# Quantitative Analysis Using Consecutive Time Window for Unobtrusive Atrial Fibrillation Detection Based on Ballistocardiogram Signal

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Signal Acquisition and Preprocessing

^{−11}C/N) was placed on the top of a regular bed mattress and located underneath the subjects’ thorax with a sampling rate of 125 Hz (see 2.1 of Figure 1). During the recording process, the raw BCG waveform was amplified, and a Butterworth band-pass filter [17,26] was designed with a passband frequency of 0.7 Hz to 10 Hz to remove the high-frequency noise and low-frequency respiratory components and the motion artifacts, which was aimed at achieving a pure BCG signal. The ECG signal was collected by a CT-08S Holter Recorder at a sampling rate of 200 Hz. In order to address the problem of different sampling rates with BCG signals, the ECG signal was down-sampled to 125 Hz based on synchronized time stamps.

#### 2.2. RP Reconstruction

#### 2.3. CTW–RQA Feature Extraction

**W**i are the time windows to be analyzed (i = 1, 2, …, n).

**W**ij refers to the jth RQA feature extracted from the ith time window (j = 1, 2, …, k), k is the number of RQA features.

**M**i represents the feature vector composed of k RQA features in the ith time window, and the CTW–RQA feature of each BCG segment is defined in Equation (5).

**M**1,

**M**2, …,

**M**n]

_{max}is the expression of the length of the longest vertical line; DIV is the reciprocal of ${L}_{max}$; ENTR is the percentage of the Shannon entropy of the probability distribution of the diagonal line lengths P(l); TREND is the percentage decrease of the RP towards its edges; CLUST is the percentage of the ratio of the number of closed triplets to the number of all triplets; $W{V}_{max}$ is the percentage of the length of the white vertical line.

#### 2.4. Feature Fusion

#### 2.4.1. Time and Time-Frequency Features and Energy Feature Extraction

#### 2.4.2. Feature Ranking and Selection

^{2}distribution of the test statistic. Its null hypothesis H0 is that the observed frequency does not differ from the expected frequency. The basic idea of this test is as follows: assume that H0 is established; then, calculate the χ

^{2}value based on this premise, which represents the degree of deviation between the observed value and the theoretical value. According to the χ

^{2}distribution and degrees of freedom, the probability p of obtaining the current statistic and more extreme cases can be determined under the condition that the H0 hypothesis holds. The chi-square test checks whether each feature is independent of the label. A small p-value for the test statistic indicates that the corresponding feature is dependent on the label, proving that the feature is important [33]. To amplify the difference between features, importance scores are proposed, as shown in Equation (9).

#### 2.4.3. Fusion Feature Extraction

## 3. Results

#### 3.1. AF Detection Based on the RP Diagram

#### 3.2. AF Detection Based on CTW–RQA Features

#### 3.3. AF Detection Based on Time and Time-Frequency Features and Energy Features

#### 3.4. AF Detection Based on Fusion Features

#### 3.5. AF Detection Based on Ranked Features

## 4. Discussion

#### 4.1. Effects of RP and RQA

#### 4.2. Effect of the Proposed CTW–RQA Features

#### 4.3. Effect of Fusion Features and Ranked Features

#### 4.4. Comparison with Existing Methods

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Method | ACC | PRE | SEN | SPE |
---|---|---|---|---|

KNN | 56.38 | 59.41 | 40.25 | 72.50 |

NB | 62.88 | 66.78 | 51.25 | 74.50 |

ENS | 77.88 | 80.38 | 73.75 | 82.00 |

RF | 83.50 | 85.64 | 80.50 | 86.50 |

DT | 79.63 | 79.70 | 79.50 | 79.75 |

Method | ACC | PRE | SEN | SPE |
---|---|---|---|---|

KNN | 56.50 | 65.52 | 36.19 | 78.95 |

NB | 69.38 | 69.15 | 75.24 | 62.89 |

ENS | 75.75 | 78.54 | 74.05 | 77.63 |

RF | 81.75 | 83.74 | 80.95 | 82.63 |

DT | 72.25 | 72.92 | 75.00 | 69.21 |

Method | ACC | PRE | SEN | SPE |
---|---|---|---|---|

KNN | 59.25 | 65.56 | 43.17 | 76.15 |

NB | 56.63 | 54.21 | 99.02 | 12.05 |

ENS | 81.25 | 80.95 | 82.93 | 79.49 |

RF | 89.38 | 90.52 | 88.54 | 90.26 |

DT | 78.88 | 78.76 | 80.49 | 77.18 |

Method | ACC | PRE | SEN | SPE |
---|---|---|---|---|

KNN | 63.13 | 67.52 | 47.31 | 78.24 |

NB | 61.13 | 55.85 | 97.70 | 26.16 |

ENS | 82.13 | 81.47 | 82.10 | 82.15 |

RF | 86.13 | 86.46 | 84.91 | 87.29 |

DT | 79.75 | 78.70 | 80.31 | 79.22 |

Method | ACC | PRE | SEN | SPE |
---|---|---|---|---|

KNN | 65.88 | 69.21 | 53.73 | 77.37 |

NB | 71.63 | 85.22 | 50.39 | 91.73 |

ENS | 84.38 | 83.33 | 84.83 | 83.94 |

RF | 87.63 | 85.89 | 89.20 | 86.13 |

DT | 79.38 | 76.79 | 82.52 | 76.40 |

Method | ACC | PRE | SEN | SPE |
---|---|---|---|---|

KNN | 58.38 | 59.00 | 50.76 | 65.76 |

NB | 72.13 | 68.31 | 80.96 | 63.55 |

ENS | 75.50 | 74.03 | 77.41 | 73.65 |

RF | 78.50 | 77.89 | 78.68 | 78.33 |

DT | 73.63 | 72.82 | 74.11 | 73.15 |

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**Figure 1.**The process of the proposed method in this paper, where 2.1, 2.2, 2.3, and 2.4 represent the corresponding sections in the Methods.

**Figure 2.**RP reconstruction schematic diagram: after the BCG signal is transformed into phase space trajectory, RP is obtained through RP reconstruction, where (

**a**) is the waveform of the 24-s BCG segment, (

**b**) is the phase space trajectory of BCG, and (

**c**) is the RP of BCG.

**Figure 3.**TRP and UTRP of AF and NAF. (

**a**) is the TRP of AF, and (

**b**) is the TRP of NAF; (

**c**) is the UTRP of AF, and (

**d**) is the UTRP of NAF.

Symbols | Measure | Definition |
---|---|---|

RQA 1 | Recurrence rate (RR) | $RR=\frac{1}{{N}^{2}}{\mathrm{sum}}_{i,j=1}^{N}{R}_{i,j}$ |

RQA 2 | Determinism (DET) | $DET=\frac{{{\displaystyle \sum}}_{l-{l}_{min}}^{N}lP(l)}{{{\displaystyle \sum}}_{l=1}^{N}lP(l)}$ |

RQA 3 | Laminarity (LAM) | $LAM=\frac{{{\displaystyle \sum}}_{v-{v}_{min}}^{N}vP(v)}{{{\displaystyle \sum}}_{v=1}^{N}vP(v)}$ |

RQA 4 | Ratio (RATIO) | $RATIO={N}^{2}\frac{{{\displaystyle \sum}}_{l-{l}_{min}}^{N}lP(l)}{{\left({{\displaystyle \sum}}_{l-1}^{N}lP(l)\right)}^{2}}$ |

RQA 5 | Averaged diagonal line length (L) | $L=\frac{{{\displaystyle \sum}}_{l-{l}_{min}}^{N}lP(l)}{{{\displaystyle \sum}}_{l-{l}_{min}}^{N}P(l)}$ |

RQA 6 | Trapping time (TT) | $TT=\frac{{{\displaystyle \sum}}_{v-{v}_{min}}^{N}vP(v)}{{{\displaystyle \sum}}_{v={v}_{min}}^{N}P(v)}$ |

RQA 7 | Longest diagonal line (${L}_{max}$) | ${L}_{max}=max\left(\left\{{l}_{i};i=1,\dots ,{N}_{l}\right\}\right)$ |

RQA 8 | Longest vertical line (${V}_{max}$) | ${V}_{max}=max\left(\left\{{v}_{i};i=1,\dots ,{N}_{v}\right\}\right)$ |

RQA 9 | Divergence (DIV) | $DIV=\frac{1}{{L}_{max}}$ |

RQA 10 | Entropy (ENTR) | $ENTR=-{\displaystyle {\displaystyle \sum}_{l-{l}_{min}}^{N}}p(l)\mathrm{ln}p(l)$ |

RQA 11 | $\mathrm{Trend}\text{}(TREND$) | $TREND=\frac{{{\displaystyle \sum}}_{i=1}^{N}(i-\tilde{N}/2)\left(R{R}_{i}-\langle R{R}_{i}\rangle \right)}{{{\displaystyle \sum}}_{i=1}^{N}{(i-\tilde{N}/2)}^{2}}$ |

RQA 12 | Clustering coefficient (CLUST) | $CLUST=\frac{\mathrm{CTN}}{\mathrm{TN}}$ |

RQA 13 | Longest white vertical line ($W{V}_{max}$) | $W{V}_{max}=max\left(\left\{w{v}_{i};i=1,\dots ,{N}_{v}\right\}\right)$ |

Symbols | Measure | Definition |
---|---|---|

TTF1 | Standard Deviation | $std\left(x\left[n\right]\right)=\sqrt{\frac{N}{N-1}{m}_{2}\left(x\left[n\right]\right)}$ |

TTF2 | Skewness | $\mathit{skewness}\left(x\left[n\right]\right)=\frac{{m}_{3}\left(x\left[n\right]\right)}{{m}_{2}{(x\left[n\right])}^{3/2}}$ |

TTF3 | Kurtosis | $kurtosis\left(x\left[n\right]\right)=\frac{{m}_{4}\left(x\left[n\right]\right)}{{m}_{2}{(x\left[n\right])}^{2}}$ |

TTF4 | Range | $pp\left(x\left[n\right]\right)=max\left(x\left[n\right]\right)-min\left(x\left[n\right]\right)$ |

TTF5 | $\mathrm{Ratio}\mathrm{of}p{p}_{10}\left(l\right)$$\mathrm{to}\mathrm{the}Mean$ | $\mathit{max}\left(p{p}_{10}\left(l\right)/mean\left(p{p}_{10}\left(l\right)\right)\right)$ |

TTF6 | $\mathrm{Standard}\mathrm{Deviation}\mathrm{of}p{p}_{10}\left(l\right)$ | $\mathit{std}\left(p{p}_{10}\left(l\right)\right)$ |

TTF7 | $\mathrm{The}\mathrm{Standard}\mathrm{Deviation}\mathrm{of}\overline{S}\left[f\right]$ | $\mathit{std}\left(\overline{S}\left[f\right]\right)$ |

TTF8 | $\mathrm{Skewness}\mathrm{of}\overline{S}\left[f\right]$ | $\mathit{skewness}\left(\overline{S}\left[f\right]\right)$ |

TTF9 | $\mathrm{Kurtosis}\mathrm{of}\overline{S}\left[f\right]$ | $\mathit{kurtosis}\left(\overline{S}\left[f\right]\right)$ |

TTF10 | $\mathrm{Standard}\mathrm{Deviation}\mathrm{of}{f}_{\mathrm{peak}}$ | $std\left(\mathsf{\Delta}{f}_{\mathrm{peak}}\left[k\right]\right)$ |

TTF11 | $\mathrm{Skewness}\mathrm{of}{f}_{\mathrm{peak}}$ | $\mathit{skewness}\left(\mathsf{\Delta}{f}_{\mathrm{peak}}\left[k\right]\right)$ |

TTF12 | $\mathrm{Kurtosis}\mathrm{of}{f}_{\mathrm{peak}}$ | $\mathit{kurtosis}\left(\mathsf{\Delta}{f}_{\mathrm{peak}}\left[k\right]\right)$ |

TTF13 | $\mathrm{Standard}\mathrm{Deviation}\mathrm{of}S\left[f,k\right]$ | $std\left(st{d}_{t}\left(S\left[f,k\right]\right)\right)$ |

TTF14 | $\mathrm{Average}\mathrm{of}{w}_{\mathrm{peak}}$ | $\mathit{mean}\left({w}_{\mathrm{peak}}\left[k\right]\right)$ |

TTF15 | $\mathrm{Standard}\mathrm{Deviation}\mathrm{of}{w}_{\mathrm{peak}}$ | $\mathit{std}\left({w}_{\mathrm{peak}}\left[k\right]\right)$ |

TTF16 | Harmonic Drama Frequency | ${\mathit{max}}_{fd}{\displaystyle {\displaystyle \sum}_{k=1}^{\left[\frac{F}{fb}\right]}}{\mathrm{log}}_{10}\left(\frac{\overline{S}{m}_{4}\left(k{f}_{b}\right)}{\overline{S}\left[\left(k+\frac{1}{2}\right){f}_{b}\right]}\right)$ |

TTF17 | Kurtosis of Continuous Time Energy Spectral Density | ${\displaystyle \sum}_{t=1}^{T-1}}\mathit{kurtosis}(\mathit{xcorr}(S[f,t],S[f,t+1]))$ |

Symbols | Definition |
---|---|

E1 | $\mathrm{Mean}(\mathit{PI}\left(i\right))$ |

E2 | $\mathrm{Variance}(\mathit{PI}\left(i\right))$ |

E3 | $\mathrm{Skewness}(\mathit{PI}\left(i\right))$ |

E4 | $\mathrm{Kurtosis}(\mathit{PI}\left(i\right))$ |

E5 | $\mathrm{Mean}(\mathit{DA}\left(i\right))$ |

E6 | $\mathrm{Variance}(\mathit{DA}\left(i\right))$ |

E7 | $\mathrm{Skewness}(\mathit{DA}\left(i\right))$ |

E8 | $\mathrm{Kurtosis}(\mathit{DA}\left(i\right))$ |

E9 | $\mathrm{Mean}(\mathit{RT}\left(i\right))$ |

E10 | $\mathrm{Variance}(\mathit{RT}\left(i\right))$ |

E11 | $\mathrm{Skewness}(\mathit{RT}\left(i\right))$ |

E12 | $\mathrm{Kurtosis}(\mathit{RT}\left(i\right))$ |

E13 | $\mathrm{Mean}(\mathit{BP}\left(i\right))$ |

E14 | $\mathrm{Variance}(\mathit{BP}\left(i\right))$ |

E15 | $\mathrm{Skewness}(\mathit{BP}\left(i\right))$ |

E16 | $\mathrm{Kurtosis}(\mathit{BP}\left(i\right))$ |

Method | ACC | PRE | SEN | SPE |
---|---|---|---|---|

TRP | 56.13 | 73.50 | 38.75 | 59.38 |

UTRP | 73.25 | 78.75 | 67.75 | 76.12 |

Features | ACC | PRE | SEN | SPE |
---|---|---|---|---|

RQA | 83.50 | 85.64 | 80.50 | 86.50 |

4 s CTW–RQA (n = 6) | 81.75 | 83.74 | 80.95 | 82.63 |

8 s CTW–RQA (n = 3) | 89.38 | 90.52 | 88.54 | 90.26 |

12 s CTW–RQA (n = 2) | 86.13 | 86.46 | 84.91 | 87.29 |

**Table 6.**AF detection performance based on time and time-frequency features with and without CTW by means of RF.

Features | ACC | PRE | SEN | SPE |
---|---|---|---|---|

Without CWT | 87.63 | 85.89 | 89.20 | 86.13 |

4 s CTW (n = 6) | 79.73 | 69.21 | 53.73 | 77.37 |

8 s CTW (n = 3) | 84.63 | 85.22 | 50.39 | 91.73 |

12 s CTW (n = 2) | 85.38 | 83.33 | 84.83 | 83.94 |

Features | ACC | PRE | SEN | SPE |
---|---|---|---|---|

Without CWT | 78.50 | 77.89 | 78.68 | 78.33 |

4 s CTW (n = 6) | 68.15 | 65.52 | 36.19 | 78.95 |

8 s CTW (n = 3) | 74.63 | 69.15 | 75.24 | 62.89 |

12 s CTW (n = 2) | 76.78 | 78.54 | 74.05 | 77.63 |

Fisher Score | MRMR (×10^{−3}) | Chi-Square Test $(-\mathbf{lg}\left(\mathit{p}\right))$ | Mean (|SHAP Value|) (×10^{−2}) | |
---|---|---|---|---|

RQA 1 | 26.7275 | 15.6968 | 86.1661 | 9.16 |

RQA 2 | 0.0069 | 36.1666 | 76.7835 | 5.83 |

RQA 3 | 0.0614 | 26.1460 | 109.6421 | 9.26 |

RQA 4 | 0.0067 | 7.4060 | 79.8617 | 4.03 |

RQA 5 | 0.0025 | 7.5923 | 126.0331 | 0.75 |

RQA 6 | 0.0117 | 9.2184 | 69.9101 | 7.84 |

RQA 7 | 0.0437 | 5.9155 | 108.9972 | 1.38 |

RQA 8 | 0.0515 | 14.0229 | 63.5000 | 2.99 |

RQA 9 | 0.0445 | 8.5346 | 83.1469 | 1.31 |

RQA 10 | 0.0136 | 14.6556 | 114.1749 | 1.69 |

RQA 11 | 0.0463 | 24.4646 | 102.5003 | 2.02 |

RQA 12 | 0.0282 | 6.8314 | 95.5515 | 3.84 |

RQA 13 | 0.0282 | 16.0161 | 118.5287 | 2.12 |

Method | ACC | PRE | SEN | SPE |
---|---|---|---|---|

KNN | 58.13 | 84.07 | 23.06 | 95.36 |

NB | 81.63 | 85.52 | 77.42 | 86.08 |

ENS | 91.75 | 95.29 | 88.35 | 95.36 |

RF | 95.63 | 95.84 | 95.63 | 95.62 |

DT | 84.50 | 85.82 | 83.74 | 85.31 |

Method | Top 13 | Top 16 | Top 17 |
---|---|---|---|

Fisher’s coefficient | 91.25% | 89.63% | 90.88% |

MRMR | 92.88% | 93.13% | 93.63% |

Chi-square test | 95.25% | 95.25% | 95.38% |

SHAP value | 93.75% | 94.13% | 94.63% |

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## Share and Cite

**MDPI and ACS Style**

Cheng, T.; Jiang, F.; Li, Q.; Zeng, J.; Zhang, B.
Quantitative Analysis Using Consecutive Time Window for Unobtrusive Atrial Fibrillation Detection Based on Ballistocardiogram Signal. *Sensors* **2022**, *22*, 5516.
https://doi.org/10.3390/s22155516

**AMA Style**

Cheng T, Jiang F, Li Q, Zeng J, Zhang B.
Quantitative Analysis Using Consecutive Time Window for Unobtrusive Atrial Fibrillation Detection Based on Ballistocardiogram Signal. *Sensors*. 2022; 22(15):5516.
https://doi.org/10.3390/s22155516

**Chicago/Turabian Style**

Cheng, Tianqing, Fangfang Jiang, Qing Li, Jitao Zeng, and Biyong Zhang.
2022. "Quantitative Analysis Using Consecutive Time Window for Unobtrusive Atrial Fibrillation Detection Based on Ballistocardiogram Signal" *Sensors* 22, no. 15: 5516.
https://doi.org/10.3390/s22155516