- Research
- Open Access

# Fast multi-scale feature fusion for ECG heartbeat classification

- Danni Ai
^{1}, - Jian Yang
^{1}Email author, - Zeyu Wang
^{1}, - Jingfan Fan
^{1}, - Changbin Ai
^{1}and - Yongtian Wang
^{1}

**2015**:46

https://doi.org/10.1186/s13634-015-0231-0

© Ai et al. 2015

**Received:**9 February 2015**Accepted:**10 May 2015**Published:**31 May 2015

## Abstract

Electrocardiogram (ECG) is conducted to monitor the electrical activity of the heart by presenting small amplitude and duration signals; as a result, hidden information present in ECG data is difficult to determine. However, this concealed information can be used to detect abnormalities. In our study, a fast feature-fusion method of ECG heartbeat classification based on multi-linear subspace learning is proposed. The method consists of four stages. First, baseline and high frequencies are removed to segment heartbeat. Second, as an extension of wavelets, wavelet-packet decomposition is conducted to extract features. With wavelet-packet decomposition, good time and frequency resolutions can be provided simultaneously. Third, decomposed confidences are arranged as a two-way tensor, in which feature fusion is directly implemented with generalized *N* dimensional ICA (GND-ICA). In this method, co-relationship among different data information is considered, and disadvantages of dimensionality are prevented; this method can also be used to reduce computing compared with linear subspace-learning methods (PCA). Finally, support vector machine (SVM) is considered as a classifier in heartbeat classification. In this study, ECG records are obtained from the MIT-BIT arrhythmia database. Four main heartbeat classes are used to examine the proposed algorithm. Based on the results of five measurements, sensitivity, positive predictivity, accuracy, average accuracy, and *t*-test, our conclusion is that a GND-ICA-based strategy can be used to provide enhanced ECG heartbeat classification. Furthermore, large redundant features are eliminated, and classification time is reduced.

## Keywords

- ECG heartbeat
- Classification
- Multi-linear subspace learning
- Wavelet-packet decomposition

## 1 Introduction

Cardiovascular diseases (CVDs) are among the most common causes of death worldwide. Although death rate caused by CVDs has decreased in developed countries, death rate has increased rapidly in developing countries. CVD-related socioeconomic burden, as well as risk factors, remains astonishingly high [1]. Behavioral risks (e.g., tobacco smoking, physical inactivity, unhealthy diet, etc.), metabolic risks (e.g., raised blood pressure/sugar/lipids), and other risk factors (e.g., gender, advancing age) increase death rates. For instance, cardiac arrhythmia, which refers to disorders of the electrical conduction system of the heart, may pose a high risk and cause medical emergencies.

Electrocardiogram (ECG), as an adjunct tool in cardiovascular diseases management, is used to non-invasively monitor the electrical activity of the heart [2]. To capture frequent occurrence of arrhythmias, medical practitioners record ECG activity for several hours. Large amounts of data are recorded in computational complexity. Therefore, automated heartbeat classification is essential for diagnostic assistance.

Thus far, simple classifiers, such as linear discriminants [3] and K-nearest neighbor classifier [4], and complex classifiers, including chaotic modeling, spectral coherence analysis, artificial neural networks, and support vector machine, have been extensively applied. Classifier combination is also used in ECG heartbeat classification to improve accuracy [5]. The final decision regarding classifier combination is achieved by considering the decisions of members or aggregating the decisions of one or a few of the members [2].

Feature extraction is one of the most important steps in classification and can capture a certain underlying property of ECG [6]. Various kinds of comprehensive features have been extracted to describe ECG; these features can be divided into three categories, including temporal, morphological, and statistical features [7]. Temporal features are exclusively acquired from time-domain signals and consist of RR- and heartbeat interval features. The hidden complexities of an ECG signal cannot be distinctly interpreted because of subtle changes. More discriminating features can be extracted in a wavelet transform (WT) domain than in a time domain [8]. Morphological and statistical features can be obtained with WT of the ECG signal, which provides good resolution in time and frequency domains [7]. However, WT only displays sufficient frequency resolution at low frequencies but poor frequency resolution at high frequencies. As an extension of WT, wavelet-packet decomposition (WPD) is developed to achieve fine frequency resolution at both low and high frequencies. WPD can also be used to investigate piecewise signal variations.

Feature combinations can improve classification results [9]. However, the algorithm of selecting and combining multiple features poses a considerable challenge [3]. In this paper, a novel multi-scale feature-fusion method for ECG heartbeat classification is proposed. In the proposed method, ECG is initially fragmented into separate heartbeats; baseline and noise are further removed from each heartbeat. Features are then extracted by wavelet-packet decomposition, in which features become more distinguishable in a wavelet-packet-transform domain than in a time domain. The fourth-level components of WPD are represented as the features of a heartbeat. All of the features of a heartbeat are arranged into a two-order tensor rather than a long vector; a two-order tensor is further processed by generalized *N* dimension independent component analysis (GND-ICA) to select and fuse effective components simultaneously. These fused components, as new features of ECG heartbeats, are fed to a support vector machine (SVM) for automated classification. Simulation results from an MIT-BIH arrhythmia database demonstrate high average accuracies of 98, 98.79, 98.87, and 99.43 % of detected normal beats (N), supraventricular ectopic beats (S), ventricular ectopic beats (V), and fusing normal and ventricular ectopic beats (F), respectively. The proposed method is compared with five currently used methods and two conventional fusion methods by using the MIT-BIH database. The proposed method can improve ECG classification results compared with other methods.

## 2 Methodology

- (1)
In the pre-processing stage, baseline and high-frequency noises are initially removed from the original input ECG signals. Heartbeats are then segmented on the detected real R points.

- (2)
In the feature extraction stage, wavelet-packet decomposition is used to extract WP coefficients as heartbeat features. Fourth-level decompositions are used as features in the following procedure.

- (3)
In the feature-fusion stage, all of the extracted features of an ECG heartbeat are arranged as a two-way tensor, in which feature-fusion procedure is implemented using a multi-linear subspace-learning method, GND-ICA.

- (4)
In the classification stage, SVM is directly used as a classifier in final-heartbeat classification.

### 2.1 Pre-processing

### 2.2 Feature extraction

After wavelet-packet analysis of a heartbeat is conducted, a rich collection of abundant information with arbitrary time-frequency resolution is obtained. This information shows that non-stationary and stationary characteristics of the extracted features are combined.

### 2.3 Feature fusion

After extracting wavelet coefficients in the fourth-level decomposition of an ECG signal, we aim to fuse all of the features to effectively classify heartbeats. A concept of tensor-based multi-linear subspace-learning method called generalized N dimensional independent component analysis (GND-ICA) is introduced to perform multiple-feature fusion. It can effectively combine and select all of the features extracted from the original signal and considers the interrelationship among different wavelet-packet coefficients. A concept of “tensor” is introduced to arrange all of the features of one heartbeat. A tensor is an *N*-way array [13], and the order of a tensor is known as mode [14].

*I*

_{1}-D), and mode-2 is represented by the number of features (

*I*

_{2}-D). This two-way tensor is presented in Fig. 6. In this manner, the factor inherent to the element of feature vectors and the factor among different features can be disentangled. An optimal de-mixing matrix on each mode is determined by GND-ICA with a series of training tensor samples [17].

where **A**
_{
z
}, *z* = 1, 2 is the pseudo-inverse of the de-mixing matrix **W**
_{
z
}, *z* = 1, 2.

**W**

_{ z },

*z*= 1, 2 in each mode of feature representation \( {X}^{te}\in {R}^{I_1\times {I}_2} \). In this process, the factor inherent to the element of feature vectors and the factor among different features are considered. Thus, we obtain the following expression:

### 2.4 Classification

After distinguishing features are extracted from each heartbeat, a classifier is applied to provide the ECG heartbeat classification. In this paper, SVM [19], as an effective tool used to solve numerous classification problems, is used in heartbeat classification.

In our study, LIBSVM package is used. For fair comparison, the optimum parameters of the kernel function (radial basis function) are assigned to SVM for each signal representation [20].

## 3 Experimental results

The MIT-BIH arrhythmia database is utilized in our study [21, 22]. Approximately 109,000 heartbeats contained in 48 ECG recordings can be achieved for approximately 30 min in each recording. MIT-BIT heartbeat types are classified into five main classes according to the standards recommended by the Association for the Advancement of Medical Instrumentation. Heartbeats belonging to class N and originating from the sinus node are normal and bundle-branch-block beat types. Supraventricular ectopic beats and ventricular ectopic beats belong to classes S and V, respectively. Fused normal and ventricular ectopic beats belong to class F. The unknown heartbeats, including paced beats, are classified in class Q. The ECG signals of the MIT-BIH arrhythmia database are sampled at 360Hz, and 200 sampling points are used for signal representation.

Training and test beats of randomly selected data for each class

Class | N | S | V | F |
---|---|---|---|---|

Training | 15019 | 1391 | 3740 | 401 |

Test | 15019 | 1390 | 3740 | 401 |

WPD was computed in each of the ECG heartbeat by using discrete approximation of the Meyer wavelet, which is considered as the most efficient decomposition of feature extraction [24]. All of the decomposition coefficients in the fourth level are used as features, with 16 sets of vectors and 107 components. The performance of the multi-linear subspace-learning method GND-ICA and the linear subspace-learning method PCA of heartbeat classification is described in terms of sensitivity, positive predictivity, accuracy, and average accuracy.

### 3.1 Evaluation criterion

*i*,

*j*∈ {N, S, V, F},

*C*

_{ i,j }is the number of heartbeats of class

*i*classified as

*j*. If ∀

*i*≠

*j*, then

*C*

_{ i,j }is an incorrectly classified heartbeat, whereas

*C*

_{ i,i }is a correctly classified heartbeat [7]. We define

*B*

_{ j }= ∑

_{∀ j }

*C*

_{ i,j }as the total number of examples originally belonging to class

*i*;

*A*

_{ j }= ∑

_{∀ i }

*C*

_{ i,j }as the total number of examples labeled as class

*j*; and

*C*

_{ total }= ∑

_{∀ i ∀ j }

*C*

_{ i,j }. We denote

*TP*

_{ i }=

*C*

_{ i,i }as the true positives of

*I*,

*TN*

_{ i }=

*C*

_{ total }−

*B*

_{ i }−

*A*

_{ i }+

*C*

_{ i,i }as the true negatives of

*I*,

*FP*

_{ i }=

*A*

_{ i }−

*C*

_{ i,i }as the false positives of

*I*, and

*FN*

_{ i }=

*B*

_{ i }−

*C*

_{ i,i }as the true negatives of

*i*. The accuracy (

*AC*

_{ i }) of

*i*is the proportion of the total number of correct predictions defined as follows:

*Sens*

_{ i }) of

*i*refers to the ability of the method to correctly identify the heartbeat with the corresponding class.

*PPV*

_{ i }) of

*i*is a proportion used to determine the probability that the result actually belongs to a particular class if the result is positive:

*MAC*

_{ total }) is defined as Eq. 22 corresponding to the average classification rate of all classes:

### 3.2 Classification performance of different features

*MAC*

_{ total }is plotted with respect to different gamma values (Fig. 9). The highest-average accuracy is provided at gamma = 0.7, and the corresponding average accuracy is 97.54 % (Fig. 9).

### 3.3 Classification Evaluation with Different Criteria

Considering that the average accuracy is changed according to dimension reduction, we select the highest-classification rate to compare our results.

Confusion matrices of (a) WPD-based classification, (b) PCA-based classification, and (c) GND-ICA based classification

(a) WPD | Algorithm label | |||||
---|---|---|---|---|---|---|

N | S | V | F | Σ | ||

Original label | N | 14869 | 81 | 60 | 9 | 15019 |

S | 230 | 1137 | 23 | 0 | 1390 | |

V | 247 | 13 | 3467 | 13 | 3741 | |

F | 56 | 3 | 43 | 299 | 401 | |

Σ | 15402 | 1234 | 3593 | 321 | 20550 | |

(b) PCA | Algorithm Label | |||||

N | S | V | F | Σ | ||

Original label | N | 14851 | 58 | 94 | 16 | 15019 |

S | 276 | 1063 | 51 | 0 | 1390 | |

V | 164 | 25 | 3527 | 24 | 3740 | |

F | 96 | 2 | 31 | 272 | 401 | |

Σ | 15387 | 1148 | 3703 | 312 | 20550 | |

(c) GND-ICA | Algorithm label | |||||

N | S | V | F | Σ | ||

Original label | N | 14884 | 65 | 58 | 12 | 15019 |

S | 143 | 1224 | 22 | 1 | 1390 | |

V | 92 | 18 | 3624 | 16 | 3740 | |

F | 52 | 0 | 37 | 312 | 401 | |

Σ | 15161 | 1307 | 3741 | 341 | 20550 |

Performance analysis of the classification with SVM based on the original WPD features, PCA-based features, and GND-ICA based features in terms of above introduced four measures in percentage

Features | N | S | V | F | MAC | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

AC | Sens | PPV | AC | Sens | PPV | AC | Sens | PPV | AC | Sens | PPV | ||

WPD | 96.68 | 99.00 | 96.54 | 98.30 | 81.80 | 92.14 | 98.06 | 92.70 | 96.49 | 99.40 | 74.56 | 93.15 | 96.21 |

PCA | 96.57 | 98.89 | 96.52 | 98.00 | 76.47 | 92.60 | 98.11 | 94.30 | 95.25 | 99.18 | 67.83 | 87.18 | 95.93 |

GND-ICA | 98.00 | 99.10 | 98.17 | 98.79 | 88.06 | 93.65 | 98.87 | 96.90 | 96.87 | 99.43 | 77.81 | 91.50 | 97.53 |

*t*-test is a statistical test that can be used to determine if two sets of groups are significantly different from each other. A

*p*value is a parameter of

*t*-test used to assess significant difference. In general, a

*p*value equal to or less than 0.05 is regarded as a significant difference and less than 0.01 is considered a highly significant difference. In addition, smaller

*p*value corresponds to greater significant difference between two groups. Table 4 shows the

*p*value obtained from algorithm-labeled class (GND-ICA) and conventional-labeled classes (WPD, PCA). After the difference between GND-ICA and WPD is evaluated, a highly significant difference is found between S and V. After the difference between GND-ICA and PCA is evaluated, a highly significant difference is found between S and V; likewise, a significant difference is observed in N. Therefore, highly significant differences are observed between GND-ICA and WPD and between GND-ICA and PCA. This result indicates that the average accuracy of the proposed method is only less than 2 % higher than that of WPD or PCA. However, highly significant differences can be achieved in ECG heartbeats classification.

p values for each class between different methods

N | S | V | F | Total | |
---|---|---|---|---|---|

GND-ICA | WPD | 0.2445 | 9.54e-10 | 1.42e-24 | 0.0930 | 1.01e-16 |

GND-ICA | PCA | 0.0127 | 1.34e-14 | 7.35e-13 | 0.1685 | 4.73e-10 |

### 3.4 Computational efficiency

Computational efficiency is investigated using the computing time of the transformation matrix of the methods with 16 dimensions. In the multi-linear subspace-learning methods, tensor mode 1 is reduced to 16-D, and mode 2 is reduced to 1-D. In all of the training heartbeats, GND-ICA requires 9.73 s to calculate the transformation matrices. This time is considerably shorter than 19.59 s, which is required by PCA.

### 3.5 Comparison with state-of-the-art methods

Comparison of different classification methods on the MIT-BIT arrhythmia database

Authors | Features | Classifier | Classes | Average accuracy |
---|---|---|---|---|

Manab Kumar Das et al. [26] | ST +WT + Temporal | MLP-NN | 5 | 97.5 % |

Inan et al. [27] | D | Neural network | 2 | 95.16 % |

Jiang et al. [28] | Hermite transform coefficients + time interval | Block-based neural networks | 5 | 96.6 % |

Ince et al. [29] | Morphological-wavelet transform + PCA, temporal features | Optimal artificial neural networks | 5 | 95.58 % |

Martis et al. [30] | Bispectrum + PCA | SVM with RBF kernel | 5 | 93.48 % |

Proposed method | WPD + GND_ICA | SVM with RBF kernel | 4 | 97.54 % |

## 4 Conclusions and discussion

ECG heartbeat classification is one of the most significant research fields in computer-aided diagnosis. A study of a feature-fusion method based on a multi-learning subspace-learning algorithm called GND-ICA for ECG heartbeat classification is proposed. The commonly used MIT-BIH arrhythmia database is employed in all of our experiments. ECG signals are segmented after baseline; high-frequency noise is removed and fiducial points are detected. Four groups labeled in the MIT-BIH arrhythmia database are selected and used in our classification study. These labeled ECG heartbeats include normal beats (N), supraventricular ectopic beats (S), ventricular ectopic beats (V), and fused normal and ventricular ectopic beats (F). Wavelet-packet decomposition, as a technique used to analyze the relationship between time and frequency information is also performed to extract features. Wavelet-packet coefficients extracted in the fourth level, which is composed of approximations and details, are used for further feature fusion. A total of 16 sets of coefficients with a size of 107 represent one ECG heartbeat simultaneously. In contrast to linear subspace-learning methods (PCA) in which all of the features should be transformed as a vector, multi-linear subspace-learning method (GND-ICA) can be used to process input data in a tensor form. Thus, 16 sets of coefficients features are further fused with GND-ICA by arranging them as a two-way tensor; in this technique, the factor inherent in the element of feature vectors and the factor among different features are considered. With SVM, the fused features are used to discriminate four different types of heartbeats. Five common evaluation criteria, including sensitivity, positive predictivity, accuracy, average accuracy, and *t*-test, are used to investigate classification performance. Based on the classification results, our conclusion is that performance of GND-ICA-based feature fusion is more distinguished than that of the linear subspace-learning method PCA. Furthermore, the computing time of the transformation matrices of GND-ICA is considerably shorter than that of conventional PCA. Thus, GND-ICA not only improves the classification time but also eliminates numerous redundant features, prevents the drawbacks of dimensionality.

## Declarations

### Acknowledgements

This work was supported by the National Basic Research Program of China (2013CB328806), the Key Projects in the National Science & Technology Pillar Program (2012BAI02B01), China Postdoctoral Science Foundation funded project (2014M560050).

## Authors’ Affiliations

## References

- S Mendis, P Puska, B Norrving, Global Atlas on cardiovascular disease prevention and control. World Health Organization, ISBN: 978 92 4 156437 3, 1-168 (2011).Google Scholar
- M Javadi, R Ebrahimpour, A Sajedin, S Faridi, S Zakernejad, Improving ECG classification accuracy using an ensemble of neural network modules. PLoS one
**6**(10), e24386 (2011). doi:10.1371/journal.pone.0024386 View ArticleGoogle Scholar - M Llamedo, JP Martinez, Heartbeat classifier using feature selection driven by database generalization criteria. IEEE Trans. Biomed. Eng.
**58**(3), 616–625 (2011)View ArticleGoogle Scholar - I Jekova, G Bortolan, I Christov, Assessment and comparison of different methods for heartbeat classification. Med. Eng. Phys.
**30**(2), 248–257 (2008)View ArticleGoogle Scholar - LI Kuncheva, Combining pattern classifiers: methods and algorithms. John Wiley & Sons, ISBN: 978-0-471-21078-8, 1-376 (2004).Google Scholar
- Y Kutlu, D Kuntalp, Feature extraction for ECG heartbeats using higher order statistics of WPD coefficients. Comput. Methods Programs Biomed.
**105**(3), 257–267 (2012)View ArticleGoogle Scholar - T Mar, S Zaunseder, JP Martinez, M Llamedo, R Poll, Optimization of ECG classification by means of feature selection. IEEE Trans. Biomed. Eng.
**58**(8), 2168–2177 (2011)View ArticleGoogle Scholar - RJ Martis, UR Acharya, CM Lim, ECG beat classification using PCA, LDA ICA and discrete wavelet transform. Biomed. Signal Process. Control
**8**(5), 437–448 (2013)View ArticleGoogle Scholar - DN Ai, GF Duan, XH Han, YW Chen, Generalized N-dimensional independent component analysis and its application to multiple feature selection and fusion for image classification. Neurocomputing
**103**, 186–197 (2013)View ArticleGoogle Scholar - P de Chazal, M O'Dwyer, RB Reilly, Automatic classification of heartbeats using ECG morphology and heartbeat interval features. IEEE Trans. Biomed. Eng.
**51**(7), 1196–1206 (2004)View ArticleGoogle Scholar - MY Gokhale, DK Khanduja, Time domain signal analysis using wavelet packet decomposition approach. Int. J. Commun. Network Syst. Sci.
**3**(3), 321–329 (2010)View ArticleGoogle Scholar - I Khalil, F Sufi, Real-time ECG data transmission with wavelet packet decomposition over wireless networks, International Conference on Intelligent Sensors. Sens. Networks Inf. Process. , E-ISBN 978-1-4244-2957-8, 267–272 (2008)Google Scholar
- TG Kolda, BW Bader, Tensor decompositions and applications. SIAM Rev.
**51**(3), 455–500 (2009)MATHMathSciNetView ArticleGoogle Scholar - L de Lathauwer, B de Moor, J Vandewalle, On the best rank-1 and rank-(R1, R2, …, Rn) approximation of higher order tensors. SIAM J. Matrix Anal. Appl.
**21**(4), 1324–1342 (2000)MATHMathSciNetView ArticleGoogle Scholar - S Yan, D Xu, Q Yang, H Zhang et al., Multilinear discriminant analysis for face recognition. IEEE Trans. Image Process.
**16**(1), 212–220 (2007)MathSciNetView ArticleGoogle Scholar - R Xu, YW Chen, Generalized N-dimensional principal component analysis (GND-PCA) and its application on construction of statistical appearance models for medical volumes with fewer samples. Neurocomputing
**72**(10), 2276–2287 (2009)View ArticleGoogle Scholar - XH Han, YW Chen, X Ruan, Multilinear supervised neighborhood embedding of a local descriptor tensor for scene/object recognition. IEEE Trans. Image Process.
**21**(3), 1314–1326 (2012)MathSciNetView ArticleGoogle Scholar - AJ Bell, TJ Sejnowski, An information-maximization approach to blind separation and blind deconvolution. Neural Comput.
**7**(6), 1129–1159 (1995)View ArticleGoogle Scholar - BM Asl, SK Setarehdan, M Mohebbi, Support vector machine-based arrhythmia classification using reduced features of heart rate variability signal. Artif. Intell. Med.
**44**(1), 51–64 (2008)View ArticleGoogle Scholar - RE Fan, PH Chen, CJ Lin, Working set selection using second order information for training SVM. J. Mach. Learn. Res.
**6**, 1889–1918 (2005)MATHMathSciNetGoogle Scholar - GB Moody, RG Mark, The impact of the MIT-BIH arrhythmia database. IEEE Eng. Med. Biol. Mag.
**20**(3), 45–50 (2011)View ArticleGoogle Scholar - AL Goldberger, LAN Amaral, L Glass, JM Hausdorff, PC Ivanov, RG Mark, JE Mietus, GB Moody, CK Peng, HE Stanley, Physiobank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals. Circulation
**101**(23), e215–e220 (2000)View ArticleGoogle Scholar - B Mali, S Zulj, R Magjarevic, D Miklavcic, T Jarm, Matlab-based tool for ECG and HRV analysis. Biomed. Signal Process. Control
**10**, 108–116 (2014)View ArticleGoogle Scholar - RJ Martis, UR Acharya, AK Ray, C Chakraborty, Application of higher order cumulants to ECG signals for the cardiac health diagnosis, Engineering in Medicine and Biology Society, EMBC, 2011 Annual International Conference of the IEEE, August 30 2011-September 3 2011, 1697–1700 (2011)Google Scholar
- RO Duda, PE Hart, DG Stork,
*Pattern classification*, 2nd edn. (John Wiley & Sons, New York, 2001)MATHGoogle Scholar - MK Das, S Ari, ECG beats classification using mixture of features. Int. Scholarly Res. Not. 2014, Article ID 178436, 12 pages (2014)Google Scholar
- OT Inan, L Giovangrandi, GTA Kovacs, Robust neural-network-based classification of premature ventricular contractions using wavelet transform and timing interval features. IEEE Trans. Biomed. Eng.
**53**(12), 2507–2515 (2006)View ArticleGoogle Scholar - W Jiang, SG Kong, Block-based neural networks for personalized ECG signal classification. IEEE Trans. Neural Networks
**18**(6), 1750–1761 (2007)View ArticleGoogle Scholar - T Ince, S Kiranyaz, M Gabbouj, A generic and robust system for automated patient-specific classification of ECG signals. IEEE Trans. Biomed. Eng.
**56**(5), 1415–1426 (2009)View ArticleGoogle Scholar - RJ Martis, UR Acharya, KM Mandana, AK Ray, C Chakraborty, Cardiac decision making using higher order spectra. Biomed. Signal Process. Control
**8**(2), 193–203 (2013)View ArticleGoogle Scholar

## Copyright

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.