# Unsupervised Learning-Based Non-Invasive Fetal ECG Muti-Level Signal Quality Assessment

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## Abstract

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## 1. Introduction

## 2. Related Work

## 3. Preliminaries

#### 3.1. Non-Invasive Fetal ECG

#### 3.2. Short-Time Fourier Transform

#### 3.3. Autoencoder

#### 3.4. Self-Organizing Map

- Initialize all the weight vectors randomly.
- Select an input sample from the training set $\mathbf{x}={({x}_{1},{x}_{2},{x}_{3},...,{x}_{n})}^{T}$.
- By computing the Euclidean distance for each neuron k, compare $\mathbf{x}$ with the weights ${\mathbf{W}}_{k}$. The neuron with the shortest distance is declared as the winning neuron.
- After updating the weights of neurons, the winning neuron should resemble the input vector $\mathbf{x}$.
- The weight vectors of neighboring neurons are changed to more closely resemble the input vector. A weight vector changes more as the neuron gets closer to the winning neuron.

## 4. Proposed Method

#### 4.1. Data Acquisition

#### 4.2. Signal Pre-Processing

#### 4.3. Feature Extraction

#### 4.3.1. AE-Based Feature

#### 4.3.2. Entropy-Based Features

- Approximate entropy (AppEn): AppEn is a common-use feature for quantifying irregularity in time series data with no knowledge about the system. Larger values of AppEn correspond to more complexity and irregularity in the data [14].
- Sample entropy (SampEn): To overcome the shortcomings of AppEn, including heavy dependency on the length of the recording and lack of relative consistency, SampEn was introduced. Compared with AppEn, SampEn avoids self-matches, so it can be independent of the length of recordings and extract relative consistency [15].
- Spectral entropy (SpecEn): Spectral entropy, based on Shannon entropy, can quantify the regularity or uncertainty of the power spectrum during a specific period. In actuality, the regularity of the power spectrum distribution is mirrored in spectral entropy. The higher SpecEn indicates a more uniform power spectrum distribution [16].
- Permutation entropy (PEn): A continuous time series can be transformed into a symbolic sequence using the permutation approach, and PEn is the output of the statistics of the symbolic sequences. PEn of time series data, which can be calculated simply and quickly, contains temporal information [17].

#### 4.3.3. Statistical Features

- Detrended fluctuation analysis (DFA): The main purpose of DFA is to extract long-range correlation in non-stationary time series. Many researchers have used DFA for analyzing cardiac interbeat intervals [18].
- Fractal dimension (FD): FD is a quantitative metric used in biomedical signal processing to gauge the complexity of discrete temporal physiological data. FD can aid in the understanding of physiological processes [19].
- Higuchi fractal dimension (HFD): Higuchi’s approach to FD calculation is proved to reach accurate and reliable estimation results, which is called HFD. This technique can be used to compute moving window estimates of FD for non-stationary signals by segmenting signals into brief quasi-stationary frames. It is also suited for estimating FD of segments with a short time duration of time series [19].

#### 4.3.4. ECG SQIs

- kSQI: The kurtosis of the ECG signal.
- sSQI: The skewness of the ECG signal.
- pSQI: The relative power in the QRS complex. pSQI is given by Equation (2):$$pSQI=\frac{{\int}_{5}^{15}P\left(f\right)\mathrm{d}f}{{\int}_{5}^{40}P\left(f\right)\mathrm{d}f},$$
- basSQI: The relative power in the baseline. basSQI is given by Equation (3):$$basSQI=1-\frac{{\int}_{0}^{1}P\left(f\right)\mathrm{d}f}{{\int}_{0}^{40}P\left(f\right)\mathrm{d}f},$$

#### 4.4. Multi-Level Signal Quality Classification

- Size of output layer: 8 × 8.
- Initial value of learning rate: 0.5.
- The number of iterations: 100,000.
- Neighborhood function: bubble.

#### 4.5. Performance Evaluation

#### 4.5.1. For Classification Performance

- Precision: the proportion of the FECG segments correctly predicted as one class in all the FECG segments predicted as the class.
- Recall: the proportion of the FECG segments correctly predicted as one class in all the FECG segments labeled as the class.
- F1-score: the harmonic mean of precision and recall.

#### 4.5.2. For Improvement of FHR Estimation

- Root mean square error (RMSE) between the estimated fetal RR interval (FRRI) value $\widehat{FRRI}$ and the reference value $FRRI$, which is given as follows:$$RMSE=\sqrt{\frac{1}{\mathsf{\Gamma}}\sum _{i=1}^{\mathsf{\Gamma}}\left|\right|{\widehat{FRRI}}_{i}-FRR{I}_{i}{\left|\right|}_{2}^{2}},\phantom{\rule{2.em}{0ex}}$$
- Averaged absolute error (AAE) between the estimated value $\widehat{FHR}$ and the reference value $FHR$$$\begin{array}{cc}\hfill AAE& =\frac{1}{\mathsf{\Gamma}}\sum _{i=1}^{\mathsf{\Gamma}}\left|\right|{\widehat{FHR}}_{i}-FH{R}_{i}\left|\right|\hfill \\ & =\frac{1}{\mathsf{\Gamma}}\sum _{i=1}^{\mathsf{\Gamma}}\left|\right|\frac{60\xb7{F}_{s}}{{\widehat{FRRI}}_{i}}-\frac{60\xb7{F}_{s}}{FRR{I}_{i}}\left|\right|,\hfill \end{array}\phantom{\rule{2.em}{0ex}}$$
- The removal rate, which is the proportion of the removed FHRs through the method over all the estimated FHRs.

## 5. Results and Discussion

#### 5.1. Feature Evaluation

#### 5.2. Classification Evaluation

#### 5.3. Improvement of FHR Estimation

#### 5.4. Limitation and Future Works

#### 5.4.1. About the Number of Quality Levels

#### 5.4.2. About the Unbalanced Dataset

#### 5.4.3. About the Coverage

#### 5.4.4. About Practical Application

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Invasive and non-invasive FECG measurement. (

**a**) The invasive FECG signals are extracted by placing the electrode on the scalp of a fetus. (

**b**) The non-invasive FECG signals are recorded from the electrodes placed on the maternal abdomen using portable, wearable devices.

**Figure 2.**The overall structure of our proposal. The 1D processed FECG signal segments are used to extract entropy-based features, statistical features, and ECG SQIs. Moreover, the 2D spectrograms generated from FECG signals are used to extract an AE-based feature associated with an FCN-based autoencoder. These extracted features are fed into SOM and three quality levels can be identified.

**Figure 3.**Examples of high, medium, and low-quality FECG signal segments and their corresponding spectrograms. Compared with the high-quality signal segment and spectrogram, the medium-quality one contains some tiny noise, and the low-quality one contains much more noise interference. (

**a**,

**b**) high-quality FECG signal segments and corresponding spectrogram; (

**c**,

**d**) medium-quality FECG signal segments and corresponding spectrogram; (

**e**,

**f**) low-quality FECG signal segments and corresponding spectrogram.

**Figure 4.**The structure of AE. There are two parts: encoder and decoder. A 2D convolutional (or deconvolution) layer, a batch normalization layer, and an activation layer are composed of an FCN layer. Both in the encoder and the decoder, there are 6 FCN layers.

**Figure 5.**Channel usability evaluation. The smaller value of the channel usability indicator means the higher usability.

**Figure 6.**MCFS score for each feature. A feature with a larger score means that this feature plays a more significant role in the classification task. Relatively, five features, including SampEn, HFD, kSQI, sSQI, and AE_MSE, have higher MCFS score than the other features.

**Figure 8.**Examples of FHR estimation results with and without removal. It is obvious that the estimated FHRs with large errors are correctly removed by our proposed method.

**Table 1.**Summary of the results obtained using different clustering methods. The F1-score of high-, medium-, and low-quality data using SOM are the highest among all five methods. The bold numbers represent the highest value of each performance indicator.

Precision | Recall | F1-Score | ||
---|---|---|---|---|

K-means | Medium | 0.61 | 0.78 | 0.68 |

High | 0.80 | 0.75 | 0.78 | |

Low | 0.88 | 0.69 | 0.77 | |

Average | 0.76 | 0.74 | 0.74 | |

K-means++ | Medium | 0.61 | 0.77 | 0.68 |

High | 0.80 | 0.75 | 0.78 | |

Low | 0.87 | 0.69 | 0.77 | |

Average | 0.76 | 0.74 | 0.74 | |

Hierarchy Clustering | Medium | 0.55 | 0.91 | 0.69 |

High | 0.88 | 0.68 | 0.77 | |

Low | 0.97 | 0.56 | 0.71 | |

Average | 0.80 | 0.72 | 0.72 | |

Spectral Clustering | Medium | 0.55 | 0.80 | 0.65 |

High | 0.79 | 0.74 | 0.76 | |

Low | 0.87 | 0.53 | 0.66 | |

Average | 0.74 | 0.69 | 0.69 | |

SOM | Medium | 0.85 | 0.85 | 0.85 |

High | 0.92 | 0.96 | 0.94 | |

Low | 0.92 | 0.88 | 0.90 | |

Average | 0.90 | 0.90 | 0.90 |

**Table 2.**Comparison of RMSE [ms] of FRRI, AAE [bpm] of FHR, and Removal Rate. The RMSE and AAE are all reduced by removing the detected low-quality segments, in the meantime, the removal rate is controlled within 15%.

No Removal | With Removal | ||||
---|---|---|---|---|---|

Subject | RMSE [ms] | AAE [bpm] | RMSE [ms] | AAE [bpm] | Removal Rate |

1 | 0.0047 | 0.4835 | 0.0033 | 0.3045 | 21.61% |

2 | 0.0075 | 1.0433 | 0.0038 | 0.4722 | 27.47% |

3 | 0.0018 | 0.3687 | 0.0016 | 0.3472 | 8.42% |

4 | 0.0021 | 0.3447 | 0.0020 | 0.3334 | 9.52% |

5 | 0.0033 | 0.3478 | 0.0029 | 0.3212 | 7.69% |

6 | 0.0010 | 0.2133 | 0.0010 | 0.2043 | 10.26% |

7 | 0.0019 | 0.2915 | 0.0011 | 0.2264 | 13.19% |

8 | 0.0191 | 1.2037 | 0.0193 | 1.0410 | 9.52% |

9 | 0.0078 | 1.0200 | 0.0075 | 0.9871 | 12.09% |

10 | 0.0036 | 0.3664 | 0.0011 | 0.2130 | 12.09% |

Average | 0.0053 | 0.5683 | 0.0044 | 0.4450 | 13.18% |

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## Share and Cite

**MDPI and ACS Style**

Shi, X.; Yamamoto, K.; Ohtsuki, T.; Matsui, Y.; Owada, K.
Unsupervised Learning-Based Non-Invasive Fetal ECG Muti-Level Signal Quality Assessment. *Bioengineering* **2023**, *10*, 66.
https://doi.org/10.3390/bioengineering10010066

**AMA Style**

Shi X, Yamamoto K, Ohtsuki T, Matsui Y, Owada K.
Unsupervised Learning-Based Non-Invasive Fetal ECG Muti-Level Signal Quality Assessment. *Bioengineering*. 2023; 10(1):66.
https://doi.org/10.3390/bioengineering10010066

**Chicago/Turabian Style**

Shi, Xintong, Kohei Yamamoto, Tomoaki Ohtsuki, Yutaka Matsui, and Kazunari Owada.
2023. "Unsupervised Learning-Based Non-Invasive Fetal ECG Muti-Level Signal Quality Assessment" *Bioengineering* 10, no. 1: 66.
https://doi.org/10.3390/bioengineering10010066