge 2 minus 120577119895119898

119894 120577119895119898

119894ge 0 forall119895 = 1 119896

forall119898 = 1 119896 (119898 = 119895) forall119894 = 1 119899119895

(11)

where 119909119894119895is the 119894th sample in class 119895 and 119899

119895is the number

of training samples in that class Herein this optimizationproblem searching the 119895th output for 119909

119894119895is larger than any

other In conclusion the penalization for any incorrectlyclassified sample will be based on the incorrectly assignedclass and on the number of outputs larger than the outputof true assigned class [57] We have focused our study onthat this simple model can be extended to solve nonlinearseparable problem So there are some studies available in theliterature which have proposed to use kernel-basedmethodsThese methods used mapping functions on the input featuresfor carrying them into a very high-dimensional space Sothe methods can construct a hyperplane in that feature spaceproperties rely on kernel functions of SVMs [54 58]

26 Adaptive Network Fuzzy Inference System (ANFIS)Adaptive network fuzzy inference system (ANFIS) is a tool forusing different purposes Its structure has a fuzzy set ldquoif-thenrulesrdquo For generating the suitable input-output pairs it hasa correct membership function [59] ANFIS has a learningability having a neuro-fuzzy-type structure and this networkhave nodes where each combination of these nodes placed inthe different layers for completed specific functions

ANFIS has some hybrid learning algorithm that isSugeno-type fuzzy inference systems for identifying param-eters Sugeno-type fuzzy system uses least-squares methodwhich is combined for trainingmembership function param-eters of fuzzy system This system emulates a given trainingdata set [59]

Sugeno-type ANFIS model has five layers for generatinginference system [59] There are several nodes in each layerThese layers are working as follows the input signals in thepresent layer are the output signals obtained from nodes in


x

y

Layer 1A1

A2

B1

B2

Layer 2

120587

120587

W1

W2

Layer 3

N

N

Layer 4

xy

x y

W1f1

W2f2

Layer 5

fΣ

w1

w2

Figure 1 Sugeno-type adaptive network fuzzy system [59]

the previous layers [59] Jang [59] has shown that first-orderSugeno-type model is given as

Rule 1 if (119909 is 1198601) (119910 is 119861

1)

then (1198911= 1199011119909 + 1199021119910 + 1199031)

Rule 2 if (119909 is 1198602) (119910 is 119861

2)

then (1198912= 1199012119909 + 1199022119910 + 1199032)

(12)

where 11990912

are inputs 119860119894and 119861

119894are fuzzy sets 119891

119894outputs

within the fuzzy region identified by the rules and the designparameters (119901

119894 119902119894 and 119903

119894) are determined during the training

process [59] ANFIS architecture is given in Figure 1In Figure 1 square nodes which are called adaptive nodes

are accepted to represent the parameter sets in these nodeswhich are adjustable [59] However circle nodes are fixednodes that are accepted to represent the fixed parameter setsin the system [59]The details of ANFISmodel can be seen in[59]

3 Results

31 DataAnalysis and Feature Extraction In this study snorebreathing and silent segments were firstly extracted from theSRSs The samples of the recorded ambient sounds in timeand time-frequency domains are shown in Figure 2 Hereinsnore breathing and silent segments were manually markedin both domains for examining the signalsrsquo characteristicsEach segment was automatically subdivided into parts having3200 samples by developed MATLAB program with thinblack lines These segmentation and subdivision procedurewere also shown in Figure 2 In Figure 2 Br1 Br2 andBr4 represent breathing segment parts Sn1 and Sn3represent snore segment parts and Sl1 Sl2 and Sl5represent silent segment parts We can see from Figure 2time duration of each segment (in case of inspiration andexpiration interval) is different from each other The fre-quency and amplitude spectrums of SRSs segments havedifferent characteristics (in Figure 2) It is seen that snoresegment parts have a few components for different frequencyrange as high and low amplitude peaks in Figure 2 How-ever breathing and silent segments have many componentswhich are similar peak values in a wide frequency bandThe separation of breathing and silent segments is difficultsince their characteristics are similar to each other andthe noise originated from ambient recordings substantially

affects breathing and silent segmentsTherefore auditory andvisual examinations were used for marking of the segments

In case of experiments the segments were normalized tobe in the range of [minus05 05] This method is used becauseof each subject having different characteristics (ie all snorebreathing and silent segmentsrsquo amplitudes of subjects aredifferent owing to their sounds intensity) Therefore chang-ing range of each sound segment could be different withoutnormalization It would affect the calculated feature values

In order to investigate the chaotic behaviour of SRSs LLEand entropy of each segment parts are calculated For the LLEcalculation all segment parts are reconstructed in the phasespace according to Takensrsquo theorem Therefore embeddingdimension (119898) and time delay (120591) valuesmust be determinedfirstly In order to make a decision about these values forall SRS segments embedding dimension (119898) and time delay(120591) values are estimated by using the false nearest neighbour(FNN) and average mutual information (AMI) methodsrespectively Looking at these results it was seen that119898 and 120591

values of snore breathing and silent segment parts are closeto each other Hence if we chose 119898 to be 5 and 120591 to be 8 forall segment parts the estimation of LLE is not significantlyaffected So it is most suitable to set 119898 = 5 and 120591 = 8

for all segment parts Herein some reconstructed attractorsdepending on SRSs chosen segments projected onto three-dimensional phase space are shown in Figure 3 Certain typeof geometrical shape of snore breathing and silent segmentscan be seen from the figure Moreover sizes of attractors giveinformation to us about how they are differentiated from eachother depending on the amplitude values of SRS segments

Figure 4 gives information about LLE and entropy fea-tures of SRS segments The graph is manually divided andmarkedwith vertical lines to show the segmentsThe LLE andentropy values of segment parts (square and trianglemarkersresp) are automatically estimated by developed MATLABprogram

It can be seen from Figure 4 that the LLE and entropyvalues can be differentiated into snore breathing and silentsegments For snore segments LLE values changing between(01 times 2) and (12 times 2) are less than breathing and silentones and entropy values changing between (01 times 5) and (1times 5) are greater than breathing and silent ones However atthe breathing segments entropy values are usually greaterand LLE values are usually less than silent segments Whenlooking at silent segments they generally have bigger valuesof LLE and smaller values of entropy Figure 5 gives us anyinformation about all snorebreathingsilent parts distribu-tion in all data sets

In Figure 5 snore breathing and silent segment partsof SRSs are denoted by square circle and triangle symbolsrespectively It is seen that snoring segment parts are usuallyclustered between 20 and 45 entropy levels and 003ndash015LLE levels however some parts of snoring segments areclustered between 00 and 10 entropy levels and 01ndash015 LLElevels Although snoring segment parts are clustered intotwo areas the results show they can be discriminated frombreathing and silent segment parts If looking at the breathingsegment parts which are usually clustered between 00 and33 entropy levels and 003ndash025 LLE levels The results


10 105 11 115 12

0

01

02

03

04

05

Time (s)

Am

plitu

de

95 10 105 11 115 12

20001000

30004000500060007000

Freq

uenc

y (H

z)

Time (s)

Sl1 Br1Sl2 Sl3 Sl4 Sl5 Br2 Br3 Br4Sn2Sn1 Sn3

Silent segment parts

Snore segment parts

Breathing segment parts

Silentsegment parts

minus01

Figure 2 Subdivision procedure of SRSs segments snore breathing and silent segment parts

x(t+2T)

005

005005

0 0

0

minus005

minus005 minus005

x(t + T) x(t)

(a)

x(t+2T)

005

005005

0

00

minus005

minus005 minus005

x(t + T)x(t)

(b)

x(t+2T)

x(t + T) x(t)

001

001

0

0

minus001

minus001

minus001minus0005

0 0005 001

(c)

Figure 3 Three reconstructed SRSsrsquo segment attractors with119898 = 3 and 119879 = 120591 = 8 (a) snore (b) breathing and (c) silent segment attractors

show that breathing segment parts cannot easily be classifieddepending on the distribution area Because feature distribu-tion of breathing parts is not significantly clustered Howeversilent segment parts are generally clustered into two areasfirst between 00 and 03 entropy levels and 015ndash025 LLElevels second between 03 and 25 entropy levels and 04ndash10 LLE levels It can be said that silent segment parts can bediscriminated and classified into their own classes

32 Experiments In this study the performance of methodsin classifying snore breathing and silent segmentsrsquo partswere evaluated in two experimental ways

Experiment I The training and test datasets were obtainedfrom the recordings of same patients The first half intervalof the recordings was training data set and the rest was testdata setThese datasets obtained from 12 patients include 672


17 175 18 185 19 195 20

0

05

1

15

Time (s)

Am

plitu

des

SRSs

Snore segmentparts

Breathingsegment parts

Silent segmentparts

Silentsegment

part

Snoresegment

parts

minus05

02 lowast entropy05 lowast LLE

Figure 4 The LLE and entropy values of SRSs segments

0 005 01 015 02 025 03 0350

051

152

253

354

455

LLE level

Entro

py le

vel

SnoreBreathingSilent

Figure 5 Distribution of data sets in LLE versus entropy

and 668 segments for training and test respectively After thesubdivision procedure of these segments training and testdatabases have 4037 and 5234 segment parts respectively

Experiment II The training and test data sets were obtainedfrom all recordings of different patients Training data setcontains 553 segments from 6 patients and the rest 6 patientsrecordingswere used for test data set with 787 segments Afterthe subdivision procedure of these segments training and testdatabases have 3322 and 4110 segment parts respectively

The details of the training and test datasets in Experi-ments I and II are summarized in Tables 2 and 3 respectively

33 Results of Classifiers In this study we presented experi-mental results obtained from the M-SVMs and ANFIS algo-rithms which are three class nonlinearly separable problems

Table 2 The details of training and test data sets in Experiment I

Subjectno

Training Test12 subjects (first half interval) 12 subjects (rest interval)Snore Breathing Silent Snore Breathing Silent

1 25 23 16 25 23 152 15 15 15 15 15 153 15 15 15 15 15 154 15 15 15 15 15 155 25 25 8 25 25 86 39 25 11 39 25 107 25 15 25 25 15 258 25 25 25 25 25 259 25 15 25 25 15 2510 25 25 10 25 25 1011 0 10 7 0 10 612 25 25 8 25 25 7Total 259 233 180 259 233 176Total 672 668

In case of experiments optimal 119862 value was chosen as 107and regularization parameter (Lambda) was 10minus7 for M-SVMs However for ANFIS predictions maximum numberof epochs was chosen as 10 It is seen that this is enoughto allow the system converge to a final value The learningrate was chosen as 00 and examined membership functionsfor ANFIS predictions are Gaussian combination Gaus-sian curve generalized bell-shaped pi-shaped sigmoidallyshaped trapezoidal-shaped and triangular-shaped member-ship functions It is observed that the best prediction resultsin the same conditions obtained by generalized bell-shapedmembership function


Table 3 The details of training and test data sets in Experiment II

Training TestSubject no Snore Breathing Silent Subject no Snore Breathing Silent2 30 30 30 1 50 46 313 30 30 30 5 50 50 164 30 30 30 6 78 50 219 50 30 50 7 50 30 5010 50 50 20 8 50 50 5011 0 20 13 12 50 50 15Total 190 190 173 Total 328 276 183Total 553 Total 787

Table 4 Training and test results of Experiment I (a) M-SVMs and (b) ANFIS

(a)

Number of segment parts Snore Breathing Silence Sensitivity () PPV () Total accuracy ()M-SVMs training

Snore 1260 1190 10 60 9444 1009279Breathing 746 0 546 200 7319 9463

Silence 2031 0 21 2010 9897 8855M-SVMs test

Snore 1175 1075 42 58 9149 97649161Breathing 746 10 457 279 6126 8574

Silence 3313 16 34 3263 9849 9064

(b)

Number of segment parts Snore Breathing Silence Sensitivity () PPV () Total accuracy ()ANFIS training

Snore 1260 1150 91 19 9126 96888697Breathing 746 32 597 117 8002 6284

Silence 2031 5 262 1764 8686 9284ANFIS test

Snore 1175 932 202 41 7931 94818675Breathing 746 35 426 285 5710 5741

Silence 3313 16 114 3183 9607 9070

For each experiment the classification performance wasevaluated in terms of sensitivity defined as 100 times TP(TP +FN) positive predictive value (PPV) defined as 100 times TP(TP + FP) and accuracy 100 times (TP + TN)(TP + TN +FP + FN) where TP TN FP and FN are the numbers oftrue positive true negative false positive and false negativeclassified segment parts respectively

Tables 4 and 5 show the classifiers performances ofExperiments I and II for snore breathing and silent segmentparts Herein all segments have different number of segmentparts (each part having 3200 samples) owing to the segmenttime interval the total numbers of segment parts in trainingand test data sets are different from each other

Tables 4 and 5 represent information about percentagesof accuracy results of training and test datasets It can beseen thatM-SVMs give a good performance concerning both

training and test procedures in Experiments I and IIThe bestdetection performance was achieved in Experiment I whereboth training and test datasets have different time intervalsof same subjectsrsquo recordings (Table 4) In Experiment II(Table 5) the SVMs test accuracy was dropped by 696(from 9161 to 8465) while in ANFIS test accuracy wasdropped by 62 (from 8675 to 8055) Herein trainingand test datasets were obtained from different individualsAdditionally looking at the testing sensitivities of snoreand silent segment parts for SVMs was close to trainingperformance especially in Experiment I However breath-ing segment partsrsquo sensitivity results are worse than othersbecause breathing segment beginning and ending parts areclose to snore or silent parts That is the entropy and LLEvalues are similar to others on segment beginning and endingparts So classifier is having difficulty in classifying breathing


Table 5 Training and test results of Experiment II (a) M-SVMs and (b) ANFIS

(a)


Snore 1156 1097 42 17 9490 96659007Breathing 721 32 525 164 7282 8255


Snore 1280 1121 135 24 8758 85578465Breathing 772 175 523 74 6775 6032

Silence 2058 14 209 1835 8916 9493

(b)


Snore 1156 971 162 23 8399 96148461Breathing 721 39 423 259 5867 6900


Snore 1280 938 303 39 7328 87918055Breathing 772 128 414 230 5362 5079

Silence 2058 1 98 1959 9519 8792

0 01 02 03 04 05 0706 08 09 10

0102030405

0706

0809

1

False positive rate

True

pos

itive

rate

ROC curve ANFIS and M-SVMs

ANFISM-SVMs

Figure 6 Receiver operating characteristics (ROC) curve of ANFISand M-SVMs

segment parts The similar results were again obtained byANFIS but the accuracy was not feasiblly good as SVMsFigure 6 gives information about ROC analyses of methods

4 Discussion and Conclusion

It can be seen from the previously performed studies thatsome different features obtained from the analysis of soundsignals in spectral and temporal domains were used forexamining the SRSs In majority of these works the energy

of sounds zero-crossing rates MFCCs and formant fre-quencies and so forth were estimated and linear frequencyanalyses such as LPC and Fourier transform were examined[17ndash20] SRSs cannot be adequately examined by linearlybased methods since they have complex nature [21 22] Thenonlinear analysis can bring out the SRSsrsquo characteristicsrelated to irregular behaviour

In this study the significant information to understand-ing of chaotic behaviour of SRSs and useful features to clas-sifying the SRSs was expected from the nonlinear measuresFor this goal the LLE and entropy measures were used forclassifying SRSs into three classes The LLE and entropyvalues of SRSs segments in Experiment II were comparedwith each other by using unpaired Studentrsquos 119905-test with level ofsignificance 119875 lt 0001 (with Bonferroni correction) statisti-callyThe LLE calculated for all SRSs segments have a positivevalue and this result can be accepted as an evidence of chaoticbehaviour It can be recognized that from experiments thatthe LLE values of breathing and silent groups were foundhigher and entropy values of these two groups were foundlower than snore group significantly However for breathinggroup the LLE value is lower and the entropy value is higherthan silent group significantly So the results have shown thatwhile the LLE values tend to decrease the entropy values tendto increase from silent to snore segments This decrementfor LLE indicates that dynamics of snore segment have low-level complex behaviour with respect to breathing and silentsegments The reason for this can be interpreted dependingon frequency characteristics of SRSs [21] SRSs segmentshave different frequency and amplitude spectrums Snoresegments generally consist of simple and complex waveformsand have irregular appearance [21]They have some high and


Table 6 Snore sound classification studies and their accuracy results

Study Duckitt et al [17] Cavusoglu et al [18] Karunajeewa et al [19] Yadollahi andMoussavi [20] Our method

Sound types Ambient sound Ambient sound Ambient sound Ambient andtracheal sound Ambient sound

Classes

Snoring and othersounds (silence

breathing and othertypes of sounds) snore

detection

Snorenonsnore Snore breathing andsilence

Snore andbreathing

Snore breathing andsilence

Features39-dimensional featurevector of energy and

MFCC

Spectral energydistributions

Zero-crossings andsignalrsquos energy

Zero-crossingssignalrsquos energy and

first formant

The largest Lyapunovexponent (LLE) and

entropy

Classifier HMM Linear regressionMinimum-

probability-of-errordecision rule

FLD M-SVMs and ANFIS

Accuracy 82ndash89 snoresensitivity

868 snoresensitivity

9074 totalsensitivity

932 for ambientsound totalaccuracy

In Exp I 9161 (SVMs)8675 (ANFIS) totalaccuracies and 9149(SVMs) 7931 (ANFIS)

snore sensitivities

low amplitude peaks for different frequency range in domain[21] However breathing and silent segments show noise-like characteristics which have many similar peak values ina wide frequency band [17 20] These segments generallyappear as intertwinedwith each other with some backgroundnoises especially originated from ambient recordings [17 20]Because of giving a measure of predictability and complexityof sounds the increments of LLE show that the predictabilityof system decreases from snore to silent segment

The entropy values may be interpreted as the averageamount of new information obtained by making the mea-surement in information theory sense [35] According toentropy values it can be said that the information expectedfrom snore segment is greater than breathing and silentThis result can be evaluated from a different perspectiveaccording to Williams [35] high entropy is interpreted ashigh accuracy in the data and it shows that the state of systemcan be determined with great accuracy The LLE and entropymeasurements produced significant values for differentiatingthese segments if these results were taken into account

The structure of SRSs shows variations such as silentbreathing and snore segments so the degree of chaoticbehaviour of SRSs can vary based on these segments Accord-ing to LLE values the complexity of snore segment haslower level than others and it can be said that consideringentropy values the state of system can be defined as moreaccurate than breathing and silent segments It is found thatthe complexity increases and amount of new informationgained from measurement decreases from snore to silentsegments Since the silent segment has not any informationbecause of noisy characteristics SRSs are actually producedduring breathing process and therefore the dynamics ofthese signals depend on the breathing cycle Cervantes andFemat [60] have studied the phenomenon of breathing ina class of piecewise continuous systems by using a model

of linear-driven switched system It is seen that chaoticand regular phases of breathing evolve irregularly in theirsystem however their average behaviour is surprisinglyregular depending on bifurcation parameter Therefore theyhave shown that breathing phenomenon occurs the similarstructural characteristics with intermittency If this result istaken into account it can be said that SRSs show intermit-tency behaviour since they have different forms of chaoticdynamics

Different from previous studies [17ndash20] although thereare many classifier methods multiclass SVMs and ANFISwere selected in this study First data was trained byone-against-all SVMs and ANFIS which provide a feasibleway to categorize and classify SRSs in experiments Whileexperiments were realized different kernel functions suchas polynomial gauss RBF gauss were used for obtainingbest accuracy results It has been shown that when gauss-based kernel functions are used for both classifiers the systemaccuracy was the best

The previous studies have shown that classificationaccuracies of them have varied values depending on theirexperimental procedures [17ndash20] Duckitt et al [17] obtainedsnoring detection sensitivity as 89 with training and testdata from same patients and 822 with training and testdata sets from different patients In Cavusoglu et alrsquos study[18] their sensitivities for snore detection were 973 withonly simple snorers and 902 with both simple snorersand OSA patients For OSA patients their sensitivity was868 These results were found when training and test datasets were formed of different individuals [18] Karunejeewaet alrsquos method [19] provided 9074 total sensitivity forsnoring breathing and silence classification They also usedthree different noise reduction techniques and obtained totalmaximum sensitivity of 9678 with proper choices of noisereduction technique and features Their test set contained


different subjectsrsquo recordings than those used in trainingset [19] Yadollahi and Moussavi [20] used both trachealand ambient sounds gathered from different body and neckpositions to classify them into breath and snore groupsTheirresults were obtained by using different subjectsrsquo samples astraining and test data sets [20] and their total accuracieswere found as 957 and 932 for tracheal and ambientrecordings respectively Table 6 gives information aboutprevious studies and our study accuracy results

In this paper it is seen that SRSs have nonlinear charac-teristics which carry any information about snore breathingand silent segments of SRSs With the help of this infor-mation these segments can be differentiated into differentgroups Two experimental procedures were implemented sothat training and test data sets were formed in twoways same(for Experiment I) or different (for Experiment II) subjectsrsquodata The total classifiers performances of Experiment II(8465 for M-SVMs and 8055 for ANFIS) were foundlower than Experiment I (9161 for M-SVMs and 8675for ANFIS) In previous studies they generally focused onestimating snore detection sensitivities (Table 6) Howeversnore detection sensitivities were found as 9149 for M-SVMs 7931 for ANFIS in Experiment I and 8758 for M-SVMs 7328 for ANFIS in Experiment II The results showthat proposed methods especially M-SVMs classificationaccuracy is as good as previous studies

Table 6 shows that previous studies have generallyfocused on linear analysis of SRSs segments and have tried todetect snore segments In fact time domain linear features areimportant for extracting any information from physiologicalsignals It can be seen from these studies that their resultswere good enough to classify and differentiate the SRSsHowever keeping in mind the chaotic behaviour of thesesounds is also considerable Experimental results have shownthat the LLE and entropy can be important features forclinical diagnosis systems

Acknowledgments

The authors would like to thank Dr Tolga Ciloglu and DrOsman Erogul for the data

References

[1] W W Flemons M R Littner J A Rowley et al ldquoHomediagnosis of sleep apnea a systematic review of the literaturerdquoChest vol 124 no 4 pp 1543ndash1579 2003

[2] J R Perez-Padilla E Slawinski L M Difrancesco R R FeigeJ E Remmers and W A Whitelaw ldquoCharacteristics of thesnoring noise in patients with and without occlusive sleepapneardquo American Review of Respiratory Disease vol 147 no 3pp 635ndash644 1993

[3] R Beck M Odeh A Oliven and N Gavriely ldquoThe acousticproperties of snoresrdquo European Respiratory Journal vol 8 no12 pp 2120ndash2128 1995

[4] F Dalmasso and R Prota ldquoSnoring analysis measurementclinical implications and applicationsrdquo European RespiratoryJournal vol 9 no 1 pp 146ndash159 1996

[5] J A Fiz J Abad R Jane et al ldquoAcoustic analysis of snoringsound in patients with simple snoring and obstructive sleepapnoeardquo European Respiratory Journal vol 9 no 11 pp 2365ndash2370 1996

[6] S Agrawal P Stone K Mcguinness J Morris and A ECamilleri ldquoSound frequency analysis and the site of snoring innatural and induced sleeprdquo Clinical Otolaryngology and AlliedSciences vol 27 no 3 pp 162ndash166 2002

[7] M Cavusoglu T Ciloglu Y Serinagaoglu M Kamasak OErogul and T Akcam ldquoInvestigation of sequential propertiesof snoring episodes for obstructive sleep apnoea identificationrdquoPhysiological Measurement vol 29 no 8 pp 879ndash898 2008

[8] J Sola-Soler R Jane J A Fiz and JMorera ldquoVariability of snoreparameters in time and frequency domains in snoring subjectswith and without Obstructive Sleep Apneardquo in Proceedings ofthe 27th Annual International Conference of the Engineering inMedicine and Biology Society (IEEE-EMBS rsquo05) pp 2583ndash2586New York NY USA September 2005

[9] J Sola-Soler J A Fiz J Morera and R Jane ldquoMulticlass clas-sification of subjects with sleep apnoea-hypopnoea syndromethrough snoring analysisrdquoMedical Engineering and Physics vol34 pp 1213ndash1220 2012

[10] K Wilson R A Stoohs T F Mulrooney L J Johnson CGuilleminault and Z Huang ldquoThe snoring spectrum acousticassessment of snoring sound intensity in 1139 individualsundergoing polysomnographyrdquo Chest vol 115 no 3 pp 762ndash770 1999

[11] S FujitaWConway F Zorick andT Roth ldquoSurgical correctionof anatomic abnormalities in obstructive sleep apnea syndromeuvulopalatopharyngoplastyrdquo Otolaryngology vol 89 no 6 pp923ndash934 1981

[12] F G Issa D Morrison E Hadjuk et al ldquoDigital monitoring ofobstructive sleep apnea using snoring sound and arterial oxygensaturationrdquo Sleep vol 16 no 8 p S132 1993

[13] P V H Lim and A R Curry ldquoA newmethod for evaluating andreporting the severity of snoringrdquo Journal of Laryngology andOtology vol 113 no 4 pp 336ndash340 1999

[14] T H Lee and U R Abeyratne ldquoAnalysis of snoring sounds forthe detection of obstructive sleep apneardquo Medical amp BiologicalEngineering amp Computing vol 37 pp 538ndash539 1999

[15] T H Lee U R Abeyratne K Puvanendran and K L GohldquoFormant-structure and phase-coupling analysis of humansnoring sounds for detection of obstructive sleep apneardquo Com-puter Methods in Biomechanics and Biomedical Engineering vol3 pp 243ndash248 2001

[16] U R Abeyratne C K K Patabandi and K PuvanendranldquoPitch-jitter analysis of snoring sounds for the diagnosis ofsleep apneardquo in Proceedings of the 23rd Annual InternationalConference of the IEEE Engineering in Medicine and BiologySociety pp 2072ndash2075 October 2001

[17] W D Duckitt S K Tuomi and T R Niesler ldquoAutomatic detec-tion segmentation and assessment of snoring from ambientacoustic datardquo Physiological Measurement vol 27 no 10 pp1047ndash1056 2006

[18] M Cavusoglu M Kamasak O Erogul T Ciloglu Y Serina-gaoglu and T Akcam ldquoAn efficient method for snorenonsnoreclassification of sleep soundsrdquo Physiological Measurement vol28 no 8 pp 841ndash853 2007

[19] A S Karunajeewa U R Abeyratne and C Hukins ldquoSilence-breathing-snore classification from snore-related soundsrdquoPhys-iological Measurement vol 29 no 2 pp 227ndash243 2008


[20] A Yadollahi and Z Moussavi ldquoAutomatic breath and snoresounds classification from tracheal and ambient sounds record-ingsrdquo Medical Engineering and Physics vol 32 no 9 pp 985ndash990 2010


[22] Y Inoue and Y Yamashiro Sleep Disordered Breathing UpdateNippon Hyoronsha Tokyo Japan 2006

[23] J J Jiang Y Zhang and J Stern ldquoModeling of chaotic vibrationsin symmetric vocal foldsrdquo Journal of the Acoustical Society ofAmerica vol 110 no 4 pp 2120ndash2128 2001

[24] R Femat J Alvarez-Ramirez andM Zarazua ldquoChaotic behav-ior from a human biological signalrdquo Physics Letters A vol 214no 3-4 pp 175ndash179 1996

[25] A L Goldberger D R Rigney and B J West ldquoChaos andfractals in human physiologyrdquo Scientific American vol 262 no2 pp 42ndash49 1990

[26] L Glass and D Kaplan ldquoTime series analysis of com-plex dynamics in physiology and medicinerdquo Medical Progressthrough Technology vol 19 no 3 pp 115ndash128 1993

[27] M S Fukunaga S Arita S Ishino and Y Nakai ldquoQuantiativeanalysisof gastric electric stress response with chaos theoryrdquoBiomedical Soft Computing and Human Sciences vol 5 pp 59ndash64 2000

[28] G Quiroz I Bonifas J G Barajas-Ramirez and R FematldquoChaos evidence in catecholamine secretion at chromaffincellsrdquoChaos Solitons and Fractals vol 45 no 7 pp 988ndash997 2012

[29] A Sakakura ldquoAcoustic analysis of snoring sounds with chaostheoryrdquo in Proceedings of the International Congress Series vol1257 pp 227ndash230 December 2003

[30] T Mikami ldquoDetecting nonlinear properties of snoring soundsfor sleep apnea diagnosisrdquo in Proceedings of the 2nd Interna-tional Conference on Bioinformatics and Biomedical Engineering(iCBBE rsquo08) pp 1173ndash1176 Shanghai China May 2006

[31] D Yılmaz and H Ankıshan ldquoAnalysis of snore sounds byusing the largest Lyapunov exponentrdquo Journal of Concrete andApplicable Mathematics vol 9 pp 146ndash153 2011

[32] H Ankıshan and F Arı ldquoChaotic analysis of snore relatedsoundsrdquo in Proceedings of the IEEE Signal Processing and Com-munications Applications Conference pp 1ndash3 IEEE Fethiye-Mugla Turkey April 2012

[33] H Ankishan and F Ari ldquoSnore-related sound classificationbased on time-domain features by using ANFIS modelrdquo inProceedings of the International Symposium on Innovations inIntelligent Systems and Applications (INISTA rsquo11) pp 441ndash444IEEE Istanbul Turkey June 2011

[34] H D I Abarbanel R Brown J J Sidorowich and L STsimring ldquoThe analysis of observed chaotic data in physicalsystemsrdquoReviews ofModern Physics vol 65 no 4 pp 1331ndash13921993

[35] G P Williams Chaos Theory Tamed Joseph Henry PressWashington DC USA 1997

[36] M P S Brown W N Grundy D Lin et al ldquoKnowledge-based analysis of microarray gene expression data by usingsupport vector machinesrdquo Proceedings of the National Academyof Sciences of the United States of America vol 97 no 1 pp 262ndash267 2000

[37] T S Furey N Cristianini N Duffy D W Bednarski MSchummer and D Haussler ldquoSupport vector machine classifi-cation and validation of cancer tissue samples using microarray

expression datardquo Bioinformatics vol 16 no 10 pp 906ndash9142000

[38] L Cao and Q Gu ldquoDynamic support vector machines for non-stationary time series forecastingrdquo Intelligent Data Analysis vol6 pp 67ndash83 2002

[39] K Polat S Yosunkaya and SGunes ldquoPairwiseANFIS approachto determining the disorder degree of obstructive sleep apneasyndromerdquo Journal of Medical Systems vol 32 no 5 pp 379ndash387 2008

[40] T Gunes and E Polat ldquoFeature selection in facial expressionanalysis and its effect on multi-svm classifiersrdquo Journal of theFaculty of Engineering and Architecture of Gazi University vol24 no 1 pp 7ndash14 2009

[41] S Issac Niwas P Palanisamy R Chibbar and W J Zhang ldquoAnexpert support system for breast cancer diagnosis using colorwavelet featuresrdquo Journal of Medical Systems vol 36 pp 3091ndash3102 2011

[42] S Abe ldquoAnalysis of multiclass support vector machinesrdquo inProceedings of the International Conference on ComputationalIntelligence for Modelling and Automation (CIMCA rsquo03) pp385ndash396 Vienna Austria 2003

[43] C Angulo X Parra and A Catala ldquoK-SVCR A support vectormachine for multi-class classificationrdquoNeurocomputing vol 55no 1-2 pp 57ndash77 2003

[44] C E Shannon ldquoAmathematical theory of communicationrdquo BellSystem Technical Journal vol 27 pp 623ndash656 1948

[45] F Takens ldquoDetecting strange attractors in turbulencerdquo LectureNotes in Mathematics vol 898 pp 366ndash381 1981

[46] M B Kennel R Brown and H D I Abarbanel ldquoDeterminingembedding dimension for phase-space reconstruction using ageometrical constructionrdquo Physical Review A vol 45 no 6 pp3403ndash3411 1992

[47] A M Fraser and H L Swinney ldquoIndependent coordinates forstrange attractors frommutual informationrdquo Physical Review Avol 33 no 2 pp 1134ndash1140 1986

[48] AWolf J B Swift H L Swinney and J A Vastano ldquoDetermin-ing Lyapunov exponents from a time seriesrdquo Physica D vol 16no 3 pp 285ndash317 1985

[49] M Sano and Y Sawada ldquoMeasurement of the lyapunov spec-trum from a chaotic time seriesrdquo Physical Review Letters vol55 no 10 pp 1082ndash1085 1985

[50] K Briggs ldquoAn improved method for estimating Liapunovexponents of chaotic time seriesrdquo Physics Letters A vol 151 no1-2 pp 27ndash32 1990

[51] M T Rosenstein J J Collins and C J De Luca ldquoA practicalmethod for calculating largest Lyapunov exponents from smalldata setsrdquo Physica D vol 65 no 1-2 pp 117ndash134 1993

[52] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[53] C J C Burges and B Scholkopf ldquoImproving the accuracyand speed of support vector machinesrdquo in Neurol InformationProcessing Systems M Mozer M Jordan and T Petsche Edspp 375ndash381 MIT press Cambridge Mass USA 1997

[54] V Vapnik Statistical Learning Theory John Wiley amp Sons NewYork NY USA 1998

[55] T Jaakola M Diekhans and D Haussler ldquoUsing the fisherkernel method to detect remote protein homologiesrdquo in Pro-ceedings of the Intelligent Systems for Molecular Biology Confer-ence (ISCB rsquo99) pp 149ndash158 AAAI press Heidelberg GermanyAugust 1999


[56] J Arenas-Garcıa and F Perez-Cruz ldquoMulti-class support vectormachines a new approachrdquo in Proceedings of the IEEE Interna-tional Conference on Accoustics Speech and Signal Processingpp 781ndash784 April 2003

[57] J Weston and C Watkins ldquoSupport vector machines formulti-class pattern recognitionrdquo in Proceedings of the EuropeanSymposium on Artificial Neural Networks (ESANN rsquo99) pp 219ndash224 ESANN Bruges Belgium April 1999

[58] T Joachims ldquoMaking large-scale SVM learning practicalrdquoin Advances in Kernel Methods-Support Vector Learning BSch119894lkopf C J C Burges and A J Smola Eds pp 169ndash184MIT Press Cambridge Mass USA 1999

[59] J-S R Jang ldquoANFIS adaptive-network-based fuzzy inferencesystemrdquo IEEE Transactions on Systems Man and Cyberneticsvol 23 no 3 pp 665ndash685 1993

[60] I Cervantes and R Femat ldquoIntermittent operation of lineardriven switched systemsrdquo International Journal of Bifurcationand Chaos vol 18 no 2 pp 495ndash508 2008

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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ObesityJournal of



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OphthalmologyJournal of


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Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


for classifying SRSsrsquo segments as snorenonsnore Theyobtained 868 accuracy for obstructive sleep apnea (OSA)patients Karunajeewa et al [19] calculated zero-crossingrates normalized autocorrelation coefficients energy andfirst predictor coefficient of linear predictive coding (LPC)analysis as features for classification of SRSs into snoringbreathing and silence They also used three noise reductiontechniques and compared their performanceWhile they hadan overall classification accuracy of 9074 their accuracyis up to 9678 with noise reduction techniques and aproper choice of features Yadollahi and Moussavi [20] triedto classify breath and snore sounds by using Fisher lineardiscriminant (FLD) based on zero-crossing rates energyand first formant of the SRSs that are recorded by twomicrophones (tracheal and ambient) They investigated thebody and neck positionsrsquo effects on the classification resultsThe overall accuracies were found as 957 and 932for tracheal and ambient recordings regardless of the neckposition respectively [20]

It is seen that these studies have focused on examiningsnoring sounds by linear features analysis such as Fouriertransform LPC but the nonlinear characteristics of SRSs forclassifications have not yet been evaluated so far SRSs areknown to have nonstationary and complex behaviours [2122] Some parts of SRSs have nonlinear acoustic vibrationsdepending on out- and in-factors such as the respiratoryairflow strength vibrations on the soft palate the shapeand differences of upper airway and the airway obstructiondue to tongue subsidence [22 23] These make it difficultto solve the identification of SRSs depending on traditionallinear frequency and time domain based methods In thesecases the nonlinear analysis can be performed to revealthe undefined characteristics of the signal It is possible touse the linear and nonlinear analyses together since theseapproximations can produce the meaningful results whichsupport each other For example a wideband spectrum maybe indicator of chaos but it cannot only identify definition ofchaos However spectral analysis may give some informationfor examining the source of variations in the signals

From the biomedical perspective nonlinear analysesmethods coming from chaos theory have been used to evalu-ate the states of biological systems and signals from systemiclevel to the cellular scale [24ndash28] The behaviours of dynam-ical biological systems are interpreted by evaluating thechaotic indicators such as Lyapunov exponents correlationdimension Poincare section and entropy While some sys-tems show a chaotic behaviour under the normal operatingconditions at the pathological conditions a degree of systemsrsquochaotic behaviour may be reduced or increased or systembehaviour can turn to a regular state [23ndash28] Hence somecontributions related to commentating of system functionscan be provided by evaluating the effects of pathological ornormal conditions on the system behaviour There are a fewstudies which investigated the nonlinear properties of SRSsin the literature [29ndash33] Sakakura [29] used Poincare sectionand the largest Lyapunov exponent (LLE) for indicatingthe chaotic characteristics of snoring sounds Mikami [30]performed surrogate analysis by using correlation integraland showed that snoring sounds have nonlinear properties

Yılmaz and Ankıshan [31] calculated the LLE values for snoresegments obtained from apneahypopnea patients and simplesnorers Their results showed that the LLE of simple snorergroup was significantly higher than apneahypopnea group[31] Ankıshan and Arı [32] showed from their experimentalresults that SRSs have chaotic behaviour and carry meaning-ful information so the LLE can be used for classification ofSRSs Moreover they also showed that entropy can be usedin classification of SRSs with time domain features [33]Thesestudies have shown that nonlinearmeasures can bring to lightsignificant outcomes for SRSs

The LLE quantifies the dynamic stability of a system andgives information about the predictability of a system [34 35]The positive value of the LLE is accepted as a key indica-tor of chaotic behaviour Entropy which has also multipledefinitions may be interpreted as the average amount ofnew information obtained by making the measurement ininformation theory sense [35] In previous studies it wasreported that these features are the quantitative measures ofchaos and frequently used in the nonlinear analysis of theexperimental time series [23ndash33] So the aims of this workare to extractmeaningful information from SRSs related to itsnonlinear characteristics to investigate the variability of thesechaotic measures for different SRSs segments and to test theavailability of these quantities for classifying SRSs For thispurpose SRSs were analysed by using entropy and the LLEand classified as snorebreathingsilence with support vectormachines (SVMs) and adaptive network fuzzy inferencesystem (ANFIS)

There have been several methods which are used forclassification of biological data Two of them are ANFISand SVMs which are effective methods for classification andmachine learning systems such as face detection speechrecognition pattern recognition and lots of biomedicalapplications [36ndash41] Recently multiclass SVMs have beenvery popular and successful for different classification issues[42 43] In previous studies for classifying SRSs someclassification methods such as the linear regression LPCHMM and FLD have been used [17ndash20] Unlike the previousones in this study it has been taken into consideration thesuccessfulness of SVMs and ANFIS in biomedical appli-cations the multiclass SVMs and ANFIS were chosen asclassifiers

2 Material and Methods

21 Data In this study Cavusoglu et alrsquos [18] data setobtained from Gulhane Military Medical Science Sleep Lab-oratory was used While recording data a Sennheiser ME64 condenser microphone with a 40Hzndash20 kHz plusmn 25 dBfrequency response was used and placed 15 cm over thepatientrsquos head So a BNC cable UA-1000model multichanneldata acquisition system and a personal computer were usedfor obtaining the data The computer was placed out of theroom for avoiding its noise Signal records were made at16 kHz sampling frequency and 16-bit resolution and storedwith patient information The details about this database arereferred to in Cavusoglu et alrsquos study [18] 12 patientsrsquo data







119894) is

given by

ℎ (119901119894) = log

2(

1

119901119894

) (1)


119894) by their


119867119896=

119899

sum

119894=1

119901119894log2(

1

119901119894

) (2)



119883119894= (119909119894 119909119894+120591

119909119894+2120591

119909119894+3120591

119909119894+(119898minus1)120591

) (3)







1) [51]

119889119895 (119894) asymp 119862

1198951198901205821(119894Δ119905)

(4)





ln 119889119895 (119894) asymp ln119862

119895+ (119894 sdot Δ119905) (5)



119910 (119894) =1

Δ119905

⟨ln 119889119895 (119894)⟩ (6)



119891 (119909) = sign(

119897

sum

119894=1

120572119894119910119894119896 (119909119894 119909)) 120572 ge 0 (7)


119894isin plusmn1



119894 119910119894)

for 119894 = 1 119899 and 119909119894isin 119877119889 and 119910



119889Φ(sdotsdot)


Minimize(119908120577119894 119887)

1

21199082+ 119862sum

119894

120577119894 (8)


119894

forall119894= 1 119899 120577

119894ge 0

(9)








119891 (119909) = arg sdotmax (120601119879 (119909) 119908119895 + 119887119895) 119895 isin 1 119896 (10)


Minimize(119908119895119887119895120577119895119898

119894)

1

2

119896

sum

119895=1

1003817100381710038171003817100381711990811989510038171003817100381710038171003817

2

+ 119862

119896

sum

119895=1

119896

sum

119898=1

119898 = 119895

119899119895

sum

119894=1

120577119895119898

119894

Subject to (120601119879(119909119895

119894)119908119895+ 119887119895) minus (120601

119879(119909119895

119894)119908119898

+ 119887119898)

ge 2 minus 120577119895119898

119894 120577119895119898

119894ge 0 forall119895 = 1 119896

forall119898 = 1 119896 (119898 = 119895) forall119894 = 1 119899119895

(11)


119895is the number








x

y

Layer 1A1

A2

B1

B2

Layer 2

120587

120587

W1

W2

Layer 3

N

N

Layer 4

xy

x y

W1f1

W2f2

Layer 5

fΣ

w1

w2



Rule 1 if (119909 is 1198601) (119910 is 119861

1)

then (1198911= 1199011119909 + 1199021119910 + 1199031)

Rule 2 if (119909 is 1198602) (119910 is 119861

2)

then (1198912= 1199012119909 + 1199022119910 + 1199032)

(12)

where 11990912

are inputs 119860119894and 119861


119894outputs


119894 119902119894 and 119903




3 Results











10 105 11 115 12

0

01

02

03

04

05

Time (s)

Am

plitu

de

95 10 105 11 115 12

20001000

30004000500060007000

Freq

uenc

y (H

z)

Time (s)



Snore segment parts


Silentsegment parts

minus01


x(t+2T)

005

005005

0 0

0

minus005

minus005 minus005

x(t + T) x(t)

(a)

x(t+2T)

005

005005

0

00

minus005

minus005 minus005

x(t + T)x(t)

(b)

x(t+2T)

x(t + T) x(t)

001

001

0

0

minus001

minus001

minus001minus0005

0 0005 001

(c)






17 175 18 185 19 195 20

0

05

1

15

Time (s)

Am

plitu

des

SRSs

Snore segmentparts


Silent segmentparts

Silentsegment

part

Snoresegment

parts

minus05



0 005 01 015 02 025 03 0350

051

152

253

354

455

LLE level

Entro

py le

vel








Subjectno


1 25 23 16 25 23 152 15 15 15 15 15 153 15 15 15 15 15 154 15 15 15 15 15 155 25 25 8 25 25 86 39 25 11 39 25 107 25 15 25 25 15 258 25 25 25 25 25 259 25 15 25 25 15 2510 25 25 10 25 25 1011 0 10 7 0 10 612 25 25 8 25 25 7Total 259 233 180 259 233 176Total 672 668






(a)


Snore 1260 1190 10 60 9444 1009279Breathing 746 0 546 200 7319 9463


Snore 1175 1075 42 58 9149 97649161Breathing 746 10 457 279 6126 8574

Silence 3313 16 34 3263 9849 9064

(b)


Snore 1260 1150 91 19 9126 96888697Breathing 746 32 597 117 8002 6284


Snore 1175 932 202 41 7931 94818675Breathing 746 35 426 285 5710 5741

Silence 3313 16 114 3183 9607 9070







(a)


Snore 1156 1097 42 17 9490 96659007Breathing 721 32 525 164 7282 8255


Snore 1280 1121 135 24 8758 85578465Breathing 772 175 523 74 6775 6032

Silence 2058 14 209 1835 8916 9493

(b)


Snore 1156 971 162 23 8399 96148461Breathing 721 39 423 259 5867 6900


Snore 1280 938 303 39 7328 87918055Breathing 772 128 414 230 5362 5079

Silence 2058 1 98 1959 9519 8792

0 01 02 03 04 05 0706 08 09 10

0102030405

0706

0809

1

False positive rate

True

pos

itive

rate


ANFISM-SVMs











Classes



detection


Snore andbreathing



MFCC




first formant


entropy









snore sensitivities











Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






















119894) is

given by

ℎ (119901119894) = log

2(

1

119901119894

) (1)


119894) by their


119867119896=

119899

sum

119894=1

119901119894log2(

1

119901119894

) (2)



119883119894= (119909119894 119909119894+120591

119909119894+2120591

119909119894+3120591

119909119894+(119898minus1)120591

) (3)







1) [51]

119889119895 (119894) asymp 119862

1198951198901205821(119894Δ119905)

(4)





ln 119889119895 (119894) asymp ln119862

119895+ (119894 sdot Δ119905) (5)



119910 (119894) =1

Δ119905

⟨ln 119889119895 (119894)⟩ (6)



119891 (119909) = sign(

119897

sum

119894=1

120572119894119910119894119896 (119909119894 119909)) 120572 ge 0 (7)


119894isin plusmn1



119894 119910119894)

for 119894 = 1 119899 and 119909119894isin 119877119889 and 119910



119889Φ(sdotsdot)


Minimize(119908120577119894 119887)

1

21199082+ 119862sum

119894

120577119894 (8)


119894

forall119894= 1 119899 120577

119894ge 0

(9)








119891 (119909) = arg sdotmax (120601119879 (119909) 119908119895 + 119887119895) 119895 isin 1 119896 (10)


Minimize(119908119895119887119895120577119895119898

119894)

1

2

119896

sum

119895=1

1003817100381710038171003817100381711990811989510038171003817100381710038171003817

2

+ 119862

119896

sum

119895=1

119896

sum

119898=1

119898 = 119895

119899119895

sum

119894=1

120577119895119898

119894

Subject to (120601119879(119909119895

119894)119908119895+ 119887119895) minus (120601

119879(119909119895

119894)119908119898

+ 119887119898)

ge 2 minus 120577119895119898

119894 120577119895119898

119894ge 0 forall119895 = 1 119896

forall119898 = 1 119896 (119898 = 119895) forall119894 = 1 119899119895

(11)


119895is the number








x

y

Layer 1A1

A2

B1

B2

Layer 2

120587

120587

W1

W2

Layer 3

N

N

Layer 4

xy

x y

W1f1

W2f2

Layer 5

fΣ

w1

w2



Rule 1 if (119909 is 1198601) (119910 is 119861

1)

then (1198911= 1199011119909 + 1199021119910 + 1199031)

Rule 2 if (119909 is 1198602) (119910 is 119861

2)

then (1198912= 1199012119909 + 1199022119910 + 1199032)

(12)

where 11990912

are inputs 119860119894and 119861


119894outputs


119894 119902119894 and 119903




3 Results











10 105 11 115 12

0

01

02

03

04

05

Time (s)

Am

plitu

de

95 10 105 11 115 12

20001000

30004000500060007000

Freq

uenc

y (H

z)

Time (s)



Snore segment parts


Silentsegment parts

minus01


x(t+2T)

005

005005

0 0

0

minus005

minus005 minus005

x(t + T) x(t)

(a)

x(t+2T)

005

005005

0

00

minus005

minus005 minus005

x(t + T)x(t)

(b)

x(t+2T)

x(t + T) x(t)

001

001

0

0

minus001

minus001

minus001minus0005

0 0005 001

(c)






17 175 18 185 19 195 20

0

05

1

15

Time (s)

Am

plitu

des

SRSs

Snore segmentparts


Silent segmentparts

Silentsegment

part

Snoresegment

parts

minus05



0 005 01 015 02 025 03 0350

051

152

253

354

455

LLE level

Entro

py le

vel








Subjectno


1 25 23 16 25 23 152 15 15 15 15 15 153 15 15 15 15 15 154 15 15 15 15 15 155 25 25 8 25 25 86 39 25 11 39 25 107 25 15 25 25 15 258 25 25 25 25 25 259 25 15 25 25 15 2510 25 25 10 25 25 1011 0 10 7 0 10 612 25 25 8 25 25 7Total 259 233 180 259 233 176Total 672 668






(a)


Snore 1260 1190 10 60 9444 1009279Breathing 746 0 546 200 7319 9463


Snore 1175 1075 42 58 9149 97649161Breathing 746 10 457 279 6126 8574

Silence 3313 16 34 3263 9849 9064

(b)


Snore 1260 1150 91 19 9126 96888697Breathing 746 32 597 117 8002 6284


Snore 1175 932 202 41 7931 94818675Breathing 746 35 426 285 5710 5741

Silence 3313 16 114 3183 9607 9070







(a)


Snore 1156 1097 42 17 9490 96659007Breathing 721 32 525 164 7282 8255


Snore 1280 1121 135 24 8758 85578465Breathing 772 175 523 74 6775 6032

Silence 2058 14 209 1835 8916 9493

(b)


Snore 1156 971 162 23 8399 96148461Breathing 721 39 423 259 5867 6900


Snore 1280 938 303 39 7328 87918055Breathing 772 128 414 230 5362 5079

Silence 2058 1 98 1959 9519 8792

0 01 02 03 04 05 0706 08 09 10

0102030405

0706

0809

1

False positive rate

True

pos

itive

rate


ANFISM-SVMs











Classes



detection


Snore andbreathing



MFCC




first formant


entropy









snore sensitivities











Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















ln 119889119895 (119894) asymp ln119862

119895+ (119894 sdot Δ119905) (5)



119910 (119894) =1

Δ119905

⟨ln 119889119895 (119894)⟩ (6)



119891 (119909) = sign(

119897

sum

119894=1

120572119894119910119894119896 (119909119894 119909)) 120572 ge 0 (7)


119894isin plusmn1



119894 119910119894)

for 119894 = 1 119899 and 119909119894isin 119877119889 and 119910



119889Φ(sdotsdot)


Minimize(119908120577119894 119887)

1

21199082+ 119862sum

119894

120577119894 (8)


119894

forall119894= 1 119899 120577

119894ge 0

(9)








119891 (119909) = arg sdotmax (120601119879 (119909) 119908119895 + 119887119895) 119895 isin 1 119896 (10)


Minimize(119908119895119887119895120577119895119898

119894)

1

2

119896

sum

119895=1

1003817100381710038171003817100381711990811989510038171003817100381710038171003817

2

+ 119862

119896

sum

119895=1

119896

sum

119898=1

119898 = 119895

119899119895

sum

119894=1

120577119895119898

119894

Subject to (120601119879(119909119895

119894)119908119895+ 119887119895) minus (120601

119879(119909119895

119894)119908119898

+ 119887119898)

ge 2 minus 120577119895119898

119894 120577119895119898

119894ge 0 forall119895 = 1 119896

forall119898 = 1 119896 (119898 = 119895) forall119894 = 1 119899119895

(11)


119895is the number








x

y

Layer 1A1

A2

B1

B2

Layer 2

120587

120587

W1

W2

Layer 3

N

N

Layer 4

xy

x y

W1f1

W2f2

Layer 5

fΣ

w1

w2



Rule 1 if (119909 is 1198601) (119910 is 119861

1)

then (1198911= 1199011119909 + 1199021119910 + 1199031)

Rule 2 if (119909 is 1198602) (119910 is 119861

2)

then (1198912= 1199012119909 + 1199022119910 + 1199032)

(12)

where 11990912

are inputs 119860119894and 119861


119894outputs


119894 119902119894 and 119903




3 Results











10 105 11 115 12

0

01

02

03

04

05

Time (s)

Am

plitu

de

95 10 105 11 115 12

20001000

30004000500060007000

Freq

uenc

y (H

z)

Time (s)



Snore segment parts


Silentsegment parts

minus01


x(t+2T)

005

005005

0 0

0

minus005

minus005 minus005

x(t + T) x(t)

(a)

x(t+2T)

005

005005

0

00

minus005

minus005 minus005

x(t + T)x(t)

(b)

x(t+2T)

x(t + T) x(t)

001

001

0

0

minus001

minus001

minus001minus0005

0 0005 001

(c)






17 175 18 185 19 195 20

0

05

1

15

Time (s)

Am

plitu

des

SRSs

Snore segmentparts


Silent segmentparts

Silentsegment

part

Snoresegment

parts

minus05



0 005 01 015 02 025 03 0350

051

152

253

354

455

LLE level

Entro

py le

vel








Subjectno


1 25 23 16 25 23 152 15 15 15 15 15 153 15 15 15 15 15 154 15 15 15 15 15 155 25 25 8 25 25 86 39 25 11 39 25 107 25 15 25 25 15 258 25 25 25 25 25 259 25 15 25 25 15 2510 25 25 10 25 25 1011 0 10 7 0 10 612 25 25 8 25 25 7Total 259 233 180 259 233 176Total 672 668






(a)


Snore 1260 1190 10 60 9444 1009279Breathing 746 0 546 200 7319 9463


Snore 1175 1075 42 58 9149 97649161Breathing 746 10 457 279 6126 8574

Silence 3313 16 34 3263 9849 9064

(b)


Snore 1260 1150 91 19 9126 96888697Breathing 746 32 597 117 8002 6284


Snore 1175 932 202 41 7931 94818675Breathing 746 35 426 285 5710 5741

Silence 3313 16 114 3183 9607 9070







(a)


Snore 1156 1097 42 17 9490 96659007Breathing 721 32 525 164 7282 8255


Snore 1280 1121 135 24 8758 85578465Breathing 772 175 523 74 6775 6032

Silence 2058 14 209 1835 8916 9493

(b)


Snore 1156 971 162 23 8399 96148461Breathing 721 39 423 259 5867 6900


Snore 1280 938 303 39 7328 87918055Breathing 772 128 414 230 5362 5079

Silence 2058 1 98 1959 9519 8792

0 01 02 03 04 05 0706 08 09 10

0102030405

0706

0809

1

False positive rate

True

pos

itive

rate


ANFISM-SVMs











Classes



detection


Snore andbreathing



MFCC




first formant


entropy









snore sensitivities











Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















x

y

Layer 1A1

A2

B1

B2

Layer 2

120587

120587

W1

W2

Layer 3

N

N

Layer 4

xy

x y

W1f1

W2f2

Layer 5

fΣ

w1

w2



Rule 1 if (119909 is 1198601) (119910 is 119861

1)

then (1198911= 1199011119909 + 1199021119910 + 1199031)

Rule 2 if (119909 is 1198602) (119910 is 119861

2)

then (1198912= 1199012119909 + 1199022119910 + 1199032)

(12)

where 11990912

are inputs 119860119894and 119861


119894outputs


119894 119902119894 and 119903




3 Results











10 105 11 115 12

0

01

02

03

04

05

Time (s)

Am

plitu

de

95 10 105 11 115 12

20001000

30004000500060007000

Freq

uenc

y (H

z)

Time (s)



Snore segment parts


Silentsegment parts

minus01


x(t+2T)

005

005005

0 0

0

minus005

minus005 minus005

x(t + T) x(t)

(a)

x(t+2T)

005

005005

0

00

minus005

minus005 minus005

x(t + T)x(t)

(b)

x(t+2T)

x(t + T) x(t)

001

001

0

0

minus001

minus001

minus001minus0005

0 0005 001

(c)






17 175 18 185 19 195 20

0

05

1

15

Time (s)

Am

plitu

des

SRSs

Snore segmentparts


Silent segmentparts

Silentsegment

part

Snoresegment

parts

minus05



0 005 01 015 02 025 03 0350

051

152

253

354

455

LLE level

Entro

py le

vel








Subjectno


1 25 23 16 25 23 152 15 15 15 15 15 153 15 15 15 15 15 154 15 15 15 15 15 155 25 25 8 25 25 86 39 25 11 39 25 107 25 15 25 25 15 258 25 25 25 25 25 259 25 15 25 25 15 2510 25 25 10 25 25 1011 0 10 7 0 10 612 25 25 8 25 25 7Total 259 233 180 259 233 176Total 672 668






(a)


Snore 1260 1190 10 60 9444 1009279Breathing 746 0 546 200 7319 9463


Snore 1175 1075 42 58 9149 97649161Breathing 746 10 457 279 6126 8574

Silence 3313 16 34 3263 9849 9064

(b)


Snore 1260 1150 91 19 9126 96888697Breathing 746 32 597 117 8002 6284


Snore 1175 932 202 41 7931 94818675Breathing 746 35 426 285 5710 5741

Silence 3313 16 114 3183 9607 9070







(a)


Snore 1156 1097 42 17 9490 96659007Breathing 721 32 525 164 7282 8255


Snore 1280 1121 135 24 8758 85578465Breathing 772 175 523 74 6775 6032

Silence 2058 14 209 1835 8916 9493

(b)


Snore 1156 971 162 23 8399 96148461Breathing 721 39 423 259 5867 6900


Snore 1280 938 303 39 7328 87918055Breathing 772 128 414 230 5362 5079

Silence 2058 1 98 1959 9519 8792

0 01 02 03 04 05 0706 08 09 10

0102030405

0706

0809

1

False positive rate

True

pos

itive

rate


ANFISM-SVMs











Classes



detection


Snore andbreathing



MFCC




first formant


entropy









snore sensitivities











Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















10 105 11 115 12

0

01

02

03

04

05

Time (s)

Am

plitu

de

95 10 105 11 115 12

20001000

30004000500060007000

Freq

uenc

y (H

z)

Time (s)



Snore segment parts


Silentsegment parts

minus01


x(t+2T)

005

005005

0 0

0

minus005

minus005 minus005

x(t + T) x(t)

(a)

x(t+2T)

005

005005

0

00

minus005

minus005 minus005

x(t + T)x(t)

(b)

x(t+2T)

x(t + T) x(t)

001

001

0

0

minus001

minus001

minus001minus0005

0 0005 001

(c)






17 175 18 185 19 195 20

0

05

1

15

Time (s)

Am

plitu

des

SRSs

Snore segmentparts


Silent segmentparts

Silentsegment

part

Snoresegment

parts

minus05



0 005 01 015 02 025 03 0350

051

152

253

354

455

LLE level

Entro

py le

vel








Subjectno


1 25 23 16 25 23 152 15 15 15 15 15 153 15 15 15 15 15 154 15 15 15 15 15 155 25 25 8 25 25 86 39 25 11 39 25 107 25 15 25 25 15 258 25 25 25 25 25 259 25 15 25 25 15 2510 25 25 10 25 25 1011 0 10 7 0 10 612 25 25 8 25 25 7Total 259 233 180 259 233 176Total 672 668






(a)


Snore 1260 1190 10 60 9444 1009279Breathing 746 0 546 200 7319 9463


Snore 1175 1075 42 58 9149 97649161Breathing 746 10 457 279 6126 8574

Silence 3313 16 34 3263 9849 9064

(b)


Snore 1260 1150 91 19 9126 96888697Breathing 746 32 597 117 8002 6284


Snore 1175 932 202 41 7931 94818675Breathing 746 35 426 285 5710 5741

Silence 3313 16 114 3183 9607 9070







(a)


Snore 1156 1097 42 17 9490 96659007Breathing 721 32 525 164 7282 8255


Snore 1280 1121 135 24 8758 85578465Breathing 772 175 523 74 6775 6032

Silence 2058 14 209 1835 8916 9493

(b)


Snore 1156 971 162 23 8399 96148461Breathing 721 39 423 259 5867 6900


Snore 1280 938 303 39 7328 87918055Breathing 772 128 414 230 5362 5079

Silence 2058 1 98 1959 9519 8792

0 01 02 03 04 05 0706 08 09 10

0102030405

0706

0809

1

False positive rate

True

pos

itive

rate


ANFISM-SVMs











Classes



detection


Snore andbreathing



MFCC




first formant


entropy









snore sensitivities











Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















17 175 18 185 19 195 20

0

05

1

15

Time (s)

Am

plitu

des

SRSs

Snore segmentparts


Silent segmentparts

Silentsegment

part

Snoresegment

parts

minus05



0 005 01 015 02 025 03 0350

051

152

253

354

455

LLE level

Entro

py le

vel








Subjectno


1 25 23 16 25 23 152 15 15 15 15 15 153 15 15 15 15 15 154 15 15 15 15 15 155 25 25 8 25 25 86 39 25 11 39 25 107 25 15 25 25 15 258 25 25 25 25 25 259 25 15 25 25 15 2510 25 25 10 25 25 1011 0 10 7 0 10 612 25 25 8 25 25 7Total 259 233 180 259 233 176Total 672 668






(a)


Snore 1260 1190 10 60 9444 1009279Breathing 746 0 546 200 7319 9463


Snore 1175 1075 42 58 9149 97649161Breathing 746 10 457 279 6126 8574

Silence 3313 16 34 3263 9849 9064

(b)


Snore 1260 1150 91 19 9126 96888697Breathing 746 32 597 117 8002 6284


Snore 1175 932 202 41 7931 94818675Breathing 746 35 426 285 5710 5741

Silence 3313 16 114 3183 9607 9070







(a)


Snore 1156 1097 42 17 9490 96659007Breathing 721 32 525 164 7282 8255


Snore 1280 1121 135 24 8758 85578465Breathing 772 175 523 74 6775 6032

Silence 2058 14 209 1835 8916 9493

(b)


Snore 1156 971 162 23 8399 96148461Breathing 721 39 423 259 5867 6900


Snore 1280 938 303 39 7328 87918055Breathing 772 128 414 230 5362 5079

Silence 2058 1 98 1959 9519 8792

0 01 02 03 04 05 0706 08 09 10

0102030405

0706

0809

1

False positive rate

True

pos

itive

rate


ANFISM-SVMs











Classes



detection


Snore andbreathing



MFCC




first formant


entropy









snore sensitivities











Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




















(a)


Snore 1260 1190 10 60 9444 1009279Breathing 746 0 546 200 7319 9463


Snore 1175 1075 42 58 9149 97649161Breathing 746 10 457 279 6126 8574

Silence 3313 16 34 3263 9849 9064

(b)


Snore 1260 1150 91 19 9126 96888697Breathing 746 32 597 117 8002 6284


Snore 1175 932 202 41 7931 94818675Breathing 746 35 426 285 5710 5741

Silence 3313 16 114 3183 9607 9070







(a)


Snore 1156 1097 42 17 9490 96659007Breathing 721 32 525 164 7282 8255


Snore 1280 1121 135 24 8758 85578465Breathing 772 175 523 74 6775 6032

Silence 2058 14 209 1835 8916 9493

(b)


Snore 1156 971 162 23 8399 96148461Breathing 721 39 423 259 5867 6900


Snore 1280 938 303 39 7328 87918055Breathing 772 128 414 230 5362 5079

Silence 2058 1 98 1959 9519 8792

0 01 02 03 04 05 0706 08 09 10

0102030405

0706

0809

1

False positive rate

True

pos

itive

rate


ANFISM-SVMs











Classes



detection


Snore andbreathing



MFCC




first formant


entropy









snore sensitivities











Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of


















(a)


Snore 1156 1097 42 17 9490 96659007Breathing 721 32 525 164 7282 8255


Snore 1280 1121 135 24 8758 85578465Breathing 772 175 523 74 6775 6032

Silence 2058 14 209 1835 8916 9493

(b)


Snore 1156 971 162 23 8399 96148461Breathing 721 39 423 259 5867 6900


Snore 1280 938 303 39 7328 87918055Breathing 772 128 414 230 5362 5079

Silence 2058 1 98 1959 9519 8792

0 01 02 03 04 05 0706 08 09 10

0102030405

0706

0809

1

False positive rate

True

pos

itive

rate


ANFISM-SVMs











Classes



detection


Snore andbreathing



MFCC




first formant


entropy









snore sensitivities











Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




















Classes



detection


Snore andbreathing



MFCC




first formant


entropy









snore sensitivities











Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




















Acknowledgments


References





































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

































































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



























of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















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Research Article Comparison of SVM and ANFIS for Snore ...downloads.hindawi.com/journals/cmmm/2013/238937.pdf · rst predictor coe cient of linear predictive coding ... group was