J Wave Autodetection Using Analytic Time-Frequency

Research ArticleJ Wave Autodetection Using Analytic Time-Frequency FlexibleWavelet Transformation Applied on ECG Signals

Deng-ao Li Jie Zhou Jumin Zhao and Xinyan Liu

College of Information and Computer Taiyuan University of Technology Taiyuan China

Correspondence should be addressed to Deng-ao Li lidengaotyuteducn

Received 18 November 2017 Revised 16 March 2018 Accepted 12 April 2018 Published 31 May 2018

Academic Editor Li Xu

Copyright copy 2018 Deng-ao Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

As a new important index of the electrocardiogram (ECG) of ventricular bipolar play J wave plays an increasingly significant rolein the clinical diagnosis The existence of J wave hints at potential crisis of fatal disease and even death Nowadays however itcan hardly meet the clinical needs where the diagnosis of J wave variation only depends on experience of clinicians Thereforea new technique which is capable of detecting J wave using analytic time-frequency flexible wavelet transformation (ATFFWT)is proposed in this paper We have used ATFFWT to decompose the processed ECG signals into the desired subbands FurtherFuzzy Entropy (FE) is computed from each subband to capture more hidden and meaningful information Feature scoring methodis applied to select optimal feature set Finally the extracted features are fed to Least Squares-Support Vector Machine (LS-SVM)classifier The 10-fold cross validation is used to obtain reliable and stable performance and to avoid the overfitting of the modelOur proposed algorithm has achieved accuracy of 9761 forMorletWavelet (MW) kernel in comparison to 9756 for Radial BasisFunction (RBF) kernel The developed effective algorithm can be used to design an expert system to aid clinicians in their regulardiagnosis

1 Introduction

Nowadays cardiovascular diseases (CVDs) cause nearly one-third of all deaths worldwide CVDs remain a leading causeof health loss for all regions of the world and a major barrierto long-term sustainable development of mankind [1] Nearly17 million people die due to cardiovascular diseases globallyevery year [2] J wave is regarded as a new important indexof the electrocardiogram (ECG) of ventricular bipolar playand it plays an increasingly significant role in the clinicaldiagnosis of cardiovascular diseases A series of diseases orconditions that can produce J waves in the ECG continues torise [3]

The J wave also referred to as an Osborn wave is adeflection immediately following the QRS complex of thesurface ECG which is usually partially buried inside theQRS often appearing as a J-point elevation it represents theend of depolarization and the start of bipolarization [4] Thepresence of J wave may lead to early repolarization syndrome(ERS) pericarditis idiopathic ventricular fibrillation (IVF)

Brugada syndrome (BrS) and even sudden unexplainednocturnal death syndrome [4] From a mechanistic point ofview these syndromes should be referred to as the J wavesyndromes [4] J wave and J wave syndrome are high-riskearly warning indicators of sudden cardiac death [5] Theappearances of prominent J waves in the ECG have longbeen reported in cases of hypothermia andhypercalcemia [6]More recently accentuation of the J wave has been associatedwith life-threatening ventricular arrhythmias Although typ-ical J waves usually are accentuated with bradycardia or longpauses the opposite has also been described [5 7] J wavesare often seen in young males with no apparent structuralheart diseases whereas intraventricular conduction delay isoften observed in older individuals or those with a history ofmyocardial infarction or cardiomyopathy [5 7]

J wave is mixed in the normal ST segment coupledwith the small amplitude existence of noise and baselinewander Accordingly the diagnosis of J wave variation andminute changes in the ECG signals only depends on thecliniciansrsquo experience which can not meet demand at present

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 6791405 11 pageshttpsdoiorg10115520186791405

2 Mathematical Problems in Engineering

Raw ECG signals Noise and baseline wander removal

Signal decomposition

based on ATFFWT

Feature selection based on Feature

Scoring

Classification based on LS-SVM

Normal class

J wave class

Computation of Fuzzy Entropy

Figure 1 Steps used for automatic J wave detection

clinical and is also apt to be misdiagnosed Therefore it ispretty essential and necessary for us to analyze J wave fromthe perspective of computer aided method with advanceddigital signal processing techniques and machine learningalgorithms which can help to capture the subtle and hiddeninformation in the ECG signals and realize the accurate andautomatic diagnosis of J wave Such an automated systemwill provide tremendous assistance to the clinicians in theirroutine screening of cardiac patients [8ndash12] In literaturealthough themethod of processing ECG signals has been verymature methods of detecting J wave signals from ECG signalwere relatively less and the detection precision is undesirableThe authors in [13] proposed the method based on locatinga break point in the descending limb of the terminal QRSThey added new logic to Glasgow ECG analysis programto automate the detection of J wave A technique based ondigital 12-lead electrocardiogram is used in [14] ECG signalswere automatically processed with the GE Marquette 12-SL program 2001 version (GE Marquette Milwaukee WI)And the functional data analysis techniques were applied tothe processed ECG signals In [15] five features includingthree time-domain features and two wavelet-based featuresare defined these features are found significantly different indiscriminate J wave and normal classes Thereafter PrincipleComponent Analysis (PCA) is used to reduce the dimensionof these features An approach for J wave autodetectionbased on SVM is proposed Curving Fitting (CF) and wavelettransform (WT) are used for feature extraction from J waveand healthy ECG segments data in [16] which have showneffective variations for J wave and normal subjects In [17]a novel J wave detection method based on massive ECGdata and MapReduce is presented The power spectrum andthe cumulative probability of ECG signals are computed asfeatures and Decision Tree (DT) is applied for classification

Compared with the existing methods of J wave detectionthe main contributions of this work are listed as follows (1)we built a J wave detection expert system with FE entropyon the coefficient of ATFFWT as feature and LS-SVM as aclassifier and it owned high accurate rate (2) we use lowernumber of features because feature scoringmethod is applied

(only entropy features) to obtain the desirable accuracy thedetection of J wave will be fast (3) it is the first time thattenfold cross validation method is applied which makes ouralgorithm more reliable and robust The objective of presentwork is to develop a noninvasion marker for some cardiacdiseases clinically that can automatically accurately and fastdetect J wave To achieve this the ECG signals are segmentedinto beats firstly Then to cope with the nonlinear andnonstationary nature of ECG signals analytic time-frequencyflexible wavelet transformation (ATFFWT) is employed todecompose the signals in terms of subbands signals FurtherFuzzy Entropy (FE) is computed on decomposed subbandThen feature scoring method is performed on these FE toselect more meaningful features and improve the classifica-tion performance Finally these clinically significant featuresare fed to Least Squares-Support Vector Machine (LS-SVM)classifier with different kernel functions The followed stepsof the proposed method are shown in Figure 1

2 Materials and Methods

21 Data Acquisition and Preprocessing In this work thenormal ECG signals (normal class) were recorded from 58normal subjects which are acquired from MITBIH NormalSinus Rhythm (NSR) database [12] and Fantasia [12 18] Fromthe MITBIH NSR dataset we have used 18 subjects (5 malesand 13 females) From the Fantasia dataset we have obtainedthe ECG records of 40 subjects (20 young and 20 old) TheECG signals with J wave (abnormal class) of 15 patients (10males and 5 females) are obtained from Shanxi Dayi Hospitalthe sampling frequency is 257Hz The age of all the subjectsvaries from 20 to 71 years ECG signals of lead II were appliedin our study All ECG signals we used were initially inspectedby experienced cardiologists To avoid the inclusion of noiseartifacts and baseline wander the digitized ECG signals werepreprocessed by using eight levelsrsquo Daubechies 6 (db6) basisfunction of wavelet [8]

22 Beats Segmentation In order to segment the ECG signalsinto single beats R-points should be detected firstly In the

Mathematical Problems in Engineering 3

Table 1 Total number of beats used in this work

Type Number of beatsJ wave 25468Normal 169426Total 194894

present study Pan-Tompkins algorithm is carried out on eachpreprocessed ECG signal to detect R-peaks [8 19] ThenECG beats are segmented or selected through the detectedR-points [20] We chose 64 samples before the R-point and105 samples after R-point for each ECG beat Hence there isa segment of 170 samples for one ECG beat and it consists ofP QRS T and UwavesThe number of ECG beats segmentedfor J wave and normal in this work are shown in Table 1

23 Decomposition of the Beats Based on ATFFWT Wavelettransform (WT) is a powerful mathematical tool for process-ing nonstationary signal [10] WT and its various improvedmethods are still playing a significant role in the signalprocessing field because it enjoys fine time-frequency con-centration and multiresolution analysis property HoweverWT and some of its improved methods are suffering froma number of limitations and shortcomings For instancethe continuous WT (CWT) suffers restricted computationalefficiency the discreteWT (DWT) suffers from the limitationof having constant time-frequency covering at all scales andit also suffers shift-variance and poor resolution at its highfrequency subbands [21] These limitations are addressedby a newly introduced time-frequency analysis tool calledATFFWT [11] which has desirable properties such as shift-invariance flexible time-frequency covering and tunableoscillatory bases [11] It has been applied to the weak fault fea-tures detection in rotating machinery [21] and the diagnosisof coronary artery disease using HRV signals [9] ATFFWTis realized by the iterated filter bank (IFB) which consistsof one low-pass channel and two high-pass channels oneof these high-pass channels analyzes ldquopositive frequenciesrdquowhile the other analyzes ldquonegative frequenciesrdquo [11] 119869th leveldecomposition ofATFFWTcan be achieved by using IFB [11]

Frequency response of the low-pass filter can be given bythe following mathematical equations [11]

119867(119908)

=

radic119901119902 |119908| lt 119908119901radic119901119902120579( 119908 minus 119908119901119908119904 minus 119908119901) 119908119901 le 119908 le 119908119904radic119901119902120579(120587 minus (119908 minus 119908119901)119908119904 minus 119908119901 ) minus119908119904 le 119908 le minus1199081199010 |119908| gt 119908119904

(1)

where 119901 and 119902 are up and down sampling parameters for low-pass filter respectively119908119904 and119908119901 represent the stop band and

pass band frequencies of the low-pass filter and are shown as[11]

119908119901 = (1 minus 120573) 120587119901 + 120576119901 119908119904 = 120587119902

(2)

The other used filter is the high-pass filter and can bedefined mathematically as [11]

119866 (119908)

=

radic119903119904120579(120587 minus (119908 + 1199080)1199081 minus 1199080 ) 1199080 lt 119908 lt 1199081radic119903119904 1199081 le 119908 le 1199082radic119903119904120579 ( 119908 minus 11990821199083 minus 1199082) 1199082 le 119908 le 11990830 119908 isin [0 1199080) cup (1199082 2120587)

(3)

where 119903 and 119904 are up and down sampling parameters for high-pass filter respectivelyThe other parameters are described asfollows [11]

1199080 = (1 minus 120573) 120587119903 + 120576119903 1199081 = 119901120587119902119903 1199082 = 120587 minus 120576119903 1199083 = 120587 + 120576119903 120576 le (119901 minus 119902 + 120573119902119901 + 119902 )120587

(4)

In this work the transition band 120579(120596) is chosen as [11]

120579 (120596) = [1 + cos (120596)]radic2 minus cos (120596)2 120596 isin [0 120587] (5)

The parameters 119901 119902 119903 119904 and 120573 provide flexibility tocontrol wavelets with the attractive quality-factor (119876-factor)119876 dilation factor 119889 and redundancy factor 119877 120573 and 120576are the nonnegative constants These parameters are notindependent of each other and are given as [11]

119876 asymp 2 minus 120573120573 119889 asymp 119901119902 120573 le 1119877 asymp (119903119904) 11 minus 119889 119877 gt 1205731 minus 119889

(6)


The perfect reconstruction filter bank can be achieved bysatisfying the following condition [11]

|120579 (119908)|2 + |120579 (120587 minus 119908)|2 = 11 minus 119901119902 le 120573 le 119903119904

(7)

Hilbert transform pairs of the wavelet bases can beobtained owing to this type of separation of positive andnegative frequencies These characters make ATFFWT flex-ible by allowing one to control the 119876-factor redundancyand dilation factor [11] Recently it has been applied forcharacterization of coronary artery disease [22 23] myocar-dial infarction ECG signals [23] and detection of conges-tive heart failure using heart rate variability (HRV) signals[24] Matlab toolbox of ATFFWT method is available athttpwebituedutribayramAnDWT

24 Nonlinear Feature Extraction from the Detail CoefficientsFuzzy Entropy is extracted as nonlinear feature from theeach beat segment from the standard ECG signalsThereforeFuzzy Entropy is computed on the real value of detailcoefficients at each level As an improvement of the sampleentropy algorithm the similarity measures are fuzzed byFuzzy Entropy (FE) using an exponential function The stepsfor the calculation of the FE are as follows [25]

(1) The sampling sequences of length 119873 are extractedfrom the detail coefficients

119906 (119894) 1 le 119894 le 119873 (8)

(2) A set of119898-dimensional vectors refactored and gener-ated in sequential order 119883119898119894 = 119906(119894) 119906(119894 + 1) 119906(119894 + 119898 minus1)minus1199060(119894) (119894 = 1 119873minus119898) 1199060(119894) represents the mean valueand can be defined as [25]

1199060 (119894) = 1119898119898minus1sum119895=0

119906 (119894 + 119895) (9)

(3)The distance 119889119898119894119895 between the sequences119883119898119894 and119883119898119895 isdefined as the largest difference and it can be expressed as

119889119898119894119895 = 119889 [119883119898119894 119883119898119895 ]= max119896isin(0119898minus1)

10038161003816100381610038161003816119906 (119894 + 119896) minus 1199060 (119894) minus 119906 (119895 + 119896) minus 1199060 (119895)10038161003816100381610038161003816(119894 119895 isin [1119873 minus 119898] 119895 = 119894)

(10)

(4) The similarity degree 119863119898119894119895 between the sequences 119883119898119894and119883119898119895 is computed by applying the fuzzy function as follows[25]

119863119898119894119895 = 120583 (119889119898119894119895 119899 119903) = exp(minus(119889119898119894119895 )119899

119903 ) (11)

where 120583 119899 and 119903 stand for the fuzzy function the gradientand the width of the exponential function boundary respec-tively

(5) The function 119876119898(119899 119903) is defined and it is shown asfollows [25]

119876119898 (119899 119903) = 1119873 minus 119898119873minus119898sum119894=1

( 1119873 minus 119898 minus 1119873minus119898sum119895=1119895 =119894

119863119898119894119895) (12)

(6) Finally FE can be computed according to the formulaas follows [25]

Fuzzy En (119898 119899 119903119873) = ln [119876119898 (119899 119903)]minus ln [119876119898+1 (119899 119903)] (13)

FE more easily identifies the abnormal activities in thesignal Therefore it is applied to discriminate nonfocal andfocal electroencephalogram signals [26] characterize thesurface electromyogram signals [25] and diagnose epilepsy[27]

25 Features Selection Based on Feature Scoring Featureselection is widely used in pattern classification and regres-sion to remove the redundant and uncorrelated features infeature space thus reducing the computational load andimproving the classification performance [28] In this inves-tigation we employed a feature scoring algorithm to choosethe optimal setThis algorithm is also known asmutual infor-mation based feature scoring [28] In this algorithm scorevalue is calculated for each feature to reflect its usefulnessThe larger 119878119902 the higher the dependency between the featurevalues and the class labels The score value of each feature isevaluated according to the following formula [29 30]

119878119902 = sum119909119902sum119910

119875 (119909119902 119910) log 119875 (119909119902 119910)119875 (119910) 119875 (119909119902) (14)

The feature matrix119883 isin 119877119901times119902 consists of 119901 number of beatsamples and 119902 number of feature attributes We gave the classlabel vector 119910 119910 isin 119877119901 for the feature matrix The values of 119910are 1 and minus1 corresponding to the class label of normal classand J wave class The score value of 119902th feature in the featurevector 119909119901 is calculated by using the probability of 119902th feature119875(119909119902) and the probability of class level 119875(119910) In this work theFE feature vectors and the new feature vectors obtained usingfeature scoring are fed to LS-SVM

26 Classification Based on LS-SVM The LS-SVM [31] anexcellent binary classifier derived from SVM has successfulapplication of pattern recognition and nonlinear functionfitting However some problems exist in SVM such as theparameter selection for hyperplane and the size of matrixis greatly influenced by the number of training samples inQuadratic Programming (QP) problem solving resultingin the huge solution dimension Therefore the improvedmethod LS-SVM makes up for the limitation of SVMThey minimize the classification error by constructing ahyperplane in higher dimensional space and maximize the


Table 2 119901 values of features computed from each level of ATFFWT decomposition for J wave and normal classes

Features Level 2 Level 3 Level 4 Level 5 Level 6FE 119901 value 8328 times 10minus19 3943 times 10minus19 1791 times 10minus19 1293 times 10minus19 4531 times 10minus18

Table 3Mean (120583) and standard deviation (120590) of features computed from each level of ATFFWTdecomposition for J wave and normal classes

Level of decomposition Features J wave class (120583 plusmn 120590) Normal class (120583 plusmn 120590)Level 1 FED1 02787 plusmn 00370 02254 plusmn 01098Level 2 FED2 02638 plusmn 02549 02396 plusmn 00723Level 3 FED3 03081 plusmn 02995 02602 plusmn 00259Level 4 FED4 02807 plusmn 00578 02340 plusmn 01492Level 5 FED5 01032 plusmn 00216 00984 plusmn 00743

distance of any one of the classes The classification decisionfunction of LS-SVM is defined mathematically as [31]

119869 = sign[ 119872sum119898=1

120572119898120596119898119870(119911 119911119898) + 119887] (15)

where 119870(119911 119911119898) represents a kernel function 120572119898 denotes theLagrangian multiplier 119911119898 is the119872th input vector 120596119898 is thetarget vector and 119887 represents bias term In this work weselected Radial Basis Function (RBF) and Morlet Wavelet(MW) as the kernel function

The expression of the RBF kernel is given as [32]

119870(119911 119911119898) = 119890minus119911minus119911119898221205902 (16)

where 120590 is the kernel parameter and it controls the width ofthe RBF kernel function MW kernel can be represented asfollows [33 34]

119870(119911 119911119898) = 119863prod119899=1

cos [V0 119911119899 minus 119911119899119898119897 ] 119890minus119911119899minus119911119899119898221198972 (17)

where 119863 is the dimension of the feature set and 119897 denotesthe scale factor of MW kernel LS-SVM is widely used in thediagnosis of diabetes [35] analysis of the heart sound signals[36] and classification of focal EEG class [37 38] seizure class[26 39] and glaucoma using fundus images [40]

3 Results and Discussion

In this present study we have segmented ECG signals intobeats Then to extract features the ECG beats are employedto ATFFWT decomposition method to obtain a series ofsubbands signals The plots of real values of coefficientsare shown in Figures 2(a) and 2(b) for J wave and normalclasses respectivelyThese subband signals are obtained fromATFFWT-based decomposition of the ECGbeats In Figure 2CN is the decomposition detail coefficient and CO stands forthe magnitude of the coefficient L1a and L1b are described asdetail coefficients of first level Similarly L2a and L1b L3a andL3b L4a and L4b and L5a and L5b represent second-levelthird-level fourth-level and fifth-level detail coefficientsrespectively The parameters of ATFFWT are selected by way

of trial and error experimentation to reach the maximumclassification accuracy In the present study the values of theparameters are 119901 = 5 119902 = 6 119903 = 1 119904 = 2 and 120573 = 08(119903119904) [921] Therefore 119889 = 56 119876 = 4 and 119877 = 3 The high 119876-factordenotes that desirable frequency analysis of ECG signalsis acquired In order to select the desirable decompositionlevel 119901 values from subbands at different levels of ATFFWT-based decomposition are computed using Kruskal-Wallis test[41] It should be noted that the lowest 119901 value indicatesthe best discrimination ability of the feature The lowest 119901values are observed at the fifth level of decomposition as canbe seen in Table 2 There was no significant improvementwhen the decomposition is increased from fifth to sixthlevel Accordingly we select fifth level of decomposition foranalyzing J wave and normal ECG signals

FE is computed from detail coefficients and the param-eters demanded to compute FE are also chosen by trial anderror experimentation thus getting maximum classificationaccuracy the values of the parameters119898 119899 and 119903 are selectedto be 5 2 and 03 separately [27] Mean (120583) and standarddeviation (120590) of the features computed from various levels ofATFFWT decomposition for J wave and normal classes areoffered in Table 3 and we can observe from the table thatfor J wave classes 120583 and 120590 of the FE features have highervalues at each decomposition level as compared to normalclasses Boxplots for FE at various levels of decompositionare depicted in Figures 3(a)ndash3(e) Feature scoring methodis employed for selection thus removing irrelevant andredundant features and search for the optimal feature subsetIn this work the dimension of the feature vector is five and itderives from the FE computation of 5 levels subbands Thescore value of each feature evaluated using feature scoringmethod is shown in Figure 4 It can be observed that FED1FED4 and FED5 have higher score values than those of FED2and FED3 features

Accuracy (ACC) sensitivity (SEN) and specificity (SPE)are computed at each level of decomposition and are tab-ulated in Table 4 It is obviously seen that the significantimprovement in classification performance occurs at secondlevel of decomposition The average accuracy average sen-sitivity and average specificity of classification are found tobe 9756 9569 and 9578 for RBF kernel and 97619776 and 9582 for MW kernel functions respectively


10 15 205CO

minus02

0

02

L5a

minus02

0

02L5

b

10 15 205CO

minus02

0

02

L4b

10 15 25205

minus02

0

02

L3b

10 15 20 25 305

minus02

0

02

L2b

10 15 20 25 30 355

minus02

0

02

L1b

10 15 20 25 30 35 405

minus02

0

02

L4a

10 15 20 255

minus02

0

02

L3a

10 15 20 25 305

minus02

0

02

L2a

10 15 20 25 30 355

minus02

0

02

L1a

10 15 20 25 30 35 405

(a)

minus002

0

002

L1a

10 15 20 25 30 35 405

minus002

0

002

L2a

10 15 20 25 30 355

minus002

0

002

L3a

10 15 20 25 305

minus002

0

002

L4a

10 15 20 255

minus002

0

002

L5a

10 15 205CO

minus002

0

002

L5b

10 15 205CO

minus002

0

002

L4b

10 15 20 255

minus002

0

002

L3b

10 15 20 25 305

minus002

0

002

L2b

10 15 20 25 30 355

minus002

0

002

L1b

10 15 20 25 30 35 405

(b)

Figure 2 Plots of real coefficients of ATFFWT decomposition (a) normal class and (b) J wave class


Normal J wave0

01

02

03

04

＄1

(a)

0

01

02

03

04

＄2

Normal J wave

(b)

0

01

02

03

＄3

Normal J wave

(c)

0

01

02

03

＄4

Normal J wave

(d)

0

01

02

03

＄5

Normal J wave

(e)

Figure 3 Boxplots for features at each decomposition level of normal ECG and J wave (a) Level 1 (b) Level 2 (c) Level 3 (d) Level 4 and(e) Level 5

Table 4 Classification performance of LS-SVM classifier using different kernel functions

Feature number Kernel function ACC () SEN () SPE ()

All features RBF 9673 9518 9517MW 9679 9547 9529

Feature selection RBF 9756 9569 9578MW 9761 9776 9582


2 3 4 51Feature number

0

01

02

03

04

05

Scor

e val

ue

Figure 4 Score value of each feature using feature scoring

ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

2 3 4 5 6 7 8 9 101Number of folds

(a) RBF

2 3 4 5 6 7 8 9 101Number of folds

ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

(b) MW

Figure 5 Plots showing performance measures versus the number of folds for LS-SVM classifier for kernel function (a) RBF (b) MW

We can also observe that after using feature selection methodthe values of average accuracy average sensitivity and averagespecificity are higher compared with using all features Thevalues of the kernel parameters we selected are 120590 = 09 forRBF kernel and 119897 = 11 and V0 = 035 forMWkernel In orderto gain a stable and reliable classification performance of LS-SVM tenfold cross validation technique is applied to avoidthe possibility of overfitting of the model [42 43]That is thedataset of features is divided into 10 subsets randomly andconsists of one testing subset and nine training subsets Theperformances are averaged after ten iterations ACC SENand SPE for tenfold cross validation method can be seen inFigures 5(a) and 5(b) for RBF and MW kernels respectively

Currently however only few research teams have studiedthe automatic detection and classification of J wave fromthe perspective of signal processing and machine learning

In [13] a method for automated detection of J wave isperformed Their method is based on locating a break pointin the descending limb of the terminal QRS New logicwas added to Glasgow ECG analysis program to automatethe detection of J wave The high sensitivity of 905and specificity of 965 are achieved using this methodA technique based on digital 12-lead electrocardiogram isproposed for the automated J wave detection in [14] ECGsignals were automatically processed with the GE Marquette12-SL program 2001 version (GE Marquette MilwaukeeWI) Thereafter the functional data analysis techniques wereapplied to the processed ECG signals The detection sensi-tivity and specificity are 89 and 86 respectively The twomethods have no parameter of accuracy In [15] a methodfor automated J wave detection and characterization based onfeature extraction is developed First five features including


Table 5 Comparison of proposed method with other existing methods of J wave automatic detection

Authors Applied methods Classification ACC () SEN () SPE ()

Clark et al (2014) Glasgow ECG analysis program with newlogic 913 895 945

Wang et al (2015) GE Marquette 12-SLprogram 2001 version

Functional dataanalysis 896 8845 878

Li et al (2015)Time-domain featuresand discrete wavelettransform (DWT)

Hidden Markovmodel (HMM) 9335 9132 922

Li et al (2015)Curve fitting andwavelet transform

(WT)SVM 9258 9321 9387

Li et al (2016)

Time-domainfeatures powerspectrum andcumulativeprobability

Decision tree (DT) 9603 951 9625

In the present work ATFFWT and FuzzyEntropy LS-SVM 9761 9776 9582

three time-domain features and two wavelet-based featuresare defined Then PCA is used to reduce the dimensionof these features Highest classification accuracy of 925 isattained using HMM An approach for J wave autodetectionis based on support vectormachine [16] CF andWT are usedfor feature extraction from ECG segments data Also 925classification accuracy is reported using SVM classifier In[17] a novel J wave detection method based on massive ECGdata and MapReduce is presented The power spectrum andthe cumulative probability of ECG signals are computed asfeatures Further DT is applied to classify and recognize ECGsignals Lastly they implemented the above process underthe parallel programming model MapReduce to handle themassive ECG data and achieved an accuracy of 9623

In the present work we have developed a novel method-ology for automatic detection of J wave ATFFWT is appliedto decompose the processed ECG signals into the desiredsubbands to capture the hidden useful information fromECGsegment beats of 100 normal and 15 J wave subjects Wehave usedATFFWT-based decomposition due to its desirableproperty it is able to extract more meaningful informationand is suitable for biomedical signals analysis FurthermoreFE is computed on the decomposed subbands to fetch theinformation from detail coefficients at each level FE canmeasure the similarity based on exponential function in thetime series [25] Feature scoring method is employed forselection thus removing irrelevant and redundant featuresand searching for the optimal feature subset Finally theseclinically significant features are fed to a LS-SVM classi-fier with different kernel functions We have observed anaccuracy of 9756 and 9761 using RBF and MW kernelfunctions respectively Finally to verify the effectiveness ofour method we have evaluated all methods with the latestcollected data and the summary of performance of otherexisting methods of J wave automatic detection is shown inTable 5

4 Conclusion

An automated detection of J wave from ECG signals withhigh speed and accuracy is a great challenge task In thisstudy a new technique is proposed to detect the J waveautomatically using ECG segment beats ATFFWT decom-position method and FE extraction are employed to catchthe hidden information from ECG signals Feature scoringmethod is used to optimize the classification performanceHighest classification performance is founded using LS-SVMclassifier with tenfold cross validation procedure while train-ing and testing The limitation of this work is small datasetwe have used only 15 J wave subjects Before the developedeffective algorithm can be used to design an expert system toaid clinicians in their regular diagnosis it needs to be testedusing large dataset And another limitation is that utilizationof a fixed beat length is not always optimum because of fastand slow varying heart rhythms Better methods of adaptivebeat size segmentation are needed to study In the futurethe work could be extended in three aspects (1) it would beof interest to develop an expert model for filter parameters119901 119902 119903 119904 and 120573 optimization of ATTFWT (2) it is highlydesirable that the large dataset would be used to evaluate theproposed technique (3) the method can be used for otherbiosignals application such as electroencephalograph (EEG)and electromyogram (EMG)

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this article

Acknowledgments

This work was supported by the National High TechnologyResearch andDevelopment Program (863Program ) ofChina


[Grant no 2015AA016901 High Linearity Laser Diode Arrayand High Saturation Power Photodiode Array] the NationalNatural Science Foundation of China [Grant no 61371062Research on the Theory and Key Technology of J WaveExtraction in ECG Signal] and the International Coopera-tion Project of Shanxi Province [Grant no 201603D421014Three-Dimensional Reconstruction Research of QuantitativeMultiple Sclerosis Demyelination]

References

[1] G Roth A C Johnson A Abajobir et al ldquoGlobal regional andnational burden of cardiovascular diseases for 10 causes 1990 to2015rdquo Journal of the American College of Cardiology 2017

[2] N D Wong ldquoEpidemiological studies of CHD and the evolu-tion of preventive cardiologyrdquo Nature Reviews Cardiology vol11 no 5 pp 276ndash289 2014

[3] M J Junttila S J Sager J T Tikkanen O Anttonen H VHuikuri and R J Myerburg ldquoClinical significance of variantsof J-points and J-waves early repolarization patterns and riskrdquoEuropean Heart Journal vol 33 no 21 pp 2639ndash2643 2012

[4] C Antzelevitch and G-X Yan ldquoJ wave syndromesrdquo HeartRhythm vol 7 no 4 pp 549ndash558 2010

[5] M Badri A Patel and G-X Yan ldquoCellular and ionic basis ofJ-wave syndromesrdquo Trends in Cardiovascular Medicine vol 25no 1 pp 12ndash21 2015

[6] H V Huikuri ldquoSeparation of Benign from Malignant J wavesrdquoHeart Rhythm vol 12 no 2 pp 384-385 2015

[7] Y Aizawa M Sato H Kitazawa et al ldquoTachycardia-dependentaugmentation of ldquonotched J wavesrdquo in a general patient pop-ulation without ventricular fibrillation or cardiac arrest nota repolarization but a depolarization abnormalityrdquo HeartRhythm vol 12 no 2 pp 376ndash383 2015

[8] R J Martis U R Acharya and L C Min ldquoECG beat classifi-cation using PCA LDA ICA and discrete wavelet transformrdquoBiomedical Signal Processing and Control vol 8 no 5 pp 437ndash448 2013

[9] M Kumar R B Pachori and U R Acharya ldquoAn efficientautomated technique for CAD diagnosis using flexible analyticwavelet transform and entropy features extracted from HRVsignalsrdquo Expert Systems with Applications vol 63 pp 165ndash1722016

[10] I Daubechies ldquoThe wavelet transform time-frequency local-ization and signal analysisrdquo IEEE Transactions on InformationTheory vol 36 no 5 pp 961ndash1005 1990

[11] I Bayram ldquoAn analytic wavelet transform with a flexible time-frequency coveringrdquo IEEE Transactions on Signal Processingvol 61 no 5 pp 1131ndash1142 2013

[12] A L Goldberger L A N Amaral L Glass et alldquoPhysioBank PhysioToolkit and PhysioNet componentsof a new research resource for complex physiologic signals[ASAQga]YYKйaAciac]rdquo Circulation vol 101 pp e215ndashe2202000

[13] E N Clark I Katibi and P W Macfarlane ldquoAutomatic detec-tion of end QRS notching or slurringrdquo Journal of Electrocardiol-ogy vol 47 no 2 pp 151ndash154 2014

[14] Y Wang H-T Wu I Daubechies Y Li E H Estes and EZ Soliman ldquoAutomated J wave detection from digital 12-leadelectrocardiogramrdquo Journal of Electrocardiology vol 48 no 1pp 21ndash28 2015

[15] D Li Y Bai and J Zhao ldquoA method for automated J wavedetection and characterisation based on feature extractionrdquoin Big Data Computing and Communications pp 421ndash433Springer International Publishing 2015

[16] D Li X Liu and J Zhao ldquoAn approach for J wave auto-detection based on support vector machinerdquo in Big DataComputing and Communications pp 453ndash461 Springer Inter-national Publishing 2015

[17] D Li W Ma and J Zhao ldquoA novel J wave detection methodbased on massive ECG data and MapReducerdquo in InternationalConference on Big Data Computing and Communications pp399ndash408 Springer International Publishing 2016

[18] N Iyengar C-K Peng R Morin A L Goldberger and L ALipsitz ldquoAge-related alterations in the fractal scaling of cardiacinterbeat interval dynamicsrdquo American Journal of Physiology-Regulatory Integrative and Comparative Physiology vol 271 no4 pp R1078ndashR1084 1996

[19] J Pan and W J Tompkins ldquoA real-time QRS detection algo-rithmrdquo IEEE Transactions on Biomedical Engineering vol 32no 3 pp 230ndash236 1985

[20] U R Acharya V K Sudarshan J E W Koh et al ldquoApplicationof higher-order spectra for the characterization of Coronaryartery disease using electrocardiogram signalsrdquo BiomedicalSignal Processing and Control vol 31 pp 31ndash43 2017

[21] C L Zhang B Li B Q Chen et al ldquoWeak fault signatureextraction of rotating machinery using flexible analytic wavelettransformrdquo Mechanical Systems and Signal Processing vol 64pp 162ndash187 2015

[22] M Kumar R B Pachori and U R Acharya ldquoCharacterizationof coronary artery disease using flexible analytic wavelet trans-form applied on ECG signalsrdquo Biomedical Signal Processing andControl vol 31 pp 301ndash308 2017

[23] U R Acharya H Fujita M Adam et al ldquoAutomated char-acterization and classification of coronary artery disease andmyocardial infarction by decomposition of ECG signals acomparative studyrdquo Information Sciences vol 377 pp 17ndash292017

[24] M Kumar R B Pachori and U R Acharya ldquoUse of accu-mulated entropies for automated detection of congestive heartfailure in flexible analytic wavelet transform framework basedon short-term HRV signalsrdquo Entropy vol 19 no 3 article 922017

[25] W T Chen Z ZWang H B Xie andW Yu ldquoCharacterizationof surface EMG signal based on fuzzy entropyrdquo IEEE Transac-tions on Neural Systems and Rehabilitation Engineering vol 15no 2 pp 266ndash272 2007

[26] R Sharma andR B Pachori ldquoClassification of epileptic seizuresin EEG signals based on phase space representation of intrinsicmode functionsrdquo Expert Systems with Applications vol 42 no3 pp 1106ndash1117 2015

[27] U R Acharya H Fujita V K Sudarshan S Bhat and J EW Koh ldquoApplication of entropies for automated diagnosis ofepilepsy using EEG signals a reviewrdquoKnowledge-Based Systemsvol 88 pp 85ndash96 2015

[28] J Pohjalainen O Rasanen and S Kadioglu ldquoFeature selectionmethods and their combinations in high-dimensional classifi-cation of speaker likability intelligibility and personality traitsrdquoComputer Speech and Language vol 29 no 1 pp 145ndash171 2015

[29] C Camara K Warwick R Bruna T Aziz F del Pozo and FMaestu ldquoA fuzzy inference system for closed-loop deep brainstimulation in Parkinsonrsquos diseaserdquo Journal of Medical Systemsvol 39 no 11 article 155 2015


[30] S AydınM A Tunga and S Yetkin ldquoMutual information anal-ysis of sleep EEG in detecting psycho-physiological insomniardquoJournal of Medical Systems vol 39 no 5 p 43 2015

[31] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[32] A H Khandoker D T H Lai R K Begg andM PalaniswamildquoWavelet-based feature extraction for support vector machinesfor screening balance impairments in the elderlyrdquo IEEE Trans-actions on Neural Systems and Rehabilitation Engineering vol15 no 4 pp 587ndash597 2007

[33] V Bajaj and R B Pachori ldquoClassification of seizure andnonseizure EEG signals using empirical mode decompositionrdquoIEEE Transactions on Information Technology in Biomedicinevol 16 no 6 pp 1135ndash1142 2012

[34] M Zavar S Rahati M-R Akbarzadeh-T and H GhasemifardldquoEvolutionary model selection in a wavelet-based support vec-tor machine for automated seizure detectionrdquo Expert Systemswith Applications vol 38 no 9 pp 10751ndash10758 2011

[35] R B Pachori M Kumar and P Avinash ldquoAn improved onlineparadigm for screening of diabetic patients using RR-intervalsignalsrdquo Journal of Mechanics in Medicine and Biology vol 16no 01 Article ID 1640003 2016

[36] S Patidar and R B Pachori ldquoClassification of cardiac soundsignals using constrained tunable-Q wavelet transformrdquo ExpertSystems with Applications vol 41 no 16 pp 7161ndash7170 2014

[37] R Sharma R B Pachori and U Rajendra Acharya ldquoAnintegrated index for the identification of focal electroencephalo-gram signals using discrete wavelet transform and entropymeasuresrdquo Entropy vol 17 no 8 pp 5218ndash5240 2015

[38] R Sharma R B Pachori and U R Acharya ldquoApplication ofentropy measures on intrinsic mode functions for the auto-mated identification of focal electroencephalogram signalsrdquoEntropy vol 17 no 2 pp 669ndash691 2015

[39] M Sharma R B Pachori and U Rajendra Acharya ldquoA newapproach to characterize epileptic seizures using analytic time-frequency flexible wavelet transform and fractal dimensionrdquoPattern Recognition Letters vol 94 pp 172ndash179 2017

[40] S Maheshwari R B Pachori and U R Acharya ldquoAutomateddiagnosis of glaucoma using empirical wavelet transform andcorrentropy features extracted from fundus imagesrdquo IEEEJournal of Biomedical and Health Informatics vol 21 no 3 pp803ndash813 2017

[41] P E McKight and J Najab ldquoKruskal-Wallis testrdquo CorsiniEncyclopedia of Psychology 2010

[42] S-N Yu and Y-H Chen ldquoElectrocardiogram beat classificationbased on wavelet transformation and probabilistic neural net-workrdquo Pattern Recognition Letters vol 28 no 10 pp 1142ndash11502007

[43] R Kohavi ldquoA study of cross-validation and bootstrap foraccuracy estimation and model selectionrdquo International JointConferences on Artificial Intelligence vol 14 no 2 pp 1137ndash11451995

Hindawiwwwhindawicom Volume 2018

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The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


Raw ECG signals Noise and baseline wander removal

Signal decomposition

based on ATFFWT

Feature selection based on Feature

Scoring

Classification based on LS-SVM

Normal class

J wave class

Computation of Fuzzy Entropy

Figure 1 Steps used for automatic J wave detection

clinical and is also apt to be misdiagnosed Therefore it ispretty essential and necessary for us to analyze J wave fromthe perspective of computer aided method with advanceddigital signal processing techniques and machine learningalgorithms which can help to capture the subtle and hiddeninformation in the ECG signals and realize the accurate andautomatic diagnosis of J wave Such an automated systemwill provide tremendous assistance to the clinicians in theirroutine screening of cardiac patients [8ndash12] In literaturealthough themethod of processing ECG signals has been verymature methods of detecting J wave signals from ECG signalwere relatively less and the detection precision is undesirableThe authors in [13] proposed the method based on locatinga break point in the descending limb of the terminal QRSThey added new logic to Glasgow ECG analysis programto automate the detection of J wave A technique based ondigital 12-lead electrocardiogram is used in [14] ECG signalswere automatically processed with the GE Marquette 12-SL program 2001 version (GE Marquette Milwaukee WI)And the functional data analysis techniques were applied tothe processed ECG signals In [15] five features includingthree time-domain features and two wavelet-based featuresare defined these features are found significantly different indiscriminate J wave and normal classes Thereafter PrincipleComponent Analysis (PCA) is used to reduce the dimensionof these features An approach for J wave autodetectionbased on SVM is proposed Curving Fitting (CF) and wavelettransform (WT) are used for feature extraction from J waveand healthy ECG segments data in [16] which have showneffective variations for J wave and normal subjects In [17]a novel J wave detection method based on massive ECGdata and MapReduce is presented The power spectrum andthe cumulative probability of ECG signals are computed asfeatures and Decision Tree (DT) is applied for classification

Compared with the existing methods of J wave detectionthe main contributions of this work are listed as follows (1)we built a J wave detection expert system with FE entropyon the coefficient of ATFFWT as feature and LS-SVM as aclassifier and it owned high accurate rate (2) we use lowernumber of features because feature scoringmethod is applied

(only entropy features) to obtain the desirable accuracy thedetection of J wave will be fast (3) it is the first time thattenfold cross validation method is applied which makes ouralgorithm more reliable and robust The objective of presentwork is to develop a noninvasion marker for some cardiacdiseases clinically that can automatically accurately and fastdetect J wave To achieve this the ECG signals are segmentedinto beats firstly Then to cope with the nonlinear andnonstationary nature of ECG signals analytic time-frequencyflexible wavelet transformation (ATFFWT) is employed todecompose the signals in terms of subbands signals FurtherFuzzy Entropy (FE) is computed on decomposed subbandThen feature scoring method is performed on these FE toselect more meaningful features and improve the classifica-tion performance Finally these clinically significant featuresare fed to Least Squares-Support Vector Machine (LS-SVM)classifier with different kernel functions The followed stepsof the proposed method are shown in Figure 1

2 Materials and Methods

21 Data Acquisition and Preprocessing In this work thenormal ECG signals (normal class) were recorded from 58normal subjects which are acquired from MITBIH NormalSinus Rhythm (NSR) database [12] and Fantasia [12 18] Fromthe MITBIH NSR dataset we have used 18 subjects (5 malesand 13 females) From the Fantasia dataset we have obtainedthe ECG records of 40 subjects (20 young and 20 old) TheECG signals with J wave (abnormal class) of 15 patients (10males and 5 females) are obtained from Shanxi Dayi Hospitalthe sampling frequency is 257Hz The age of all the subjectsvaries from 20 to 71 years ECG signals of lead II were appliedin our study All ECG signals we used were initially inspectedby experienced cardiologists To avoid the inclusion of noiseartifacts and baseline wander the digitized ECG signals werepreprocessed by using eight levelsrsquo Daubechies 6 (db6) basisfunction of wavelet [8]

22 Beats Segmentation In order to segment the ECG signalsinto single beats R-points should be detected firstly In the







119867(119908)

=


(1)



119908119901 = (1 minus 120573) 120587119901 + 120576119901 119908119904 = 120587119902

(2)


119866 (119908)

=


(3)



(4)





(6)



|120579 (119908)|2 + |120579 (120587 minus 119908)|2 = 11 minus 119901119902 le 120573 le 119903119904

(7)




119906 (119894) 1 le 119894 le 119873 (8)


1199060 (119894) = 1119898119898minus1sum119895=0

119906 (119894 + 119895) (9)


119889119898119894119895 = 119889 [119883119898119894 119883119898119895 ]= max119896isin(0119898minus1)


(10)


119863119898119894119895 = 120583 (119889119898119894119895 119899 119903) = exp(minus(119889119898119894119895 )119899

119903 ) (11)



119876119898 (119899 119903) = 1119873 minus 119898119873minus119898sum119894=1


119863119898119894119895) (12)





119878119902 = sum119909119902sum119910

119875 (119909119902 119910) log 119875 (119909119902 119910)119875 (119910) 119875 (119909119902) (14)









119869 = sign[ 119872sum119898=1

120572119898120596119898119870(119911 119911119898) + 119887] (15)



119870(119911 119911119898) = 119890minus119911minus119911119898221205902 (16)


119870(119911 119911119898) = 119863prod119899=1









10 15 205CO

minus02

0

02

L5a

minus02

0

02L5

b

10 15 205CO

minus02

0

02

L4b

10 15 25205

minus02

0

02

L3b

10 15 20 25 305

minus02

0

02

L2b

10 15 20 25 30 355

minus02

0

02

L1b

10 15 20 25 30 35 405

minus02

0

02

L4a

10 15 20 255

minus02

0

02

L3a

10 15 20 25 305

minus02

0

02

L2a

10 15 20 25 30 355

minus02

0

02

L1a

10 15 20 25 30 35 405

(a)

minus002

0

002

L1a

10 15 20 25 30 35 405

minus002

0

002

L2a

10 15 20 25 30 355

minus002

0

002

L3a

10 15 20 25 305

minus002

0

002

L4a

10 15 20 255

minus002

0

002

L5a

10 15 205CO

minus002

0

002

L5b

10 15 205CO

minus002

0

002

L4b

10 15 20 255

minus002

0

002

L3b

10 15 20 25 305

minus002

0

002

L2b

10 15 20 25 30 355

minus002

0

002

L1b

10 15 20 25 30 35 405

(b)



Normal J wave0

01

02

03

04

＄1

(a)

0

01

02

03

04

＄2

Normal J wave

(b)

0

01

02

03

＄3

Normal J wave

(c)

0

01

02

03

＄4

Normal J wave

(d)

0

01

02

03

＄5

Normal J wave

(e)








0

01

02

03

04

05

Scor

e val

ue


ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

2 3 4 5 6 7 8 9 101Number of folds

(a) RBF

2 3 4 5 6 7 8 9 101Number of folds

ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

(b) MW














(WT)SVM 9258 9321 9387

Li et al (2016)






4 Conclusion




Acknowledgments




References




















































Journal of












Journal of







Volume 2018






Volume 2018














119867(119908)

=


(1)



119908119901 = (1 minus 120573) 120587119901 + 120576119901 119908119904 = 120587119902

(2)


119866 (119908)

=


(3)



(4)





(6)



|120579 (119908)|2 + |120579 (120587 minus 119908)|2 = 11 minus 119901119902 le 120573 le 119903119904

(7)




119906 (119894) 1 le 119894 le 119873 (8)


1199060 (119894) = 1119898119898minus1sum119895=0

119906 (119894 + 119895) (9)


119889119898119894119895 = 119889 [119883119898119894 119883119898119895 ]= max119896isin(0119898minus1)


(10)


119863119898119894119895 = 120583 (119889119898119894119895 119899 119903) = exp(minus(119889119898119894119895 )119899

119903 ) (11)



119876119898 (119899 119903) = 1119873 minus 119898119873minus119898sum119894=1


119863119898119894119895) (12)





119878119902 = sum119909119902sum119910

119875 (119909119902 119910) log 119875 (119909119902 119910)119875 (119910) 119875 (119909119902) (14)









119869 = sign[ 119872sum119898=1

120572119898120596119898119870(119911 119911119898) + 119887] (15)



119870(119911 119911119898) = 119890minus119911minus119911119898221205902 (16)


119870(119911 119911119898) = 119863prod119899=1









10 15 205CO

minus02

0

02

L5a

minus02

0

02L5

b

10 15 205CO

minus02

0

02

L4b

10 15 25205

minus02

0

02

L3b

10 15 20 25 305

minus02

0

02

L2b

10 15 20 25 30 355

minus02

0

02

L1b

10 15 20 25 30 35 405

minus02

0

02

L4a

10 15 20 255

minus02

0

02

L3a

10 15 20 25 305

minus02

0

02

L2a

10 15 20 25 30 355

minus02

0

02

L1a

10 15 20 25 30 35 405

(a)

minus002

0

002

L1a

10 15 20 25 30 35 405

minus002

0

002

L2a

10 15 20 25 30 355

minus002

0

002

L3a

10 15 20 25 305

minus002

0

002

L4a

10 15 20 255

minus002

0

002

L5a

10 15 205CO

minus002

0

002

L5b

10 15 205CO

minus002

0

002

L4b

10 15 20 255

minus002

0

002

L3b

10 15 20 25 305

minus002

0

002

L2b

10 15 20 25 30 355

minus002

0

002

L1b

10 15 20 25 30 35 405

(b)



Normal J wave0

01

02

03

04

＄1

(a)

0

01

02

03

04

＄2

Normal J wave

(b)

0

01

02

03

＄3

Normal J wave

(c)

0

01

02

03

＄4

Normal J wave

(d)

0

01

02

03

＄5

Normal J wave

(e)








0

01

02

03

04

05

Scor

e val

ue


ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

2 3 4 5 6 7 8 9 101Number of folds

(a) RBF

2 3 4 5 6 7 8 9 101Number of folds

ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

(b) MW














(WT)SVM 9258 9321 9387

Li et al (2016)






4 Conclusion




Acknowledgments




References




















































Journal of












Journal of







Volume 2018






Volume 2018










|120579 (119908)|2 + |120579 (120587 minus 119908)|2 = 11 minus 119901119902 le 120573 le 119903119904

(7)




119906 (119894) 1 le 119894 le 119873 (8)


1199060 (119894) = 1119898119898minus1sum119895=0

119906 (119894 + 119895) (9)


119889119898119894119895 = 119889 [119883119898119894 119883119898119895 ]= max119896isin(0119898minus1)


(10)


119863119898119894119895 = 120583 (119889119898119894119895 119899 119903) = exp(minus(119889119898119894119895 )119899

119903 ) (11)



119876119898 (119899 119903) = 1119873 minus 119898119873minus119898sum119894=1


119863119898119894119895) (12)





119878119902 = sum119909119902sum119910

119875 (119909119902 119910) log 119875 (119909119902 119910)119875 (119910) 119875 (119909119902) (14)









119869 = sign[ 119872sum119898=1

120572119898120596119898119870(119911 119911119898) + 119887] (15)



119870(119911 119911119898) = 119890minus119911minus119911119898221205902 (16)


119870(119911 119911119898) = 119863prod119899=1









10 15 205CO

minus02

0

02

L5a

minus02

0

02L5

b

10 15 205CO

minus02

0

02

L4b

10 15 25205

minus02

0

02

L3b

10 15 20 25 305

minus02

0

02

L2b

10 15 20 25 30 355

minus02

0

02

L1b

10 15 20 25 30 35 405

minus02

0

02

L4a

10 15 20 255

minus02

0

02

L3a

10 15 20 25 305

minus02

0

02

L2a

10 15 20 25 30 355

minus02

0

02

L1a

10 15 20 25 30 35 405

(a)

minus002

0

002

L1a

10 15 20 25 30 35 405

minus002

0

002

L2a

10 15 20 25 30 355

minus002

0

002

L3a

10 15 20 25 305

minus002

0

002

L4a

10 15 20 255

minus002

0

002

L5a

10 15 205CO

minus002

0

002

L5b

10 15 205CO

minus002

0

002

L4b

10 15 20 255

minus002

0

002

L3b

10 15 20 25 305

minus002

0

002

L2b

10 15 20 25 30 355

minus002

0

002

L1b

10 15 20 25 30 35 405

(b)



Normal J wave0

01

02

03

04

＄1

(a)

0

01

02

03

04

＄2

Normal J wave

(b)

0

01

02

03

＄3

Normal J wave

(c)

0

01

02

03

＄4

Normal J wave

(d)

0

01

02

03

＄5

Normal J wave

(e)








0

01

02

03

04

05

Scor

e val

ue


ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

2 3 4 5 6 7 8 9 101Number of folds

(a) RBF

2 3 4 5 6 7 8 9 101Number of folds

ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

(b) MW














(WT)SVM 9258 9321 9387

Li et al (2016)






4 Conclusion




Acknowledgments




References




















































Journal of












Journal of







Volume 2018






Volume 2018














119869 = sign[ 119872sum119898=1

120572119898120596119898119870(119911 119911119898) + 119887] (15)



119870(119911 119911119898) = 119890minus119911minus119911119898221205902 (16)


119870(119911 119911119898) = 119863prod119899=1









10 15 205CO

minus02

0

02

L5a

minus02

0

02L5

b

10 15 205CO

minus02

0

02

L4b

10 15 25205

minus02

0

02

L3b

10 15 20 25 305

minus02

0

02

L2b

10 15 20 25 30 355

minus02

0

02

L1b

10 15 20 25 30 35 405

minus02

0

02

L4a

10 15 20 255

minus02

0

02

L3a

10 15 20 25 305

minus02

0

02

L2a

10 15 20 25 30 355

minus02

0

02

L1a

10 15 20 25 30 35 405

(a)

minus002

0

002

L1a

10 15 20 25 30 35 405

minus002

0

002

L2a

10 15 20 25 30 355

minus002

0

002

L3a

10 15 20 25 305

minus002

0

002

L4a

10 15 20 255

minus002

0

002

L5a

10 15 205CO

minus002

0

002

L5b

10 15 205CO

minus002

0

002

L4b

10 15 20 255

minus002

0

002

L3b

10 15 20 25 305

minus002

0

002

L2b

10 15 20 25 30 355

minus002

0

002

L1b

10 15 20 25 30 35 405

(b)



Normal J wave0

01

02

03

04

＄1

(a)

0

01

02

03

04

＄2

Normal J wave

(b)

0

01

02

03

＄3

Normal J wave

(c)

0

01

02

03

＄4

Normal J wave

(d)

0

01

02

03

＄5

Normal J wave

(e)








0

01

02

03

04

05

Scor

e val

ue


ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

2 3 4 5 6 7 8 9 101Number of folds

(a) RBF

2 3 4 5 6 7 8 9 101Number of folds

ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

(b) MW














(WT)SVM 9258 9321 9387

Li et al (2016)






4 Conclusion




Acknowledgments




References




















































Journal of












Journal of







Volume 2018






Volume 2018









10 15 205CO

minus02

0

02

L5a

minus02

0

02L5

b

10 15 205CO

minus02

0

02

L4b

10 15 25205

minus02

0

02

L3b

10 15 20 25 305

minus02

0

02

L2b

10 15 20 25 30 355

minus02

0

02

L1b

10 15 20 25 30 35 405

minus02

0

02

L4a

10 15 20 255

minus02

0

02

L3a

10 15 20 25 305

minus02

0

02

L2a

10 15 20 25 30 355

minus02

0

02

L1a

10 15 20 25 30 35 405

(a)

minus002

0

002

L1a

10 15 20 25 30 35 405

minus002

0

002

L2a

10 15 20 25 30 355

minus002

0

002

L3a

10 15 20 25 305

minus002

0

002

L4a

10 15 20 255

minus002

0

002

L5a

10 15 205CO

minus002

0

002

L5b

10 15 205CO

minus002

0

002

L4b

10 15 20 255

minus002

0

002

L3b

10 15 20 25 305

minus002

0

002

L2b

10 15 20 25 30 355

minus002

0

002

L1b

10 15 20 25 30 35 405

(b)



Normal J wave0

01

02

03

04

＄1

(a)

0

01

02

03

04

＄2

Normal J wave

(b)

0

01

02

03

＄3

Normal J wave

(c)

0

01

02

03

＄4

Normal J wave

(d)

0

01

02

03

＄5

Normal J wave

(e)








0

01

02

03

04

05

Scor

e val

ue


ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

2 3 4 5 6 7 8 9 101Number of folds

(a) RBF

2 3 4 5 6 7 8 9 101Number of folds

ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

(b) MW














(WT)SVM 9258 9321 9387

Li et al (2016)






4 Conclusion




Acknowledgments




References




















































Journal of












Journal of







Volume 2018






Volume 2018









Normal J wave0

01

02

03

04

＄1

(a)

0

01

02

03

04

＄2

Normal J wave

(b)

0

01

02

03

＄3

Normal J wave

(c)

0

01

02

03

＄4

Normal J wave

(d)

0

01

02

03

＄5

Normal J wave

(e)








0

01

02

03

04

05

Scor

e val

ue


ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

2 3 4 5 6 7 8 9 101Number of folds

(a) RBF

2 3 4 5 6 7 8 9 101Number of folds

ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

(b) MW














(WT)SVM 9258 9321 9387

Li et al (2016)






4 Conclusion




Acknowledgments




References




















































Journal of












Journal of







Volume 2018






Volume 2018










0

01

02

03

04

05

Scor

e val

ue


ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

2 3 4 5 6 7 8 9 101Number of folds

(a) RBF

2 3 4 5 6 7 8 9 101Number of folds

ACCSENSPE

93

94

95

96

97

98

99

Perfo

rman

ce m

easu

res (

)

(b) MW














(WT)SVM 9258 9321 9387

Li et al (2016)






4 Conclusion




Acknowledgments




References




















































Journal of












Journal of







Volume 2018






Volume 2018

















(WT)SVM 9258 9321 9387

Li et al (2016)






4 Conclusion




Acknowledgments




References




















































Journal of












Journal of







Volume 2018






Volume 2018










References




















































Journal of












Journal of







Volume 2018






Volume 2018






























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

J Wave Autodetection Using Analytic Time-Frequency