Weighted multi-scale limited penetrable visibility graph for exploring atrial fibrillation rhythm

Atrial fibrillation (AF) is a common cause of serious diseases such as stroke, heart failure and coronary artery disease, and electrocardiogram (ECG) detection is an important means of identifying AF. However, the ECG signal is quite noisy, making it difficult to detect AF through this method. Removing noise interference in ECG signals is a challenging problem. Traditional methods usually adopt various filtering methods to tackle this problem. Inspired by complex network theory, in this paper we present an innovative denoising approach for ECG detection called weighted multi-scale limited penetrable visibility graph (WMS-LPVG), which allows us to detect the rhythms characterizing AF in noisy ECG signals. To our knowledge, this is the first model that represents the AF rhythm series from the perspective of multi-scale complex networks. Furthermore, our WMS-LPVG model characterizes the AF rhythms in more detail, enabling us to identify AF sufferers more accurately. To demonstrate the effectiveness of our WMSLPVG method, we first propose a new concept, called local efficiency entropy (LEE), which is utilized to identify the dynamic characteristics of time series. We then study the LEE-fluctuation trend under different scale factors. The experimental results show that the proposed LEE criterion can identify four kinds of ECG waveforms at a large scale. We then fuse the extracted LEE features with the original sequential features of ECG signals to build a multi-model complex network and feed the fused features into an XGboost model to identify AF patients. To demonstrate the generality of our WMS-LPVG model, we construct complex networks with WMS-LPVG for periodic and chaotic time series, respectively, and further discuss their degree distributions. The results show that our WMS-LPVG method perfectly retains information about original sequences and offers good anti-noise ability. (c) 2021 Elsevier B.V. All rights reserved.