Velichko Andrei, Heidari Hanif
Institute of Physics and Technology, Petrozavodsk State University, 185910 Petrozavodsk, Russia.
Department of Applied Mathematics, School of Mathematics and Computer Sciences, Damghan University, Damghan 36715-364, Iran.
Entropy (Basel). 2021 Oct 29;23(11):1432. doi: 10.3390/e23111432.
Measuring the predictability and complexity of time series using entropy is essential tool designing and controlling a nonlinear system. However, the existing methods have some drawbacks related to the strong dependence of entropy on the parameters of the methods. To overcome these difficulties, this study proposes a new method for estimating the entropy of a time series using the LogNNet neural network model. The LogNNet reservoir matrix is filled with time series elements according to our algorithm. The accuracy of the classification of images from the MNIST-10 database is considered as the entropy measure and denoted by NNetEn. The novelty of entropy calculation is that the time series is involved in mixing the input information in the reservoir. Greater complexity in the time series leads to a higher classification accuracy and higher NNetEn values. We introduce a new time series characteristic called time series learning inertia that determines the learning rate of the neural network. The robustness and efficiency of the method is verified on chaotic, periodic, random, binary, and constant time series. The comparison of NNetEn with other methods of entropy estimation demonstrates that our method is more robust and accurate and can be widely used in practice.
使用熵来衡量时间序列的可预测性和复杂性是设计和控制非线性系统的重要工具。然而，现有方法存在一些缺点，与熵对方法参数的强烈依赖性有关。为克服这些困难，本研究提出一种使用LogNNet神经网络模型估计时间序列熵的新方法。根据我们的算法，LogNNet储层矩阵用时间序列元素填充。来自MNIST - 10数据库的图像分类准确率被视为熵度量，并记为NNetEn。熵计算的新颖之处在于时间序列参与了储层中输入信息的混合。时间序列中更高的复杂性导致更高的分类准确率和更高的NNetEn值。我们引入一种新的时间序列特征，称为时间序列学习惯性，它决定神经网络的学习率。该方法在混沌、周期、随机、二进制和恒定时间序列上的鲁棒性和效率得到验证。NNetEn与其他熵估计方法的比较表明，我们的方法更鲁棒、更准确，可在实际中广泛应用。
