Signal simplification is a processing technique that reduces the number of samples in a signal. It has been employed in various applications and methods while handling huge amounts of data. One well-known method is the Douglas-Peucker (DP) algorithm which performs signal simplification using an appropriate tolerance value to determine whether to retain or remove a given sample point. That would mean the performance of the DP algorithm is sensitive to the selection of the tolerance value. In this paper, we introduce a new signal simplification method insensitive to parameter dependence changes. We first construct a connectivity-based visibility relationship matrix to find the most important points in the signal. Then, we use the degree threshold value to construct a degree matrix determining key anchors of the simplification process that preserve the essential features of the signal. This signal is simplified by measuring the perpendicular distances of the intermediate points from line segments defined by these key points. The proposed technique was tested on three simulated signal models and an electroencephalography (EEG) signal. Our results obtained are visually and quantitatively compared in terms of root mean square error (RMSE), R², number of simplified points, and compression ratio with the DP algorithm. The results indicate that the proposed method is robust to parameter changes and provides better simplification than the DP algorithm. In the future, we plan to validate our algorithm with a huge database.

中文翻译：

---

一种使用可见性关系和垂直距离递归细化的生理信号的新型复杂性降低技术


信号简化是一种减少信号中样本数的处理技术。它已被用于各种应用程序和方法，同时处理大量数据。一种众所周知的方法是 Douglas-Peucker （DP） 算法，该算法使用适当的容差值执行信号简化，以确定是保留还是删除给定的采样点。这意味着 DP 算法的性能对 tolerance 值的选择很敏感。在本文中，我们介绍了一种对参数依赖性变化不敏感的新信号简化方法。我们首先构建一个基于连接的可见性关系矩阵，以找到信号中最重要的点。然后，我们使用度阈值来构建一个度矩阵，确定保留信号基本特征的简化过程的关键锚点。通过测量中间点与这些关键点定义的线段的垂直距离，可以简化此信号。所提出的技术在三个模拟信号模型和一个脑电图 （EEG） 信号上进行了测试。我们获得的结果与 DP 算法在均方根误差 （RMSE） 、R²、简化点数和压缩率方面进行了视觉和定量比较。结果表明，所提方法对参数变化具有鲁棒性，并且比DP算法具有更好的简化性。将来，我们计划使用庞大的数据库来验证我们的算法。