标题： 将信号的大小变化性纳入序模式分析中 显示英文标题

标题： Including the magnitude variability of a signal into the ordinal pattern analysis

摘要： 最流行且创新的信号分析方法之一是使用序模式（OPs）。 OP编码基于将（单变量）信号转换为OP的符号序列，其中每个OP表示需要多少次排列来排序信号幅度的小子集。 这意味着OP概念清晰，实现方法简单，对噪声鲁棒，并且可以应用于短信号。 此外，它们简化了可以对信号执行的统计分析，例如熵和复杂度的量化。 然而，由于相对排序，丢失了信号在每个时间戳处幅度的信息——这是该方法的主要缺点之一。 在这里，我们提出了一种方法，即将OP编码中丢弃的信号幅度用作置换熵的互补变量。 为了说明我们的方法，我们分析了来自逻辑和Hénon映射的合成轨迹——带有和不带有附加噪声——以及不同睡眠-清醒状态下的大鼠皮层内脑电记录。 我们的结果显示，当用信号幅度的变化补充置换熵时，映射和睡眠-清醒状态的动力学行为表征得到了改善。 这表明我们的方法对于特征工程和改进AI分类器可能很有用，在这些情况下，典型的机器学习算法需要互补的信号特征作为输入以提高分类准确性。 显示英文摘要

摘要： One of the most popular and innovative methods to analyse signals is by using Ordinal Patterns (OPs). The OP encoding is based on transforming a (univariate) signal into a symbolic sequence of OPs, where each OP represents the number of permutations needed to order a small subset of the signal's magnitudes. This implies that OPs are conceptually clear, methodologically simple to implement, robust to noise, and can be applied to short signals. Moreover, they simplify the statistical analyses that can be carried out on a signal, such as entropy and complexity quantifications. However, because of the relative ordering, information about the magnitude of the signal at each timestamp is lost -- this being one of the major drawbacks in the method. Here, we propose a way to use the signal magnitudes discarded in the OP encoding as a complementary variable to its permutation entropy. To illustrate our approach, we analyse synthetic trajectories from logistic and H{\'e}non maps -- with and without added noise -- and intracranial electroencephalographic recordings from rats in different sleep-wake states. Our results show that, when complementing the permutation entropy with the variability in the signal magnitudes, the characterisation of the dynamical behaviours of the maps and the sleep-wake states is improved. This implies that our approach can be useful for feature engineering and improving AI classifiers, where typical machine learning algorithms need complementary signal features as inputs to improve classification accuracy.