# A New 12-Lead ECG Signals Fusion Method Using Evolutionary CNN Trees for Arrhythmia Detection

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## Abstract

**:**

## 1. Introduction

## 2. ECG Data

## 3. The Proposed Method

- Employing the approach of trajectory image creation at ECG signals instead of raw signals to increment the integration of the proposed model;
- Proposing a genetic programming-based model to learn deep features at ECG signals and employing several genes at GP to fusion these features.

#### 3.1. Wavelet Decomposition of ECG Signal

#### 3.2. Calculate Cross-Correlation between 12-Lead ECG

#### 3.3. ECG Trajectory Image Presentation

#### 3.4. Feature Learning Using the Evolutionary CNN Tree

## 4. Results

^{−3}for the first half and then multiplied by 0.1 per quarter [25].

#### 4.1. Results Analysis Method

#### 4.2. Evaluating the Proposed Method through 12 Leads

#### 4.3. Comparing the Proposed Fusion Algorithm with the Other Deep-Learning Methods

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**A sample of the signals of the Chapman ECG dataset, which has undergone noise reduction operation: (

**a**) ECG raw signal with 3000 samples; (

**b**) spectrogram of the raw signal; (

**c**) smoothed ECG signal; (

**d**) spectrogram of the smoothed signal.

**Figure 2.**The proposed model for 12-lead electrocardiogram signals fusion approach for heart defect detection.

**Figure 3.**Calculate cross-correlation between 12-lead ECG, (

**a**) lead I signal, (

**b**) lead I signal approximation, (

**c**) lead II signal, (

**d**) lead II signal approximation.

**Figure 4.**Cross-correlation output between the approximation signal of the leads I and II of the ECG signals, (

**a**) lead I and II signals, (

**b**) cross correlation between lead I and II.

**Figure 5.**ECG trajectories in the frequency domain for 12-lead ECG signal, (

**a**) the graphic display of the calculation of correlation between lead I and lead III, (

**b**) the obtained trajectory of the spectrogram of lead I and lead III.

**Figure 6.**An instance of CNN tree: the green nodes are the input layers, the blue nodes are the morphological convolutional layers, the red nodes are the pooling layers, the black nodes are the concatenation layers, and the gray node is the output layer.

**Figure 7.**The confusion matrix of the proposed fusion algorithm with all ECG 12 leads and its convergence rate curve, (

**a**) confusion matrix, (

**b**) convergence rate curve.

Description | Method |
---|---|

$\mathrm{Carrying}\mathrm{out}\mathrm{morphology}\mathrm{convolution}\mathrm{operations}\mathrm{on}{S}_{1}\mathrm{matrix}\mathrm{with}\mathrm{Kernel}\mathrm{filter}k$ | $\mathrm{Conv}({S}_{1},k)$ |

$\mathrm{Subtraction}\mathrm{of}\mathrm{matrices}\mathrm{of}{S}_{1}$$\mathrm{and}{S}_{2}$$,\mathrm{bearing}\mathrm{weights}\mathrm{of}{n}_{1}$$\mathrm{and}{n}_{2}$ | $\mathrm{Sub}({S}_{1}$$,{S}_{2}$$,{n}_{1}$$,{n}_{2}$) |

$\mathrm{Addition}\mathrm{of}\mathrm{matrices}\mathrm{of}{S}_{1}$$\mathrm{and}{n}_{2}$$,\mathrm{bearing}\mathrm{weights}\mathrm{of}{n}_{1}$$\mathrm{and}{n}_{2}$ | $\mathrm{Add}({S}_{1}$$,{S}_{2}$$,{n}_{1}$$,{n}_{2}$) |

$\mathrm{Return}\mathrm{of}max\left(0,x\right)\mathrm{for}\mathrm{each}x\mathrm{in}{S}_{1}$ matrix | $\mathrm{ReLU}({S}_{1}$) |

$\mathrm{Return}\mathrm{of}\sqrt{x}\mathrm{for}\mathrm{each}x\mathrm{in}{S}_{1}$ matrix | $\mathrm{Sqrt}({S}_{1}$) |

$\mathrm{Return}\mathrm{of}\left|x\right|\mathrm{for}\mathrm{each}x\mathrm{in}{S}_{1}$ matrix | $\mathrm{Abs}({S}_{1}$) |

$\mathrm{Applying}\mathrm{max}\text{-}\mathrm{pooling}\mathrm{to}{S}_{1}$$\mathrm{matrix}\mathrm{using}\mathrm{Kernel}\mathrm{filter}\mathrm{with}\mathrm{a}\mathrm{measurement}\mathrm{of}{k}_{1}$$\mathrm{and}{k}_{2}$ | $\mathrm{MaxP}({S}_{1}$$,{k}_{1}$$,{k}_{2}$) |

$\mathrm{Connecting}\mathrm{two}{S}_{1}$$\mathrm{and}{S}_{2}$ matrices together as a diagram | $\mathrm{Concat}2({S}_{1}$$,{S}_{2}$) |

$\mathrm{Connecting}\mathrm{three}{S}_{1}$$\mathrm{to}{S}_{3}$ matrices together as a diagram | $\mathrm{Concat}3({S}_{1}$$,{S}_{2}$$,{S}_{3}$) |

$\mathrm{Connecting}\mathrm{four}{S}_{1}$$\mathrm{to}{S}_{4}$ matrices together as a diagram | $\mathrm{Concat}4({S}_{1}$$,{S}_{2}$$,{S}_{3}$$,{S}_{4}$) |

Description | Value Range | Terminal |
---|---|---|

The input matrix includes functional relativity information | [−1,1] | ${x}_{i}$ |

$\mathrm{Filter}\mathrm{at}\mathrm{the}\mathrm{size}\mathrm{of}3\times 3$ in MConv function | {0,1} [24] | $filte{r}_{3\times 3}$ |

$\mathrm{Filter}\mathrm{at}\mathrm{the}\mathrm{size}\mathrm{of}5\times 5$ in MConv function | {0,1} | $filte{r}_{5\times 5}$ |

$\mathrm{Filter}\mathrm{at}\mathrm{the}\mathrm{size}\mathrm{of}7\times 7$ in MConv function | {0,1} | $filte{r}_{7\times 7}$ |

Random numbers that are the inputs of Add and Sub functions. | [0.000,1.000] | ${n}_{1}$$,{n}_{2}$ |

The kernel measurement of MaxP function | {2,4} | ${k}_{1}$$,{k}_{2}$ |

Predicted Label | ||||||||
---|---|---|---|---|---|---|---|---|

AF | SB | SVT | ST | SR | AFIB | SI | ||

True Label | AF | ${c}_{AF,AF}$ | ${c}_{AF,SB}$ | ${c}_{AF,SVT}$ | ${c}_{AF,ST}$ | ${c}_{AF,SR}$ | ${c}_{AF,AFIB}$ | ${c}_{AF,SI}$ |

SB | ${c}_{SB,AF}$ | ${c}_{SB,SB}$ | ${c}_{SB,SVT}$ | ${c}_{SB,ST}$ | ${c}_{SB,SR}$ | ${c}_{SB,AFIB}$ | ${c}_{SB,SI}$ | |

SVT | ${c}_{SVT,AF}$ | ${c}_{SVT,SB}$ | ${c}_{SVT,SVT}$ | ${c}_{SVT,ST}$ | ${c}_{SVT,SR}$ | ${c}_{SVT,AFIB}$ | ${c}_{SVT,SI}$ | |

ST | ${c}_{ST,AF}$ | ${c}_{ST,SB}$ | ${c}_{ST,SVT}$ | ${c}_{ST,ST}$ | ${c}_{ST,SR}$ | ${c}_{ST,AFIB}$ | ${c}_{ST,SI}$ | |

SR | ${c}_{SR,AF}$ | ${c}_{SR,SB}$ | ${c}_{SR,SVT}$ | ${c}_{SR,ST}$ | ${c}_{SR,SR}$ | ${c}_{SR,AFIB}$ | ${c}_{SR,SI}$ | |

AFIB | ${c}_{AFIB,AF}$ | ${c}_{AFIB,SB}$ | ${c}_{AFIB,SVT}$ | ${c}_{AFIB,ST}$ | ${c}_{AFIB,SR}$ | ${c}_{AFIB,AFIB}$ | ${c}_{AFIB,SI}$ | |

SI | ${c}_{SI,AF}$ | ${c}_{SI,SB}$ | ${c}_{SI,SVT}$ | ${c}_{SI,ST}$ | ${c}_{SI,SR}$ | ${c}_{SI,AFIB}$ | ${c}_{SI,SI}$ |

Class Name | $\mathit{P}\mathit{R}\mathit{E}{\mathit{C}}_{\mathit{c}\mathit{l}}$ (%) | $\mathit{S}\mathit{E}{\mathit{N}}_{\mathit{c}\mathit{l}}(\%)$ | $\mathit{S}\mathit{P}\mathit{E}{\mathit{C}}_{\mathit{c}\mathit{l}}(\%)$ | $\mathit{A}\mathit{C}{\mathit{C}}_{\mathit{c}\mathit{l}}(\%)$ |
---|---|---|---|---|

AF | 97.47 ± 0.5 | 97.93 ± 0.4 | 96.64 ± 0.2 | 97.25 ± 0.3 |

SB | 97.83 ± 0.7 | 97.59 ± 0.6 | 96.26 ± 0.7 | 97.45 ± 0.7 |

SVT | 97.58 ± 0.8 | 97.37 ± 0.6 | 96.44 ± 1.0 | 96.87 ± 1.0 |

ST | 96.93 ± 0.0 | 97.93 ± 0.4 | 96.69 ± 0.6 | 96.36 ± 0.3 |

SR | 97.60 ± 0.2 | 97.96 ± 1.1 | 97.69 ± 0.8 | 96.70 ± 1.0 |

AFIB | 98.94 ± 0.7 | 96.79 ± 1.0 | 97.00 ± 1.1 | 97.56 ± 1.1 |

SI | 96.88 ± 0.4 | 96.38 ± 0.7 | 97.47 ± 0.7 | 97.47 ± 0.7 |

Average | 97.09 ± 0.7 | 96.88 ± 0.7 | 97.42 ± 0.7 | 97.60 ± 0.5 |

Training Phase | Validation Phase | Testing Phase | |
---|---|---|---|

CPU Time | 15:10:30 | 00:30:50 | 00:31:40 |

**Table 6.**Comparing the proposed fusion algorithm with the other state-of-the-art methods in performance.

References | #Subjects | #Records | #Rhythm | Method | Performance |
---|---|---|---|---|---|

Acharya et al. [30] | 47 | 109,449 | 5 Class | CNN | Acc: 94.03 |

Xu et al. [31] | 22 | 50,977 | 5 Class | DNN | Acc: 93.10 |

Gao et al. [32] | - | 93,371 | 8 Heartbeats | LSTM | Acc: 90.26 |

Hannun et al. [33] | 53,549 | 91,232 | 12 Rhythm | CNN | F1: 83.00 |

Yildirim et al. [34] | 45 | 1000 | 5 Heartbeats | CNN | Acc: 91.33 |

Shaker et al. [35] | 44 | 102,098 | 12 Class | CNN | Acc: 94.30 |

Oh et al. [27] | 47 | 16,499 | 5 Heartbeats | UNet | Acc: 93.10 |

Xiong et al. [36] | 12,186 | 12,186 | 4 Class | CNN + RNN | F1: 82.00 |

Oh et al. [28] | 170 | 150,268 | 3 Cardiac Disease | CNN + LSTM | Acc: 94.51 |

Mousavi et al. [37] | - | 750 | 5 Rhythm | CNN + LSTM | Acc: 93.75 |

Wu et al. [38] | - | 8528 | 4 Class | Binarized CNN | F1: 86.00 |

Fujita et al. [26] | 47 | 109,449 | 4 Class | Normalization + CNN | Acc: 93.45 |

Salem et al. [39] | 22 | 7000 | 4 Class | STFT + CNN | Acc: 94.23 |

Xia et al. [40] | - | - | 2 Class | SWT + CNN | Acc: 95.63 |

Yildirim et al. [29] | 10,436 | 10,436 | 7 Rhythm | CNN + LSTM | Acc: 92.24 |

Mehari et al. [41] | 10,646 | 10,646 | 7 Rhythm | Single Classifier | Acc: 92.89 |

Rahul et al. [42] | 10,646 | 10,646 | 7 Rhythm | 1-D CNN | Acc: 94.01 |

Kang et al. [43] | 10,646 | 10,646 | 7 Rhythm | RNN | Acc: 96.21 |

Proposed Method | 10,646 | 10,646 | 7 Rhythm | 12 Lead Fusion + CNN Trees | Acc: 97.60 |

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**MDPI and ACS Style**

Meqdad, M.N.; Abdali-Mohammadi, F.; Kadry, S.
A New 12-Lead ECG Signals Fusion Method Using Evolutionary CNN Trees for Arrhythmia Detection. *Mathematics* **2022**, *10*, 1911.
https://doi.org/10.3390/math10111911

**AMA Style**

Meqdad MN, Abdali-Mohammadi F, Kadry S.
A New 12-Lead ECG Signals Fusion Method Using Evolutionary CNN Trees for Arrhythmia Detection. *Mathematics*. 2022; 10(11):1911.
https://doi.org/10.3390/math10111911

**Chicago/Turabian Style**

Meqdad, Maytham N., Fardin Abdali-Mohammadi, and Seifedine Kadry.
2022. "A New 12-Lead ECG Signals Fusion Method Using Evolutionary CNN Trees for Arrhythmia Detection" *Mathematics* 10, no. 11: 1911.
https://doi.org/10.3390/math10111911