Nonlinear interpolation fractal classifier for multiple cardiac arrhythmias recognition

Chaos, Solitons and Fractals 42 (2009) 2570–2581

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Nonlinear interpolation fractal classifier for multiple cardiac arrhythmias recognition Chia-Hung Lin a,b,*, Yi-Chun Du b, Tainsong Chen b a b

Department of Electrical Engineering, Kao-Yuan University, No. 1821, Jhongshan Rd., Lujhu Township, Kaohsiung County 821, Taiwan The Institute of Biomedical Engineering, National Cheng-Kung University, Tainan 70101, Taiwan

a r t i c l e

i n f o

Article history: Accepted 31 March 2009

Communicated by Prof. M. Wadati

a b s t r a c t This paper proposes a method for cardiac arrhythmias recognition using the nonlinear interpolation fractal classifier. A typical electrocardiogram (ECG) consists of P-wave, QRS-complexes, and T-wave. Iterated function system (IFS) uses the nonlinear interpolation in the map and uses similarity maps to construct various data sequences including the fractal patterns of supraventricular ectopic beat, bundle branch ectopic beat, and ventricular ectopic beat. Grey relational analysis (GRA) is proposed to recognize normal heartbeat and cardiac arrhythmias. The nonlinear interpolation terms produce family functions with fractal dimension (FD), the so-called nonlinear interpolation function (NIF), and make fractal patterns more distinguishing between normal and ill subjects. The proposed QRS classifier is tested using the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database. Compared with other methods, the proposed hybrid methods demonstrate greater efficiency and higher accuracy in recognizing ECG signals. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Electrocardiogram (ECG) signal is a non-invasive measurement for providing information of heart function and myocardium electric activity. Cardiac arrhythmias are not fatal diseases but may require therapy to prevent further problems. The electrical signals provide symptomatic information for classifying cardiac arrhythmias. Electrocardiograph as Holter recorder is used to record the electrical activity with surface electrodes placed on the chest. The measurement devices can record large amounts of signals, but do not automatically classify abnormalities and require off-line analysis. To develop an automated detector, diagnostic methods have been applied to detect cardiac arrhythmias in conjunction with time-, frequency-, and time–frequency-domain techniques. Different electrical potentials of the heartbeat provide information of different disturbances in the electrical activity. In the time-domain, ECG features include heartbeat interval, amplitude parameters, duration parameters, combined parameters, area of QRS-complex, and QRS morphology [1,2]. When the activation pulse does not travel through the normal conduction path, the QRS-complex becomes wide, and the high-frequency components are attenuated. Spectra of QRS-complexes in ventricular tachycardia (VT) and ventricular fibrillation (VF) appear signatures that are different from those in normal heartbeats. To quantify the frequency components among the various cardiac arrhythmias, such as Fourier spectrum [3,4] and Wenckebach-like frequency [5], frequency-domain features are used to classify the cardiac arrhythmias. In the time–frequency technique, the wavelet transform (WT) is applied to extract the features of cardiac arrhythmias using discrete wavelet transform [6–8]. WT is robust to time-varying signal analysis, but it is not capable of recognition. Applying these significant features, artificial-intelligent (AI) methods including wavelet neural networks * Corresponding author. Address: Department of Electrical Engineering, Kao-Yuan University, No. 1821, Jhongshan Rd., Lujhu Township, Kaohsiung County 821, Taiwan. Tel.: +886 7 6077014. E-mail address: [email protected] (C.-H. Lin). 0960-0779/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2009.03.204

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[7,8], multilayer neural network [9,10], Fuzzy hybrid neural networks [11], and grey relational analysis [12] have been proposed parallel computing systems and provide the mathematical models for biomedical signal, physical, and biological systems. The above-mentioned methods provide promising results for cardiac arrhythmia discrimination. Time–frequency domain technique has good performance in the analysis of time-varying signals. However, the shape and type of wavelet (continuous or discrete transform) have to be chosen, and the wavelet coefficients, such as dilation and translation parameters, have also to be determined. The ANN is well known for its learning and recognition ability, it is limited to the problems of determining architectures of supervised learning. ANN uses error back propagation to adjust network parameters and achieve a nonlinear mapping relationship. The local minimum problem, slow learning speed, and the weight interferences between different patterns are the major drawbacks. Considering these limitations, nonlinear interpolation fractal model and GRA are applied to develop the QRS-complexes classifier. Clinical diagnosis is dependent on the ability to record and analyze fluctuating signals. The morphology variations of ECG signals are different for different patients, and even for the same patient or for the same type [1]. Fractal analysis is an approach with FDs and results the data self-similarity. Fractal patterns are used to construct the information from time-series signals. NIFs require fewer map parameters for constructing fractal patterns of normal and abnormal heartbeats. The grey theory combines the techniques of cluster analysis, relational analysis, prediction, and decision and applied them to the grey system [13,14]. The ‘‘grey” terminology is used to signify that the system information is incomplete, unclear, or uncertain. Its analysis makes use of less data and does not demand strict statistical procedures and inference rules. For an adaptation application, the GRA has a function for processing numerical data or binary data, a flexible pattern mechanism with add-in and delete-off patterns without parameter adjustment [4,12]. The advantages of above-mentioned methods, NIFs with FDs and GRA are integrated into a classifier for cardiac arrhythmias recognition. NIFs construct the segmented fractal patterns of various cardiac arrhythmias. GRA is used to recognize normal and abnormal heartbeats. Test data are obtained from the MIT-BIH arrhythmia database. Seven categories are recommended by the AAMI (Association for the Advancement of Medical Instrumentation) standard. The results will show computational efficiency and accurate recognition for ECG signals. 2. Mathematical method description 2.1. Nonlinear interpolation function (NIF) IFS has been proposed for signal modeling that is simple in form and capable of producing complicated functions which are fractal in nature. It has been used to create images and various waveforms that resemble those found naturally. The fractal method of modeling data involves selecting interpolation points from the sampling data and creating IFS patterns. These patterns can be used to recreate the original data. An IFS is a finite set of contraction mappings for interpreting the data to be modeled as a graph. In modeling the graph of a function or data sequence x½n, n ¼ 1; 2; 3; . . ., N, the P interpolation maps, wj , j ¼ 1; 2; 3; . . ., P, can be presented as [15,16]

    ej aj bj n þ fj cj dj x½n x½n  wj ðnÞ ¼ aj n þ bj x½n þ ej wj



n





ð1Þ

¼

ð2Þ

wjx ðx½nÞ ¼ cj n þ dj x½n þ fj

Eq. (1) can be separated into two equations wj ðnÞ and wjx ðx½nÞ. The bj term is set to be zero, confirming that the resulting attractor is single-valued. The interpolation points fix the aj and ej terms as [15,16]

aj ¼

Mj2  M j1 ; N1

ej ¼ M j1

ð3Þ

For each j, the wj maps the data sequence x½n onto the subsequences with Mj sampling data in the interval [M j1 , M j2 ], and the patterns can be constructed adjacently. The method involves two stages: (1) to determine the interpolation points, and (2) to determine the best map parameters. The remaining map parameters cj , dj , and fj can be solved by minimizing the sum of squared errors between the transformed data and the original data in the range of the jth map, and can be justified by the Collage Theorem [17,18]:

ej ¼

M j2 X  2 wjx ðx½nÞ  x½i

ð4Þ

i¼M j1

where n ¼ int

h

iM j1 M j2 M j1

i ðN  1Þ , and M j ¼ Mj2  M j1 +1. An IFS is implemented with similarity maps, and the resulting data

shows self-similarity. To improve the self-similarity constraint, nonlinear interpolation is used in the maps and makes the model flexible. The nonlinear equation, the so-called nonlinear interpolation function (NIF), can be presented as

wjx ðx½nÞ ¼ cj n þ dj x½n þ fj þ g j sin

pn

N

þ hj sin

  2pn N

ð5Þ

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The NIFs project the mapped data onto a sinusoidal interpolation. The remaining map parameters cj , dj , fj , g j , and hj can be solved by

2

cj

3

6d 7 6 j7 X Mj Mj X 6 7 T 6 ½Si  Si 6 fj 7 Si  x½i 7¼ 6 7 i¼1 i¼1 g 4 j5 hj  0  0  0  T Si ¼ n x½i 1 sin pDn ; sin 2pDn

ð6Þ

n0 ¼



 D1 i Mj  1

Consider input sequence xj ½i; i ¼ 1; 2; 3; . . . , M j , with P segments, j ¼ 1; 2; 3; . . . , P, from the ECG signal, its segmented fractal pattern can be constructed as

uji ¼ cj n0 þ dj xj ½i þ fj þ g j sin



pn0



D

þ hj sin

  2pn0 D

ð7Þ

where D is a FD parameter between 1 and 2 for processing one-dimensional signals [19]. FD will change ECG signals into fractal features at different scales. Input sequences xj ½i are the sample data from the QRS-complexes. Fractal patterns can be constructed as





U uji ¼

P [

uji ; i ¼ 1; 2; 3; . . . ; Mj

ð8Þ

j¼1

Eq. (7) is used to extract the features from the ECG signals, and Eq. (8) is utilized to construct the fractal patterns of normal beat (Þ and cardiac arrhythmias including premature ventricular contraction (V), atrial premature beat (A), right bundle branch block beat (R), left bundle branch block beat (L), paced beat (P), and fusion of paced and normal beat (F). 2.2. Grey relational analysis (GRA) GRA includes ‘‘local relation” and ‘‘global relation” analysis. Based on similarity and dissimilarity, a relation is the relational measurement of an attribute in different sequences. It is a method for determining the relationship between reference data and other comparative data. Assume a reference sequence Uref ¼ ½u11 ð0Þ; . . . ; u1M1 ð0Þ; . . . ; uj1 ð0Þ; . . . ; ujMj ð0Þ; . . . ; uP1 ð0Þ; . . . ; uPMP ð0Þ, and K comparative sequences UðkÞ ¼ ½u11 ðkÞ; . . . ; u1M1 ðkÞ; . . . ; uj1 ðkÞ; . . . ; ujMj ðkÞ; . . . ; uP1 ðkÞ; . . . ; uPMP ðkÞ; k ¼ 1; 2; 3; . . . ; K, can be represented as

Ucomp ¼ ½ Uð1Þ Uð2Þ    UðkÞ    UðKÞ 

ð9Þ

Compute the absolute deviation of reference sequence Uref and k comparative sequence UðkÞ by

DujMj ðkÞ ¼ jujM ð0Þ  ujMj ðkÞj

ð10Þ

j

The grey relational grades r(k) can be computed by [12]

" rðkÞ ¼ exp n



EDðkÞ Dumax  Dumin

2 #

3 0rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2 12 PP D u ðkÞ 6 B jMj j¼1 C 7 6 C 7 ¼ exp 6nB 7; 4 @ Dumax  Dumin A 5 2

n 2 ð0; 1Þ

ð11Þ

Dumin ¼ min8k ½mim8j DujMj ðkÞ

ð12Þ

Dumax ¼ max8k ½max8j DujMj ðkÞ

ð13Þ

where ED(k) is the Euclidean distance (ED) between two vectors Uref and U(k); Dumin and Dumax are the minimum and maximum values of absolute deviation DujMj (k), k = 1, 2, 3, . . . , K, respectively; and n is the recognition coefficient with parameter interval (0,1Þ. GRA satisfies the following four properties [15]:    

Normal interval: rðUref ; UðkÞÞ 2 [0, 1], if Uref ¼ U(k), then rðUref ; UðkÞÞ ¼ 1. Dual symmetry: If k = 2, then rðUref ; UðkÞÞ ¼ rðUðkÞ; Uref Þ. Wholeness: If k P 3, then rðUref ; UðkÞÞ – rðUðkÞ; Uref Þ. Approachability: If ED is smaller, the relational grade rðUref ; UðkÞÞ is larger.

The grey relational grades r(k) are inversely proportional to the distances. If the vector Uref is similar to any comparative vector U(k), the grader(k) will be a maximum value. The grey relational grade has been used in GRA to measure the relation-

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ship between the reference sequence data and comparative sequence data. This concept can be used for analyzing pattern relations. For each reference sequence ujMj 2 Uref , j = 1, 2, 3, . . . , M j , and all comparative sequences ujMj (k)2 Ucomp , k = 1, 2, 3, . . . , K, the least number of the comparative patterns, K, is two. We see that ED(k) counts every component difference between two considered patterns. For a reference sequence Uref , we see that EDmin 6ED(k)6 EDmax [15]:

EDmin 6 EDðkÞ 6 EDmax ) 0 6

EDmax  EDðkÞ 61 EDmax  EDmin

ð14Þ

where EDmax ¼ maxfEDðkÞg; EDmin ¼ minfEDðkÞg; EDmin – EDmax , and then rðkÞ 2 ½0; 1; 8n 2 ð0; 1Þ. Therefore, r(k) approaches one as ED(K) is close to EDmin , and approaches zero as ED(K) is close to EDmax (ED(k) ! EDmax , r(k) ! 0 and ED(k) ! EDmin , r(k) ! 1). Grey grade r(k) can be used to measure the degree of similarity between the reference and comparative sequences when ED represents the largest similarity. No matter how large ED is, the range of the grey grade is in the interval [0, 1]. The selection of the recognition coefficient depends on numerical considerations. If the difference between EDmin and EDmax is very small, the coefficient n is selected to >>1 in order to make grey grades more distinguishable. The dimension of grey relational vector C ¼ ½rð1Þ; rð2Þ; . . . ; rðkÞ; . . . ; rðKÞ can be reduced from K-dimension to C-dimension by Eqs. (15) and (16)

cc ¼

K X

rðkÞxkc ;

c ¼ 1; 2; 3; . . . ; C

ð15Þ

k¼1

xkc ¼



1; 0;

k 2 Class c k R Class c

ð16Þ

For the classification of c classes, the associated class for input vector Uref could be expressed as weighting factor xkc 2{0,1}, where C is the total number of possible classes, c = 1, 2, 3 , . . ., C. If vector Uref belongs to class c, the weighted factor wkc equals one, and the rest of the factors are zero as in Eq. (16). The final grey grade g c that an unknown vector xkc belongs to Class c can be presented as C X

cc

g c ¼ PC

c

c¼1 c

!

gc ¼ 1

ð17Þ

c¼1

which defines the decision for classifying an unknown vector Uref . The final grey grades represent seven classes (C = 7) as defining vector G¼ ½g 1 ; g 2 ; g 3 ; g 4 ; g 5 ; g 6 ; g 7  ¼ ½g Nor ; g V ; g A ; g L ; g R ; g P ; g F . The selection sort is then applied to find the maximum grade, gmax ¼ maxfg Nor ; g V ; g A ; g L ; g R ; g P ; g F g. The maximum grade g max indicates the arrhythmic type. 3. Features creation with nonlinear interpolation function 3.1. QRS-complex extraction In this study, the datasets of QRS-complexes are taken from the MIT-BIH arrhythmia database (from Record 100 to Record 233) as shown in Table 1 [20]. The subjects are 25 men aged 32–89 years, and 22 women aged 23–89 years. The records include complex ventricular, junctional, supraventricular arrhythmias, and conduction abnormalities. In these records, the upper signal is a modified limb lead II (ML II), and the lower signal is a modified lead V1 (Occasionally V2 or V5, and in one instance V4). An normal ECG signal represents the changes in electrical potential during the heartbeat as recorded with non-invasive electrodes on the limbs and chest; a typical ECG signal consists of the P-wave, QRS-complex, and T-wave. The morphology of ECG signal varies with rhythm origin and conduction path, when the activation pulse originates in the atrium (Atrial Rhythm) and travels through the normal conduction path (Atrioventricular Bundle), the QRS-complex has a sharp and narrow deflection. The activation pulse originates in the ventricle and does not travel through the normal conduction path, the QRS-complex becomes broad and distorted. ECG signals have various morphological features, which can be used to discriminate the arrhythmic types. The QRS-complex of the ECG is some distinct information in monitoring heart rate and diagnosis of cardiac diseases. ECG signals are obtained from the MIT-BIH arrhythmia database for recognition. In the preprocessing step, R-wave peaks are detected by a peak detection algorithm [3] or the Tompkins algorithm [21]. R-wave peaks detection begins by scanning for local maxima in the absolute value of ECG data. For certain window duration, the search continues to look for a larger value. If this search finishes without finding a larger maximum, the current maximum is assigned as the R-wave peak [3]. Centered on the detected R-wave peak, the QRS-complex portion is extracted by applying a window of 280 ms, and P-wave and T-wave are excluded by this window duration. With the 180 Hz sampling rate, 50 samples can be acquired around the R-wave peak (sampling point N ¼50, 25 points before and 25 points after) as shown in Fig. 1(a). After sampling and analog-to-digital conversion, individual QRS-complexes are extracted in the time-domain. Each sample is preprocessed by removing the mean value to eliminate the offset effect and dividing it by the standard deviation. This process is used to reduce the possible signal amplitude biases resulting from instrumental and human differences [22]. The overall QRS-complexes could be selected from patient numbers 100, 103, 107, 109, 111, 118 119, 124, 200, 202, 207, 209, 212, 213, 214, 217, 221, 231, 232, and 233. For numerical experiments, the seven heartbeat classes included in the investigations are normal beat, V, A, L, R, P, and F. The arrhythmic types, patient numbers, and symbols are shown in Table 1.

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Table 1 Heartbeat classes of human ECG. AAMI

MIT-BIH

Record

Normal

Normal beat

MIT-100 MIT-103 MIT-119 MIT-200 MIT-209 MIT-212 MIT-221

(M) (M) (F) (M) (M) (F) (M)

Symbol 

Ventricular ectopic beat

Ventricular premature contraction

MIT-119 MIT-200 MIT-221 MIT-233

(F) (M) (M) (M)

V

Supraventricular ectopic beat

Atrium premature beat

MIT-202 (M) MIT-232 (F)

A

Bundle branch ectopic beat

Left bundle branch block beat

MIT-109 MIT-111 MIT-207 MIT-214

(F) (F) (F) (M)

L

Right bundle branch block beat

MIT-118 MIT-124 MIT-212 MIT-231

(M) (M) (F) (F)

R

Unknown beat

Paced beat

MIT-107 (M) MIT-217 (M)

P

Fusion beat

Fusion of paced and normal beat Fusion of ventricular and normal beat

MIT-217 (M) MIT-213 (M)

F

Note. (1) AAMI: Association for the Advancement of Medical Instrumentation Recommended Standard; (2) MIT-BIH: Massachusetts Institute of TechnologyBeth Israel Hospital Arrhythmia Database; (3) F, female; (4) M, male.

3.2. Fractal patterns creation From the subject records, QRS-complexes (ML II Signal) are obtained and classified into seven types. Symptomatic patterns are produced by the NIFs and linear interpolation functions (LIFs). Centered on the R-wave peak, the QRS-complex of normal beat (Patient No. 103) can be divided into the Q–R segment and R–S segment, segment number j ¼ 1, 2, and sampling points M j ¼ 25ðN ¼ M1 þ M 2 ¼ 50). For nonlinear interpolation, the remaining map parameters can be solved by Eq. (6). By using fractal dimension between 1 and 2, fractal patterns are constructed with Eqs. (7) and (8) as shown in Fig. 1(b). NIFs with fractal dimension D = 1.6 is chosen in this study, and the related parameters are shown in Table 2. With the same samples, the remaining map parameters of linear interpolation are solved and also shown in Table 2. For various QRS-complexes, symptomatic patterns are produced by the LIFs. Obviously, it is difficult to distinguish the seven symptomatic types from the linear interpolation patterns as shown in Fig. 1(c). The morphological variations of ECG signals are irregular in their inflections and have different shapes. Therefore, we used the NIFs with D = 1.6 to construct the various fractal patterns as shown in Fig. 2. These patterns have various morphologies that could be used for discriminating the arrhythmic types including normal beat, V, A, L, R, P, and F. With data self-similarity, the number of datasets of the same type can be reduced. The numbers of QRScomplexes from the same class are 1-, 6-, 2-, 6-, 4-, 4-, and 2-set data, respectively. According to the various symptomatic patterns, we can systematically create comparative sequences UðkÞ with Eq. (9). The number of comparative sequences is equal to 25-set data (K ¼ 25). For the classification of c classes, the associated class for comparative sequences could be expressed as weighting factors. The weighting factors xkc ; k ¼ 1, 2, 3, . . . , 25, c ¼ 1, 2, 3, . . . , 7, are encoded as binary values by Eq. (16) with signal ‘‘1” for belonging to Class c and the rest of the factors are zero, can be presented as

3

2

Uð1Þ 6 Uð2Þ 7 7 6 6 . 7 6 . 7 6 . 7 7 6 6 UðkÞ 7 7 6 7 6 6 .. 7 4 . 5

UðKÞ

) ) .. . ) .. . )

½ 2 1 6 61 6 6 6 6 60 6 6 6 4 0

V A L R

P F

0 0 0 0 0 0

3

7 0 0 0 0 0 07 7 .. .. .. 7 7 . . . 7 1 0 0 0 0 07 7 7 .. .. .. 7 . . . 5 0 0 0 0 0 1

ð18Þ

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Fig. 1. QRS morphological features. (a) QRS-complex feature in the time-domain (Patient No. 103); (b) QRS-complex extraction using nonlinear interpolation function with fractal dimension (D ¼ 1.0, 1.2, 1.4, 1.6, 1.8, 2.0); and (c) QRS-complex extraction using linear interpolation function.

The final grey grades can be computed by Eq. (17). The selection sort is then applied to find the maximum grade gmax , and the maximum one indicates the possible type. Table 2 The remaining map parameters of linear and nonlinear interpolation function.

Note. Linear interpolation function: uji ¼ cj n þ dj xj ½i þ fj ; j ¼ 1; 2.

2 3 cj Mj Mj X 7 X T 6 ½Si  Si 4 dj 5 ¼ Si  xj ½i; i¼1 i¼1 fj

 T Si ¼ i xj ½i 1 :

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Fig. 2. Various symptomatic patterns with nonlinear interpolation function.

Cardiac arrhythmias recognition can be divided into a sequence of stages, starting with feature extraction from the occurring heartbeats. Next, meaningful features are selected to represent the given symptomatic patterns without redundant parameters. Finally, the pattern-recognition task is carried out by GRA. The tests will be shown in the next section. 4. Experimental results and discussion The proposed detection method was developed on a PC Pentium-IV 3.0GHz with 480 MB RAM and Matlab software, using the MIT-BIH arrhythmias database including patient numbers 100, 103, 107, 109, 111, 118 119, 124, 200, 202, 207, 209, 212, 213, 214, 217, 221, 231, 232, and 233. The overall diagnostic procedures for ECG recognition divided into three stages: (1) signal preprocessing; (2) fractal feature extraction; (3) heartbeat recognition with fractal classifier. The numbers and types of ECG samples are selected for comparative sequences and the other for reference sequences. We have 25-set comparative sequences for the GRA with seven classes, and relative recognition coefficient n ¼ [10,20] is chosen in this study. The performance of the proposed method was tested with diagnostic accuracy for reference sequences (unrecorded data). Matlab colormap function was also used to display the test results in specific grayscale range from white (Grade ¼ 1) and black (Grade ¼ 0), as detailed below. 4.1. Cardiac arrhythmias recognition The features are used for extraction from QRS-complexes within the movable window with each shift in time. The content of each window is applied to the proposed procedure, and each R-wave peak is detected by a peak detection algorithm. Fig. 3(a) shows that the ECG signals consist of the normal heartbeat (Þ and premature ventricular contraction (V) in the

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time-domain. The effect of noise in the ECG measurement, such as power-line interference (50 or 60 Hz) or quantification error, is also considered. Fig. 3(b) shows ECG signals with 60-Hz power-line interference in the time domain. After feature extraction with nonlinear interpolation function, the same types always have similar symptomatic patterns. When a QRScomplex has different pathological shape in the QR-segment or RS-segment due to rhythm origin and conduction abnormalities, the differences will obviously reveal the rise or dip characteristics. The DifferenceðMj Þ ¼ UNor ðMj Þ  UV ðMj Þ, j ¼ 1, 2, between normal beats and abnormal beats are shown in Fig. 4. For normal heartbeats and abnormal heartbeats, the symptomatic patterns show morphological variations in shape, the critical times for starting and ending of occurrences are noted by observing the differences, and the number of abnormal rhythm beats are clearly counted. 4.1.1. Single cardiac arrhythmia Results of Test 1 using 100 heartbeats (about 1.5 min long) of the patient numbers 119 and 200 containing normal beats and arrhythmia Vs reveal that the overall accuracies are 100% and 94% as shown in Table 3, respectively. For patient number 200, the processes recognized 38 V-beats with six failures, and the expected sensitivities as the fraction of Class V correctly classified are 100% and 84.2%, respectively, and the specificity for normal heartbeats is 100%. The results confirm that the major class is premature ventricular contraction. ECG signals may be disturbed by noise such as power-line interference. We have considered a 60-Hz interference in ECG signals whose amplitude is approximately 5–6 times less than the R-wave peak. Test 2 shows the results of ECG signals involving noisy interference as shown in Table 3. The sensitivities for class V are respectively 100% and 81.6%, and the specificity for normal heartbeats is also 100%. Positive predictivity of more than 80% is obtained to quantify the performance of the proposed method without or with a noisy background. This confirms that proposed method have high confidence of detection results in the tests. 4.1.2. Multiple cardiac arrhythmias Clinical diagnostic subjects have multiple cardiac arrhythmias such as supraventricular ectopic beat, ventricular ectopic beat, bundle branch ectopic beat, fusion, and paced beats. For example, patient numbers 214 and 217 have premature ven-

Fig. 3. ECG signals (Record 119). (a) ECG signals of normal beat and V in time domain; (b) ECG signals of normal beat and V with 60 Hz power-line interference.

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Fig. 4. Symptomatic patterns for Record 119. (a) Fractional features of normal beat and V; (b) Fractional features of normal beat and V with noisy interference.

tricular contraction (V), left bundle branch block beat (L), paced beat (P), and fusion of paced and normal beat (F). Fig. 5(a) shows that the ECG signals (Patient No. 217) consist of the V-beats, P-beats, and F-beats in the time domain, and their symptomatic patterns for P-beats and F-beats are shown in Fig. 5(b). As seen in Table 3, the results of Test 1 confirm that the major cardiac arrhythmias are class L and class P. The processes recognized 95 L-beats with three failures, and 94 P-beats with four failures. The sensitivities for ectopic beats are 96.8% and 95.7%, and the overall accuracies are 95% and 96%, respectively. Fig. 6 shows the recognition results of patient number 217 and four misclassification errors () of class L and class F in the outputs g L and g F . In Fig. 6, the horizontal axis is the sample number and the vertical axis is the arrhythmia class. The Matlab images and colormap functions scale the numerical data of 100 test results to the full range of the grey grade between 0.0 and 1.0. The maximum grey grade indicates the possible arrhythmia class. Test 2 shows the results of multiple cardiac arrhythmias involving noisy interference as shown in Table 3. The overall accuracies are also greater than 90%. The proposed method can also recognize multiple cardiac arrhythmias with good accuracy. 4.2. Comparative results of beat recognition Table 4 compares the results of the proposed method (M1) and other hybrid methods, including the adaptive wavelet network (M2), hybrid NIFs with fractal dimension D ¼ 1.6 and traditional GRA (M3), hybrid LIFs and proposed GRA (M4), and hybrid LIFs and traditional GRA (M5). The topology of M2 is 100-43-8-7, including 100 wavelet nodes, 43 hidden nodes, 8 summation nodes, and 7 output nodes [8]. Owing to various available heartbeats in the MIT database, the number of different types of diseases used in the experiments (Patient Nos. 107, 119, 200, 212, 214, and 217). For the same number of heartbeats, the test results are shown in Table 4. The methods M1 and M2 have the same accuracy (Accuracyave ¼ 97.00%) for heartbeat recognition, and the sensitivities for ectopic beats are 95.44% and 95.76%, respectively. However, the optimum method was used to adjust the network parameters to enhance detection accuracy, and the wavelet types and wavelet coefficients also need to be chosen. Significant features are suited to classify different patterns at specific

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Table 3 The test results of cardiac arrhythmias.

Note. (1) Accuracy (%) ¼ ðN r =N t Þ100%, the overall accuracy is the fraction of the total heartbeats correctly classified. (2) N r : the number of correctly discriminated beats; N t : total number of heartbeats.

Fig. 5. Symptomatic patterns for Record 217. (a) ECG signals of P and F in time domain; (b) fractional features of P and F.

dilation and translation parameters. We will obtain many wavelet functions with different wavelet coefficients to represent the features of ECG signals with a tedious procedure of wavelet decomposition and experiences. With the LIFs, symptomatic

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Fig. 6. Recognition results of patient number 217.

Table 4 Comparison of results between the proposed method and other hybrid methods.

Note: (1) M1: the proposed method; (2) M2: adaptive wavelet network [7]; (3) M3: hybrid NIFs with fractal dimension D ¼ 1.6 and traditional GRA; the grey relational grade can be presented as [15]

cðkÞ ¼

Dmin in þ n  Dmax ; EDðkÞ þ n  Dmax

k ¼ 1; 2; 3; . . . ; K; n 2 ð0; 1Þ

(4) M4: hybrid LIFs and proposed GRA; (5) M5: hybrid LIFs and traditional GRA.

patterns appear too similar; therefore, it is difficult to distinguish the symptoms such as normal beat and class R/L, and class V and class P. This is the main reason why misclassification occurs when using the LIFs and traditional GRA. Owing to the enhancement in features by the NIFS, the number of comparative sequences can be reduced. Parameters of NIFs can be directly computed by Collage theorem. The proposed method needs less parameter assignment for constructing NIFs with 5 remaining map parameters for the Q–R segment and R–S segment, respectively, and GRA needs no iteration process to adjust the parameters. It takes about 9 s to recognize 600 heartbeats. The outcomes of the proposed method are better than those of other hybrid methods. 5. Conclusion In this paper, a classifier with NIFs with FD and GRA has been proposed for cardiac arrhythmias recognition. The classifier is developed from the fact that the morphology of QRS-complexes changes with the origination and conduction path of the rhythm. NIFs act to extract and enhance the features from QRS-complexes in the time-domain. The process results in data

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self-similarity, thus reducing the amount of datasets required. Then GRA uses these fractal patterns to recognize multiple cardiac arrhythmias. For various available heartbeats in the MIT database, the experimental results show the efficiency of the proposed method. Compared with other hybrid methods, the proposed method shows higher accuracy, faster processing time, and less data and parameters required. References [1] de Chazal Philip, O’Dwyer Maraia, Reilly Richard B. Automatic classification of heartbeats using ECG morphology and heartbeat interval features. IEEE Trans Biomed Eng 2004;51(7):1196–206. [2] Bortolan Giovanni, Brohet Christian, Fusaro Sergio. Possibilities of using neural networks for ECG Classification. J Electrocardiol 1996;29(Suppl.):10–6. [3] Minami Kei-ichiro, Nakajima Hiroshi, Toyoshima Takesshi. Real-time discrimination of ventricular tachyarrhythmia with Fourier-transform neural network. IEEE Trans Biomed Eng 1999;46(2):179–85. [4] Lin Chia-Hung. Frequency-domain features for ECG beat discrimination using grey relational analysis based classifier. Comput Math Appl 2008;55(4):680–90. [5] Biktashev VN, Holden AV, Mironov SF, Pertsov AM, Zaitsev AV. Three-dimensional organization of re-entrant propagation during experimental ventricular fibrillation. Chaos, Soltions & Fractals – Appl Sci Eng 2002;13(8):1713–33. [6] Qin Shuren, Ji Zhong, Zhu Hongjun. The ECG recording analysis instrumentation based on virtual instrument technology and continuous wavelet transform. In: Proceedings of the 25th annual international conference of the IEEE EMBS Cancun, Mexico, September 17–21; 2003. p. 3176–9. [7] Dickhaus Hartmut, Heinrich Hartmut. Classifying biosignals with wavelet networks – a method for noninvasive diagnosis. IEEE Eng Med Biol 1996:103–11. [8] Lin Chia-Hung, Du Yi-Chun, Chen Tainsong. Adaptive wavelet network for multiple cardiac arrhythmias recognition. Expert Syst Appl 2008;34(4):2601–11. [9] Holden AV, Poole MJ, Tucker JV, Zhang H. Coupling CMLs and the synchronization of a multiplayer neural computing system. Chaos, Soltions & Fractals – Appl Sci Eng 1994;4(12):2249–68. [10] Yu Sung-Nien, Chou Kuan-To. Combining independent component analysis and back-propagation neural network for ECG beat classification. In: Proceeding of the 28th IEEE EMBS annual international conference, New York City, August 30–September 3; 2006. p. 3090–3. [11] Wang Yang, Zhu Yi-Sheng, Thakor Nitish V, Xu Yu-Hong. A short-time multifractal approach for arrhythmias detection based on fuzzy neural network. IEEE Trans Biomed Eng 2001;48(9):989–95. [12] Lin Chia-Hung. Classification enhancible grey relational analysis for cardiac arrhythmias discrimination. Med Biol Eng Comput 2006;44(4):311–20. [13] Wu John H, Chen Chie-Bein. An alternative form for grey relational grades. J Grey Syst 1999;1:7–12. [14] Chang Wei-Che. A comprehensive study of grey relational generating. J Chin Grey Assoc 2000;1:53–62. [15] Chang K-C, Yeh M-F. Grey relational analysis based approach for data clustering. IEE Proc Vis Image Signal Process 2005;152(2):165–72. [16] Mazel DS, Hayes MH. Using iterated function systems to model discrete sequences. IEEE Trans Signal Process 1992;40(7):1724–34. [17] Barnsley Michael. Fractal functions and interpolation. Constr Approx 1986;2:303–29. [18] Barnsley Michael. Fractals everywhere. New York, NY: Academic Press, Inc.; 1988. [19] Vines Greg, Hayes III Monson H. Nonlinear address maps in a one-dimensional fractal model. IEEE Trans Signal Process 1993;41(4):1721–4. [20] Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, lvanov PCh, Mark RG, et al. PhysioBank, Physio Toolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation 2000;101(23):e215–e220 (June 13) [Circulation electronic Pages; http://circ/cgi/ content/full/101/23/e215]. [21] Pan J, Tompkins WJ. A real-time QRS detection algorithm. IEEE Trans Biomed Eng 1985;32(3):230–6. [22] Yu Sung-Nien, Chou Kuan-To. Combining independent component analysis and back-propagation neural network for ECG beat classification. In: Proceeding of the 28th IEEE EMBS annual international conference, New York City, August 30–September 3; 2006. p. 3090–3.