Research Article ECG Prediction Based on Classification via …downloads.hindawi.com/journals/tswj/2015/205749.pdf · 2019-07-31 · Research Article ECG Prediction Based on Classification

Research ArticleECG Prediction Based on Classification via Neural Networks andLinguistic Fuzzy Logic Forecaster

Eva Volna Martin Kotyrba and Hashim Habiballa

University of Ostrava 30 Dubna 22 70103 Ostrava Czech Republic

Correspondence should be addressed to Martin Kotyrba martinkotyrbaosucz

Received 16 July 2014 Accepted 20 November 2014

Academic Editor Mohammed Chadli

Copyright copy 2015 Eva Volna 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

The paper deals with ECG prediction based on neural networks classification of different types of time courses of ECG signals Themain objective is to recognise normal cycles and arrhythmias and perform further diagnosis We proposed two detection systemsthat have been created with usage of neural networks The experimental part makes it possible to load ECG signals preprocessthem and classify them into given classes Outputs from the classifiers carry a predictive character All experimental results fromboth of the proposed classifiers aremutually compared in the conclusionWe also experimented with the newmethod of time seriestransparent prediction based on fuzzy transform with linguistic IF-THEN rules Preliminary results show interesting results basedon the unique capability of this approach bringing natural language interpretation of particular prediction that is the propertiesof time series

1 Background

Biometrical data is typically represented as an image ora quantification of measured physiological or behaviouralcharacteristics As this data should refer to very complexhuman behaviour or describe very precisely physiologicalcharacteristic (typically iris scan fingerprint palm veinimage hand scan voice walk pattern etc) this data caneasily become very large and hard to process For this reasonmodern ways of data processing and classification are appliedfor biometrical data The leading method is the usage ofneural networks [1]

For more than four decades computers have been usedin the classification of the electrocardiogram (ECG) resultingin a huge variety of techniques [2] all designed to enhancethe classification accuracy to levels comparable to that of aldquogold standardrdquo of expert cardiology opinion Included inthese techniques are multivariate statistics decision treesfuzzy logic expert systems and hybrid approaches [3] Therecent interest in neural networks coupled with their highlevels of performance has resulted in many instances of theirapplication in this field [4]

The electrocardiogram is a technique of recording bio-electric currents generated by the heart Clinicians canevaluate the conditions of a patientrsquos heart from the ECG andperform further diagnosis ECG records are obtained by sam-pling the bioelectric currents sensed by several electrodesknown as leads A typical one-cycle ECG tracing is shown inFigure 3

11 Backpropagation Neural Networks A neural networkis a parallel distributed information processing structureconsisting of processing elements (which can possess a localmemory and can carry out localized information process-ing operations) interconnected together with unidirectionalsignal channels called connections Each processing elementhas a single output connection which branches into as manycollateral connections as desired (each carrying the samesignal the processing element output signal) The processingelement output signal can be of any mathematical typedesired All of the processing that goes on within eachprocessing element must be completely local that is it mustdepend only upon the current values of the input signals

Hindawi Publishing Corporatione Scientific World JournalVolume 2015 Article ID 205749 10 pageshttpdxdoiorg1011552015205749

2 The Scientific World Journal

x1

x2

f1(e)

f2(e)

f3(e)

f4(e)

f5(e)

f6(e) y

Figure 1 A backpropagation network architecture

arriving at the processing element via impinging connectionsand upon values stored in the processing elementrsquos localmemory [5]

The backpropagation neural network architecture is ahierarchical design consisting of fully interconnected layersor rows of processing units (with each unit itself comprisedof several individual processing elements) Backpropagationbelongs to the class of mapping neural network architecturesand therefore the information processing function that itcarries out is the approximation of a bounded mappingor function 119891 119860 sub 119877119899 rarr 119877119898 from a compactsubset A of n-dimensional Euclidean space to a boundedsubset 119891[A] of m-dimensional Euclidean space by meansof training on examples (119909

1 1199111) (1199092 1199112) (119909

119896 119911119896) It

will always be assumed that such examples of a mapping 119891are generated by selecting xk vectors randomly from A inaccordance with a fixed probability density function 119901(x)The operational use to which the network is to be put aftertraining is also assumed to involve random selections ofinput vectors x in accordancewith119901(x)The backpropagationarchitecture described in this paper is the basic classicalversion (Figure 1) The backpropagation learning algorithmis composed of two procedures (a) forward propagation ofsignals and (b) backpropagation weight training [5]

Feed-Forward Assume that each input factor in the inputlayer is denoted by 119909

119894 the 119910

119895and 119911

119896represent the output in

the hidden layer and the output layer respectively And the 119910119895

and 119911119896can be expressed as follows (1)

119910119895= 119891 (119883

119895) = 119891(119908

119900119895+119868

sum119894=1

119908119894119895119909119894)

119911119896= 119891 (119884

119896) = 119891(119908

119900119896+119869

sum119895=1

119908119894119896119910119895)

(1)

where the 119908119900119895

and 119908119900119896

are the bias weights for settingthreshold values 119891 is the activation function used in bothhidden and output layers and 119883

119895and 119884

119896are the temporarily

computing results before applying activation function 119891 Inthis study a sigmoid function is selected as the activation

function Therefore the actual outputs 119910119895and 119911

119896in hidden

and output layers respectively can be also written as

119910119895= 119891 (119883

119895) =

1

1 + 119890minus119883119895

119911119896= 119891 (119884

119896) =

1

1 + 119890minus119884119896

(2)

The activation function 119891 introduces the nonlinear effect tothe network and maps the result of computation to a domain(0 1) This sigmoid function is differentiable The derivativeof the sigmoid function in (2) can be easily derived as 1198911015840 =119891(1 + minus119891)

Backpropagation Weight Training The error function isdefined as

119864 =1

2

119870

sum119896=1

1198902119896=119870

sum119896=1

(119905119896minus 119911119896)2

(3)

where 119905119896is a predefined network output (or desired output or

target value) and 119890119896is the error in each output nodeThe goal

is to minimize 119864 so that the weight in each link is accordinglyadjusted and the final output can match the desired outputTo get the weight adjustment the gradient descent strategyis employed In the link between hidden and output layerscomputing the partial derivative of 119864 with respect to theweight 119908

119895119896produces

120597119864

120597119908119895119896

= minus1198901198961198911015840(119884119896)119910119895

= minus120575119896119910119895

where 120575119896= (119905119896minus 119911119896) 1198911015840 (119884

119896)

(4)

Theweight adjustment in the link between hidden and outputlayers is computed by Δ119908

119895119896= 120572 times 119910

119895times 120575119896 where 120572 is

the learning rate a positive constant between 0 and 1 Thenew weight herein can be updated by the following 119908

119895119896(119899 +

1) = 119908119895119896(119899) + Δ119908

119895119896(119899) where 119899 is the number of iterations

Similarly the error gradient in links between input andhidden layers can be obtained by taking the partial derivativewith respect to 119908

119894119895as

120597119864

120597119908119894119895

= minusΔ119895119909119895= 1198911015840 (119883

119895)119870

sum119896=1

120597119896119908119895119896 (5)

The new weight in the hidden-input links can be nowcorrected as Δ119908

119894119895= 120572 times 119909

119894times Δ119895and 119908

119894119895(119899 + 1) = 119908

119894119895(119899) + Δ

119895

Training the BP-networks with many samples is sometimesa time-consuming task The learning speed can be improvedby introducing the momentum term 120578 Usually 120578 falls in therange ⟨0 1⟩ For the iteration 119899 the weight change Δ119908 can beexpressed The backpropagation learning algorithm used inartificial neural networks is shown in many text books [3ndash6]

12 Fuzzy Logic Fuzzy logics form heterogeneous family offormalisms capable of successful modelling of uncertain andvague information processing [7] The usage of fuzzy logicfor analysis and prediction of time series can be perceived

The Scientific World Journal 3

as a complement method to neural network based methodsThe symbolic background of fuzzy logic brings an advantageof human readable symbolic representation of predictioninterpretation It does not necessarily mean that fuzzy logicbased time series analysis is more accurate and more efficientbut its power lies in transparent and interpretable results thatit gives [8ndash11]

Time series analysis and prediction are an importanttask that can be used in many areas of practice The task ofgetting the best prediction to given series may bring inter-esting engineering applications in wide number of areas likeeconomics geography or industry Solution to the problemof obtaining best results in prediction of time series can bebased on well-known and simple methods like Winters orLinear method In this paper we use a method based on twomethods originally developed by members of Institute forResearch andApplications of FuzzyModeling which is a partofUniversity ofOstravaThe aimof the paper is not to presentthe details of the methods already published but to presenta tool implementing them The first method is based on thenotion of F-transform (fuzzy transform) devised by the groupof Professor Perfilieva et al [12] The second approach usesthe linguistic rules utilizing fuzzy logic and deduction that isa well-known formalism with very good results in variety ofpractical applications like industrial ones

The idea of the fuzzy transform is to transform a givenfunction defined in one space into another usually simplerspace and then to transform it back The simpler spaceconsists of a finite vector of numbers The reverse transformthen leads to a function which approximates the original oneMore details can be found in [12]

The fuzzy transform is defined with respect to a fuzzypartition which consists of basic functions Let 119888

1lt sdot sdot sdot lt 119888

119899

be fixed nodes within [119886 119887] such that 1198881

= 119886 119888119899

= 119887 and119899 ge 2 We say that fuzzy sets 119860

1 119860

119899isin 119865([119886 119887]) are basic

functions forming a fuzzy partition of [119886 119887] if they fulfill thefollowing conditions for 119894 = 1 119899

(1) 119860119894(119888119894) = 1

(2) 119860119894(119909) = 0 for 119909 isin (119888

119894minus1 119888119894+1

) where for uniformity ofnotation we put 119888

0= 1198881= 119886 and 119888

119899+1= 119888119899= 119887

(3) 119860119894is continuous

(4) 119860119894strictly increases on [119888

119894minus1 119888119894] and strictly decreases

on [119888119894 119888119894+1

](5) for all 119909 isin [119886 119887]

119899

sum119894=1

119860119894(119909) = 1 (6)

Let a fuzzy partition of [119886 119887] be given by basic functions1198601 119860

119899 119899 ge 2 and let 119891 [119886 119887] rarr 119877 be a function that is

known on a set 1199091 119909

119879 of points

The n-tuple of real numbers [1198651 119865

119899] given by

119865119894=

sum119879

119905=1119891 (119909119905) 119860119894(119909119905)

sum119879

119905=1119860119894(119909119905)

119894 = 1 119899 (7)

is a fuzzy transform of 119891 with respect to the given fuzzypartition

The numbers 1198651 119865

119899are called the components of the

fuzzy transform of 119891Let 119865119899[119891] be the fuzzy transform of 119891 with respect to

1198601 119860

119899isin 119865([119886 119887])

Then the function 119891119865119899

given on [119886 119887] by

119891119865119899

(119909) =119899

sum119894=1

119865119894119860119894(119909) (8)

is called the inverse fuzzy transform of 119891Fuzzy IF-THEN rules can be understood as a specific

conditional sentence of natural language of the form IF1198831is

1198601AND sdot sdot sdot AND 119883

119899is 119860119899THEN 119884 is 119861 where 119860

1 119860

119899

and 119861 are evaluative expressions (very small roughly bigetc) An example fuzzy IF-THEN rule is as follows

IF the number of cars sold in the current year is more or lesssmall and the half-year sales increment is medium THEN theupcoming half-year increment will be medium

The part of the rule before THEN is called the antecedentand the part after it is consequent Fuzzy IF-THEN rules areusually gathered in a linguistic description

1198771= IF 119883

1is 11986011

AND sdot sdot sdotAND 119883119899

is 1198601119899

THEN 119884 is 1198611

119877119898

= IF 1198831is 1198601198981

AND sdot sdot sdotAND 119883119899

is 119860119898119899

THEN 119884 is 119861119898

(9)

Time series prediction based on these two mainapproaches works as follows Let time series 119909

119905 119905 = 1 119879

be viewed as a discrete function 119909 on a time axis 119905 Then119865119899[119909] = [119883

1 119883

119899] is the fuzzy transform of the function

119909 with respect to a given fuzzy partition The inverse fuzzytransform then serves us as a model of the trend-cycle ofa given time series By subtracting the trend-cycle (inversefuzzy transform) values from the time series lags we get pureseasonal components This is how the fuzzy transform helpsus to model and decompose a given time series

Logical dependencies between components1198831 119883

119899of

the fuzzy transform may be described by the fuzzy rulesThese rules are generated automatically from the given dataand are used for forecasting the next components Fuzzytransform components as well as their first and second orderdifferences are used as antecedent variables For forecastingfuture fuzzy transform components based on the generatedfuzzy rules a special inference methodmdashperception-basedlogical deduction is used The seasonal components are fore-casted autoregressively Finally both forecasted componentstrend-cycle and seasonal are composed together to obtainthe forecast of time series lags These methods are integratedinto an implementation PC application called linguistic fuzzylogic forecaster (LFLF) which enables as to produce linguisticdescriptions that describe properties of data treated like atime series

4 The Scientific World Journal(m

V)

+20

0

minus90

0 100 200 300 400

(ms)

Figure 2 The cardiac action potentials

2 Basic Principles of ECG Evaluation

ECG scanning has its own rules which are in accordancewith the laws of physics The heart irritation spreads inall directions In the case that the depolarisation spreadstowards the electrode which is placed on the body surfacea positive deflection is recorded on an ECG monitor Anegative deflection is recorded at the opposite end of thebody The ECG waveform is written with a chart speed of25mmsdotsminus1 An algorithm describing the curve goes in thefollowing steps First we evaluate the shape and rhythm ofventricular complexes or atrial which can be either regularor irregular Then we evaluate the frequency of ventricularcomplexes and atrial fibrillations Contraction of eachmuscleof the human body (and thus the heart as well) is associatedwith electrical changes called depolarization which can bedetected by electrodes The heart contains two basic types ofcells myocardial cells which are responsible for generatingthe pressure necessary to pump blood throughout the bodyand conduction cells which are responsible for rapidlyspreading electrical signals to the myocardial cells in orderto coordinate pumping A graph of an action potential of amuscle of cardiac cells is shown in Figure 2

A normal electrocardiogram is illustrated in Figure 3The figure also includes definitions for various segmentsand intervals in the ECG The deflections in this signalare denoted in alphabetic order starting with the letterP which represents atrial depolarization The ventriculardepolarization causes the QRS complex and repolarizationis responsible for the T-wave Atrial repolarization occursduring the QRS complex and produces such a low signalamplitude that it cannot be seen apart from the normal ECG

3 Signal Processing Using NeuralNetworks and Fuzzy Logic

In practice a relatively reliable diagnostic program storedin ECG monitors has been used which is a guideline fordetermining the final diagnosis of heart disorders This pro-gramworks according to the principle of IF-THEN rulesThevalues of the electrical signal are discretized and uploaded

P

R

TU

Q

QRSinterval

interval interval

segment segment

S

P-R

P-R

S-T

S-T

Figure 3 A typical one-cycle ECG tracing (adapted fromhttpwwwnicomwhite-paperapplargeimagelang=csampimageurl=2Fcms2Fimages2Fdevzone2Ftut2F2007-07-09141618jpg)

0

500

1000

1500

2000

1 101 201 301

Healthy personsSick persons

minus500

Figure 4 Comparison of mean values of ECG waveforms forhealthysick persons

into expert systems in the form of thousand rules The aim ofthis paper is to use a different approach based on the principleof neural networks The proposed methodology of solutioncould be summarized into the following steps

(1) a conversion of analog signal from the ECG monitorto a computer

(2) using multilayer networks that are fully connected(3) obtaining ECG waveforms in collaboration with the

University Hospital in Poruba specifically at theDepartmentCardiac Surgery from sick patients and atthe Department Traumatology from healthy patients(ie ldquohealthyrdquo with regard to heart diseases)

(4) ECG waveforms built trainingtest sets(5) neural network adaptation(6) testing phases

31 Technical Equipment ECG measurements were per-formed using ADDA Junior with converter ADDA Junior

The Scientific World Journal 5

0

10

20

30

40

50

0-01 01-02 04-05

()

Test error

Healthy personsSick persons

02ndash04 gt05

Figure 5 Experimental results test error for healthysick persons

002040608

112

1 2 3 4 5 6 7 8 9 10

H1H2

H3H4

Figure 6 Patterns representing healthy persons

which was connected to a computer via bidirectional parallelcable (CETRONICS) Technical parameters of the AD con-verter (8-bit conversion) were the following

(i) 3 measuring ranges(ii) measuring of a frequency of AC voltage at any

channel(iii) autoranging for measuring the frequency of 100Hz

1 kHz and 10 kHz(iv) input resistance of 300 kΩ(v) measurement accuracy 1

Technical parameters of the DA converter (a pro-grammable voltage source plusmn10V) were the following

(i) maximum current consumption of 15mA (after opti-mizing 4A at the output)

(ii) power of the converter plusmn15 V (stabilized)

4 Experimental Results

41 Time Series Classification and Prediction via NeuralNetworks The training set consisted of modified ECG wave-forms We used a backpropagation neural network withtopology 101-10-1 The output unit represents a diagnose 01a healthysick person A smaller number of inputs would

002040608

112

1 2 3 4 5 6 7 8 9 10

S1S2

S3S4

Figure 7 Patterns representing sick persons

0

500

1000

1500

1 26 51 76 101

Sick persons

S2S3

S4

minus500

Figure 8 Some recognized patterns that occur in ECG time series

not be appropriate due to the nature of the ECG waveformWe use 34 ECG time series associated with sick personsand 36 ECG time series associated with healthy persons25 time series of each group were used as a training setand the rest as a test set Figure 4 shows a comparison ofmean values of ECG waveforms for healthysick persons Weused the backpropagation method [5 6] for the adaptationwith the following parameters the learning rate value is 01and momentum is 0 The conducted experimental studiesalso showed that training patterns are mixed randomly ineach cycle of adaptation This ensures their greater diversitywhich acts as a measure of system stability Uniform systemin a crisis usually collapses entirely while system with suchdiversity of trained patterns remains functional despite ofcrisis of its individual parts The condition of end of theadaptation algorithm specified the limit value of the overallnetwork error 119864 lt 01

The test set consisted of 20 samples (11 health and 9sick persons) that were not included in the training set Thesummary results for this type of experiment are shown in agraph in Figure 5 For clarity the results of testing are givenin percentage The average test error was 0194 A healthypopulation was detected with an average error of 0263 andsick population with an average error of 0109

411 Pattern Recognition Classifier Leading to Prediction Forthe purpose of adaptation of the pattern recognition classifierit is necessary to remark that determination of trainingpatterns is one of the key tasks Improperly chosen patternscan lead to confusion of neural networks During our exper-imental work we made some study which included ECGpattern recognition When creating appropriate patterns ofthe training set we used characteristic curves shown as mean

6 The Scientific World Journal

0100

1 2 3 4 5 6 7 8 9 10

S2 trainS2 test

S2 test

minus500

minus400

minus300

minus200

minus100

050

100150200250

1 2 3 4 5 6 7 8 9 10

S3 trainS3 test

S3 test

minus150

minus100

minus50

0100200300400500600

1 2 3 4 5 6 7 8 9 10

Train H3Test H3

minus200

minus100

Figure 9 Training patterns their representation in used test sets

values from ECG waveforms for healthy and sick persons(Figure 4) We use two different groups of patterns PatternsH1ndashH4 (Figure 6) represent healthy persons and patterns S1ndashS4 (Figure 7) represent sick personsThe whole training set isshown in Table 1

Pattern recognition classifier is based on backpropagationneural network and is able to recognise wave structures ingiven time series [13 14] Artificial neural networks needtraining sets for their adaptation In our experimental workthe training set consisted of 8 patterns representing thebasic structure of the various waves in ECG graphs seeFigures 6 and 7 Input data is sequences always including119899 consecutive numbers which are transformed into interval⟨0 1⟩ by formula (10) Samples are adjusted for the needs ofbackpropagation networks with sigmoid activation functionin this way [5 6]

1199091015840119895=

119909119895minusmin (119909

119894 119909

119894+119899minus1)

max (119909119894 119909

119894+119899minus1) minusmin (119909

119894 119909

119894+119899minus1)

(119895 = 119894 119894 + 119899 minus 1)

(10)

where 1199091015840119895is normalized output value of the 119895th neuron (119895 =

119894 119894 + 119899minus1) and (119909119894 119909119894+119899minus1

) are 119899minus1 consecutive outputvalues that specify sequences (patterns) from the trainingset (eg training pars of input and corresponding outputvectors) Input vector contains 10 components Output vectorhas got 8 components and each output unit represents oneof 8 different types of ECG wave samples A neural networkarchitecture is 10-10-8 (eg 10 units in the input layer 10 unitsin the hidden layer and 8 units in the output layer)The net isfully connected Adaptation of the neural network starts withrandomly generated weight values

We used the backpropagation method for the adaptationwith the following parameters the learning rate value is 01and momentum is 0 We have utilized our experience fromearlier times that is training patterns were mixed randomlyin each cycle of adaptation The condition of end of theadaptation algorithm specified the limit value of the overallnetwork error 119864 lt 01

In order to test the efficiency of the method we appliedthe same set of data that we used in the previous experimentalpart Outputs from the classifier produce sets of values thatare assigned to each recognized training pattern in the giventest time series It is important to appreciate what can beconsidered as an effective criterion related to consensusof similarity The proposed threshold resulting from ourexperimental study was determined at least 119901 = 70Figure 9 shows a comparison of patterns how were learned(S2 S3 H3 train) and how were recognized in test time series(S2 S3 H3 test) The neural network is able to discover someconnections which are almost imperceptible Illustration ofsome recognized patterns that occur in ECG time seriesis shown in Figure 8 Outputs from the classifier carry apredictive character The neural network determines if thetime series belongs to a healthy or sick person on the basis ofthe recognised ECG patterns which appear in the time serieshistory

The methodology of testing is shown in Figure 10 Thismeans that if the test pattern S1 S2 S3 or S4 appearedin ECG waveform with probability 119901S ge 119901 (119901 = 70)thus it was predicted to be ldquoa sick personrdquo Then we workonly with the remaining time series If the test pattern H1H2 H3 or H4 appeared in ECG waveform with probability119901H ge 119901 (119901 = 70) thus it was predicted to be ldquoahealthy personrdquo In all other cases the ECG time series wasunspecifiedWe examined a total of 20 data sets Each of them

The Scientific World Journal 7

Table 1 The training set

Patterns Inputs OutputsH1 1000 0672 0155 0000 0045 0057 0049 0049 0053 0055 1 0 0 0 0 0 0 0H2 0000 0273 0600 0782 1000 0945 0945 0799 0618 0418 0 1 0 0 0 0 0 0H3 0485 0449 0147 0007 0007 0000 0169 0632 1000 0757 0 0 1 0 0 0 0 0H4 0035 0000 0170 0338 0356 0309 0430 0719 1000 0946 0 0 0 1 0 0 0 0S1 1000 0740 0228 0000 0045 0091 0098 0101 0104 0107 0 0 0 0 1 0 0 0S2 0000 0123 0304 0495 0536 0883 0851 1000 0796 0761 0 0 0 0 0 1 0 0S3 0044 0000 0045 0319 0748 1000 0868 0440 0154 0050 0 0 0 0 0 0 1 0S4 0033 0000 0000 0085 0360 0779 1000 0820 0399 0079 0 0 0 0 0 0 0 1

ECG time series

A sick person

A healthy person

Unspecified

Yes

Yes

No

No

Is the occurrence PS of

Is the occurrence PH of

S1 S2 S3 or S4 ge P

H1 H2 H3 or H4 ge P

Figure 10 The methodology of testing

0

20

40

60

80

100

Sick persons Healthy persons Unidentify

TrueFalse

Unidentify

()

Figure 11 Experimental results test error

contains 101 values that assign 92 possible patternsThewholenumber of examined patterns is 1840 The graph in Figure 11demonstrates a summary of results where ldquosick personsrdquorepresent patterns S1ndashS4 and ldquohealthy personsrdquo representpatterns H1ndashH4 The resulting prediction is based on themethodology see Figure 10

Figure 12 LFLF application

Figure 13 Winning predictor linguistic description (trend-cyclemodel)

42 Time Series Classification and Prediction via LinguisticFuzzy Logic Forecaster We tried also to utilize above pre-sentedmethod of time series analysis through linguistic fuzzylogic forecaster (LFLF) [15] see Figure 12

Basic usage of the application is to analyse given timeseries and find best predictor with respect to validation partof time series given We evaluate efficiency of predictorsby SMAPE (symmetric mean absolute percentage error) Itenables us to make analysis of trend-cycle of a time seriesand also seasonal part The main advantage lies in predictionbased on transparent linguistic descriptions that provide themodel of a time series behaviour Linguistic variables are ofthe following types

(i) value we directly mean the components of the fuzzytransform

(ii) difference first order differences of fuzzy transformcomponents that are given as follows differencesbetween components Δ119883

119894= 119883119894minus 119883119894minus1

8 The Scientific World Journal

Healthypattern

typical series (HS)

Sick patterntypical series

(SS)

Tested series (TS)

and set TS as validationinterval

Evaluate bestpredictor

TS validationinterval

and set TS as validationinterval

Evaluate bestpredictor

TS validationinterval

TS is ldquohealthyrdquo TS is ldquosickrdquo

Yes No

Find best predictorfor TS as validation

interval

Find best predictorfor TS as validation

interval

Concatenate series (SS + TS)Concatenate series (HS + TS)

+ TS) forSMAPE (HS SMAPE (SS + TS) for

If SMAPE (HS + TS) lt SMAPE (SS + TS)

Figure 14 Recognition by linguistic fuzzy logic predictors for typical learning series

(iii) second difference these are values of second orderdifferences of components of the fuzzy transform asfollows Δ2119883

119894= Δ119883

119894minus Δ119883119894minus1

LFLF application enables us to define minimal andmaximal number of these particular variables in a ruleof linguistic description as well as the total number ofantecedent variables

A rule consisting of these variables has the followingstructure and can be described as a signature (fuzzy rulesdescribing the trend-cycle model) Particularly 119878 denotes the

trend-cycle components 119889119878 their differences and 1198892119878 theirsecond order differences The argument (119905) (119905 minus 1) and soforth denotes the time lag of the component

For example taking signature 119878(119905)amp119889119878(119905) rarr 119889119878(119905 + 1)denotes the fact that119883

119894and Δ119883

119894are the antecedent variables

and Δ119883119894+1

is the consequent variable of the winning modeland hence we deal with rules of the form

IF 119883119894is 119860119894AND Δ119883

119894is 119860Δ119894

THEN Δ119883119894+1

is 119860Delta119894(11)

The Scientific World Journal 9

Table 2 Example of algorithm evaluation on 10 ldquohealthyrdquo and 10 ldquosickrdquo patients

Patient SMAPE (HS + TS) SMAPE (SS + TS) Result Actual MatchH11 338232 330989 Sick Healthy NOH12 133555 340168 Healthy Healthy YESH13 273377 458243 Healthy Healthy YESH14 344581 237995 Sick Healthy NOH15 204677 230998 Healthy Healthy YESH16 373377 398572 Healthy Healthy YESH17 103658 220151 Healthy Healthy YESH18 322689 238111 Sick Healthy NOH19 243544 342159 Healthy Healthy YESH20 263355 379940 Healthy Healthy YESS11 172265 131922 Sick Sick YESS12 204804 038562 Sick Sick YESS13 299464 051305 Sick Sick YESS14 252248 067941 Sick Sick YESS15 265972 175233 Sick Sick YESS16 263674 239694 Sick Sick YESS17 257638 165941 Sick Sick YESS18 424496 285006 Sick Sick YESS19 296533 101009 Sick Sick YESS20 323630 110960 Sick Sick YES

Every single fuzzy rule can be taken as a sentence ofnatural language for example first rule from Figure 13

IF 119883119894is ml sm AND Δ119883

119894is qr sm THEN Δ119883

119894+1is minusme

may be read as followsIf the number of cars sold in the current year is more or

less small and the half-year sales increment is quite roughlysmall then the upcoming half-year increment will be negativemedium

421 Recognition of ldquoHealthyrdquo and ldquoSickrdquo Patterns by LFLFOur method to use linguistic fuzzy logic forecasting isbased on simple idea that best predictor learning from bothldquohealthyrdquo and ldquosickrdquo pattern samples respectively can be usedfor validation with tested pattern taken as validation part ofthe seriesThen we can evaluate SMAPE for both these casescompound series SMAPE (ldquohealthyrdquo + tested) and SMAPE(ldquosickrdquo + tested)

If SMAPE (ldquohealthyrdquo + tested) lt SMAPE (ldquosickrdquo + tested)then the tested pattern is supposed to be ldquohealthyrdquo otherwisethe tested pattern is supposed to be ldquosickrdquo

The idea is schematically shown in Figure 14For testing purposes we created two necessary typical

learning time series ldquohealthyrdquo (HS) and ldquosickrdquo (SS) accordingto the algorithm above They both consist of 1010 samplesmade from 10 typical series of ldquohealthyrdquo and ldquosickrdquo patientswith 101 measured ECG values Then we have created 10concatenated series according to the scheme in Figure 14with 10 randomly selected patients with ldquohealthyrdquo ECGmeasurement that is 20 files were produced (10x HS + TSand 10x SS + TS) The same concatenated series were alsomade from 10 ldquosickrdquo patients measurements This made usadditional 20 files with concatenated series (10x HS + TS and

0102030405060708090

100

Sick Healthy

FalseTrue

()

Figure 15 Experimental results LFLF

10x SS + TS) For 20 patients (Table 2) tested ECG we have2 concatenated series giving SMAPE (HS + TS) and SMAPE(SS + TS)

Our method based on LFLF proved very good results forright identification of sick patient records Nevertheless itproduces large amount of false positive identification of sickpattern for healthy patients (Figure 15) This result is con-sistent with our approach using neural networks Of courseour preliminary research has a limited extent and should beperceived only as narrative result which shows interestingproperties especially in complementation of neural networkresults

10 The Scientific World Journal

5 Conclusion

In this paper a short introduction into the field of ECGwaves recognition using backpropagation neural network hasbeen given Main objective was to recognise the normalcycles and arrhythmias and perform further diagnosis Weproposed two detection systems that have been created withusage of neural networks One of them is adapted accordingto the training set Here each pattern represents the wholeone ECG cycle Then an output unit represents a diagnose01 a healthysick person The second one approach usesneural network in which training set contains two differentgroups of patterns for healthysick persons According to theresults of experimental studies it can be stated that ECGwaves patterns were successfully extracted in given timeseries and recognised using suggestedmethod as can be seenfrom figures in Experimental Result section It might resultin better mapping of the time series behaviour for betterprediction

Both approaches were able to predict with high probabil-ity if the ECG time series represents sick or healthy persons Itis interesting that a sick diagnose was recognised with higheraccuracy in both experimental works

The third approach based on LFLF is currently only inthe stage of preliminary experiments but it conforms to theformer results based on neural networks This approach isnovel and could be good supplement to other soft-computingmethods for this task

Disclaimer

Anyopinions findings and conclusions or recommendationsexpressed in this material are those of the authors and do notnecessarily reflect the views of the sponsors

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The research described here has been financially sup-ported by University of Ostrava Grants SGS16PrF2014 andSGS14PrF2014

References

[1] P Tangkraingkij C Lursinsap S Sanguansintukul and TDesudchit ldquoSelecting relevant EEG signal locations for personalidentification problem using ICA and neural networkrdquo inProceedings of the 8th IEEEACIS International Conference onComputer and Information Science (ICIS rsquo09) pp 616ndash621 June2009

[2] C D Nugent J A C Webb N D Black and G T H WrightldquoElectrocardiogram 2 classificationrdquo Automedica vol 17 pp281ndash306 1999

[3] S Russell and P Norvig Artificial IntelligencemdashA ModernApproach Prentice Hall 2nd edition 2003

[4] C D Nugent J A Lopez A E Smith and N D BlackldquoReverse engineering of neural network classifiers in medicalapplicationsrdquo in Proceedings of the 7th EFOMP Congress vol 17p 184 Physica Medica 2001

[5] L Fausett Fundamentals of Neural Network PrenticeHall 1994[6] D E Rumelhart G E Hinton and R J Williams ldquoLearning

representations by back-propagating errorsrdquo Nature vol 323no 6088 pp 533ndash536 1986

[7] V Novak Fuzzy Sets and Their Applications Adam HilgerBristol UK 1989

[8] S Aouaouda M Chadli P Shi and H R Karimi ldquoDiscrete-time119867

minus119867infinsensor fault detection observer design for nonlin-

ear systems with parameter uncertaintyrdquo International Journalof Robust and Nonlinear Control 2013

[9] M Chadli A Abdo and S X Ding ldquo119867minus119867infin

fault detectionfilter design for discrete-time Takagi-Sugeno fuzzy systemrdquoAutomatica vol 49 no 7 pp 1996ndash2005 2013

[10] M Chadli and H R Karimi ldquoRobust observer design forunknown inputs takagi-sugeno modelsrdquo IEEE Transactions onFuzzy Systems vol 21 no 1 pp 158ndash164 2013

[11] S Aouaouda M Chadli and H Karimi ldquoRobust static output-feedback controller design against sensor failure for vehicledynamicsrdquo IET Control Theory amp Applications vol 8 no 9 pp728ndash737 2014

[12] I Perfilieva V Novak V Pavliska A Dvorak andM StepnickaldquoAnalysis and prediction of time series using fuzzy transformrdquoin Proceedings of the International Joint Conference on NeuralNetworks (IJCNN rsquo08) pp 3876ndash3880 Hong Kong June 2008

[13] E Volna M Kotyrba and R Jarusek ldquoMulti-classifier basedon Elliott waversquos recognitionrdquo Computers amp Mathematics withApplications vol 66 no 2 pp 213ndash225 2013

[14] E Volna M Kotyrba and R Jarusek ldquoPrediction by means ofElliott waves recognitionrdquo in Nostradamus Modern Methods ofPrediction Modeling and Analysis of Nonlinear Systems vol 192of Advances in Intelligent Systems and Computing pp 241ndash250Springer Berlin Germany 2013

[15] H Habiballa V Pavliska and A Dvorak ldquoSoftware systemfor time series prediction based on F-transform and linguisticrulesrdquo in Proceedings of the 8th International Conference onApplied Mathematics Aplimat pp 381ndash386 Bratislava Slovakia2009

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