A Method for Estimating the Entropy of Time Series Using Artificial Neural Networks

TL;DR

This paper introduces a novel neural network-based method for estimating the entropy of time series, leveraging classification accuracy as a measure, and demonstrates its robustness and improved accuracy over existing methods.

Contribution

The study proposes a new entropy estimation technique using LogNNet neural networks that overcomes parameter dependence issues of traditional methods.

Findings

The method accurately estimates entropy across various time series types.

NNetEn correlates higher classification accuracy with greater complexity.

The approach outperforms existing entropy estimation methods in robustness and accuracy.

Abstract

Measuring the predictability and complexity of time series using entropy is essential tool de-signing 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 res-ervoir. 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.