Exploring the Entropy-Based Classification of Time Series Using Visibility Graphs from Chaotic Maps

J. Alberto Conejero (), Andrei Velichko, Òscar Garibo-i-Orts, Yuriy Izotov and Viet-Thanh Pham
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J. Alberto Conejero: Instituto Universitario Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
Andrei Velichko: Institute of Physics and Technology, Petrozavodsk State University, 185910 Petrozavodsk, Russia
Òscar Garibo-i-Orts: Instituto Universitario Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
Yuriy Izotov: Institute of Physics and Technology, Petrozavodsk State University, 185910 Petrozavodsk, Russia
Viet-Thanh Pham: Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam

Mathematics, 2024, vol. 12, issue 7, 1-22

Abstract: The classification of time series using machine learning (ML) analysis and entropy-based features is an urgent task for the study of nonlinear signals in the fields of finance, biology and medicine, including EEG analysis and Brain–Computer Interfacing. As several entropy measures exist, the problem is assessing the effectiveness of entropies used as features for the ML classification of nonlinear dynamics of time series. We propose a method, called global efficiency (GEFMCC), for assessing the effectiveness of entropy features using several chaotic mappings. GEFMCC is a fitness function for optimizing the type and parameters of entropies for time series classification problems. We analyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) for four discrete mappings, the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn has greater GEFMCC in the classification task compared to NNetEn. However, NNetEn classification efficiency is higher than FuzzyEn for some local areas of the time series dynamics. The results of using horizontal visibility graphs (HVG) instead of the raw time series demonstrate the GEFMCC decrease after HVG time series transformation. However, the GEFMCC increases after applying the HVG for some local areas of time series dynamics. The scientific community can use the results to explore the efficiency of the entropy-based classification of time series in “The Entropy Universe”. An implementation of the algorithms in Python is presented.

Keywords: chaotic maps; NNetEn; neural network entropy; horizontal visibility graphs; fuzzy entropy; classification; entropy global efficiency; GEFMCC; Python (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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