# Data Fusion of Multivariate Time Series: Application to Noisy 12-Lead ECG Signals
## 4 Application of NDFA in 12-Lead ECG Signals
### Realistic Signals Experiments  
As an important database, PhysioNet/Computing in Cardiology Challenge 2011 has been widely used for testing the ECG quality assessment algorithms. In the database, standard 12-lead ECG signal is sampled at 500 Hz and recorded for 10 s. There are 1000 12-lead ECG records to be employed as the train set (Set A), with the signal quality being quantified by a group of annotators being professional in ECG analysis. In Set A, 773 ECG records were acceptable, 225 signals were unacceptable, and the remaining were indeterminate. In this subsection, four sets of realistic 12-lead ECG signals were randomly selected from set A for assessing the performance of NDFA. The quality of No. 1027085 and No. 1075113 was acceptable, and the quality of No. 1063069 and No. 1003574 was unacceptable. In order to analyze the ECG signal quality, the realistic ECG signals needed to be pre-processed before quality assessment. Firstly, each lead of the 12-lead ECG signals was examined for the constant signal detection. If some constant signals were contained in the ECG signals, then the realistic signal needed further processing and it was identified as being unacceptable. Otherwise, the 12-lead ECG signals were transformed into VCG signals by the inverse Dower transformation matrix [36] under the following equation:  
\[VCG=D_{int}\times ECG, \tag{17}\]  
where \(D_{int}\) is given by  
\[D_{int}=\left[ \begin{array}{cccccccc}-0.172&-0.074&0.122&0.231&0.239&0.194&0. 156&-0.010\\ 0.057&-0.019&-0.106&-0.022&0.041&0.048&-0.227&0.887\\ -0.229&-0.310&-0.246&-0.063&0.055&0.108&0.022&0.102\end{array} \right] \tag{18}\]  
Based on the transformation, the quality characteristics of original signals can be completely inherited by VCG signals. Via NDFA, the VCG signals and reconstructed trajectory of fused result for the signals of No. 1027085 and No. 1075113 are shown in Figure 6a,b. As the qualities of the two signals were acceptable, the VCG signals demonstrated periodic changes and significant physiological meaning. Furthermore, the reconstructed trajectories of the fused results implied the regular evolutionary \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**SNR (dB)** & **12** & **6** & **0** & \(\mathbf{-6}\) \\ \hline \(Cor_{\overline{x}}\) & 0.3498 & 0.3192 & 0.2476 & 0.1539 \\ \(Cor_{\overline{y}}\) & 0.5439 & 0.5221 & 0.4970 & 0.4379 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: _Cor_ for MA under different SNR levels. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**SNR (dB)** & **6** & **0** & \(\mathbf{-6}\) & \(\mathbf{-12}\) \\ \hline \(Cor_{\overline{x}}\) & 0.3281 & 0.2598 & 0.1665 & 0.0944 \\ \cline{2-6} \(Cor_{\overline{y}}\) & 0.5347 & 0.5156 & 0.4728 & 0.4080 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cor_ for EM under different SNR levels. characteristics. On the contrary, the other two realistic signals were unacceptable. From Figure 6c,d, the VCG signals and fused results indicated discursive and unsystematic evolutionary characteristics. Figure 6: Three-lead VCG signals by realistic 12-lead ECG signals transformation and reconstructed trajectories of fused results. **(a–d)** are results of the signal of No.1027085, No.1075113, No.1027085, and No.1075113, respectively. In order to intuitively estimate the performance of NDFA further, the ECG segment of No. 106 from MIT-BIH database was extracted. The duration of the ECG segment was 1.11 s, which was sufficient for all features of the ECG signal to be contained. Via NDFA, two lead ECG signals of the signal segment were fused and the results are shown in Figure 7. Figure 7a is the reconstructed trajectory of the lead _MLII_, and two characteristics of the trajectory morphology can be well reflected. In the figure, there is a longer closed trajectory (Feature 2), which is the reconstructed trajectory of the QRS complex. Furthermore, the reconstructed trajectory of the P wave appears as the unordered characteristic of the closed trajectory (Feature 1).