# Data Fusion of Multivariate Time Series: Application to Noisy 12-Lead ECG Signals
## 1 Introduction  
ECG records the physiological information of cardiac activity by deploying electrodes placed at different positions of the body, which is widely applied in clinical diagnosis and monitoring. However, ECG recordings gathered in clinical settings are often contaminated by noise and artifacts. Due to the overlapping frequency bands and similar morphologies in noise and ECG signal [1; 2], the distorted characteristics of ECG signal result in false alarms (FA) in intensive care unit (ICU), and imprecise measurement of ECG signals [2]. Thus, ECG signal quality assessment is necessary for further ECG signal processing. The aim of ECG quality assessment algorithm is to extract the characteristics of the ECG signal appropriately [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. Time-domain characteristics or frequency-domain characteristics are used, among the majority of the proposed algorithms. For the time-domain instance, [PERSON] et al. adopted the Karhumem-Loeve basis functions to represent the QRS complex and employed the residual error of the reconstructed QRS complex to estimate the instantaneous noise of the original signal [3]. In the frequency-domain instance, via a long-term ECG recording from the coronary care unit, the frequency content and the number of times ECG exceeds a preset limit were used to analyze the ECG quality [4]. [PERSON] et al. employed machine learning methods to identify data collection problems at 12-leads ECG [5]. In [6], [PERSON] et al. devised five simple rules to detect the most common distortions of theECG signal. In [7], an ensemble of decision trees was used to assess the usability of ECG signals. In [8], [PERSON] et al. presented a method for scoring the noise level via the ECG amplitude, powerline noise, baseline wander, electromyography (EMG), and peak artifacts. [PERSON] et al. proposed some signal quality indices (SQIs), which involve both time-domain and frequency-domain characteristics, and can partly reflect the state of the ECG quality [9]. In [10], [PERSON] et al. developed four novel signal quality indices and enriched SQIs in some way. In [11], [PERSON] et al. studied a multi-level ECG quality assessment method based on a support vector machine. In this paper, thirteen signal quality indices were derived from the ECG signals, which were used for multi-level ECG quality classification. In [12], a naive Bayes classifier, a novel set of signal quality indices (SQIs), and an existing adaptive Kalman filter were used for noninvasive fetal ECG signal quality assessment. In [13], multiple signal quality indices and machine learning were used to divide the acceptable and unacceptable ECG segments. [PERSON] et al. presented an overview of ECG signal quality assessment methods and highlighted the limitations of these algorithms [14]. [PERSON] et al. introduced Dower transformation to convert 12-lead ECG signals to 3-lead vectorcardiogram (VCG), which are properly decomposited by multiscale recurrence analysis in each scale [15]. Wavelet analysis is also an effective algorithm for handling nonlinear and nonstationary signals. However, VCG signals are decomposed into a series of multiple wavelet scales and this increases the amount of pending data observably. In other words, in [15], the application of multiscale recurrence analysis virtually weakens the original intention of the Dower transformation. [PERSON] et al. employed a structural similarity measure to compare images of two ECG signals and the representative ECG images were chosen as templates for the ECG signal quality assessment [16]. In [17], via the features of 12-lead ECG signals, [PERSON] et al. addressed the identification of different human individuals, where the autocorrelation method and linear discriminant analysis were used to extract the features of the ECG segments from different leads. These features were combined further at the decision level by various voting principles. [PERSON] et al.