Properly measuring the complexity of time series is an important issue. The permutation entropy (PE) is a widely used as an effective complexity measurement algorithm, but it is not suitable for the complexity description of multi-dimensional data. In this paper, in order to better measure the complexity of multi-dimensional time series, we proposed a modified multivariable PE (MMPE) algorithm with principal component analysis (PCA) dimensionality reduction, which is a new multi-dimensional time series complexity measurement algorithm. The analysis results of different chaotic systems verify that MMPE is effective. Moreover, we applied it to the comlexity analysis of EEG data. It shows that the person during mental arithmetic task has higher complexity comparing with the state before mental arithmetic task. In addition, we also discussed the necessity of the PCA dimensionality reduction.

中文翻译：

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一种改进的多变量复杂度测度算法及其在识别心算任务中的应用

正确测量时间序列的复杂性是一个重要问题。置换熵（PE）是一种广泛使用的有效复杂度度量算法，但不适用于多维数据的复杂度描述。在本文中，为了更好地度量多维时间序列的复杂度，我们提出了一种带有主成分分析（PCA）降维的改进多变量PE（MMPE）算法，这是一种新的多维时间序列复杂度度量算法。 . 不同混沌系统的分析结果验证了MMPE的有效性。此外，我们将其应用于 EEG 数据的复杂性分析。表明心算任务中的人比心算任务前的状态复杂度更高。此外，