On the Connections of Generalized Entropies With Shannon and Kolmogorov–Sinai Entropies

Falniowski, Fryderyk

doi:10.3390/e16073732

Cited by 14 publications

(10 citation statements)

References 27 publications

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“…By describing the chaos in a dynamic system, the Kolmogorov entropy is expected to be strongly connected with the Lyapunov exponent λ; see [21]. For more information about the theoretical aspects of entropy, its generalizations and entropy-like measures, which can be used to measure the complexity of a system, see [22][23][24][25][26]. Kolmogorov entropy for 1D-regular, chaotic-deterministic and random systems.…”

Section: Definition 3 (Kolmogorov Entropy)mentioning

confidence: 99%

Entropy and Fractal Antennas

Guariglia

2016

Entropy

170

103

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Section: Definition 3 (Kolmogorov Entropy)mentioning

confidence: 99%

Entropy and Fractal Antennas

Guariglia

2016

Entropy

170

103

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“…where p i denotes the probability mass associated with the variable (a) X i such that ∑ p i = 1, and the maximum entropy value is given by H max = log 2 m. This definition of the Shannon entropy has a relation with KSE in terms of its supremum as (Falniowski (2014))…”

Section: Entropy and Correlation Coefficientsmentioning

confidence: 99%

Lyapunov Exponent Enhancement in Chaotic Maps with Uniform Distribution Modulo One Transformation

Ablay

2022

Chaos Theory and Applications

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Most of the chaotic maps are not suitable for chaos-based cryptosystems due to their narrow chaotic parameter range and lacking of strong unpredictability. This work presents a nonlinear transformation approach for Lyapunov exponent enhancement and robust chaotification in discrete-time chaotic systems for generating highly independent and uniformly distributed random chaotic sequences. The outcome of the new chaotic systems can directly be used in random number and random bit generators without any post-processing algorithms for various information technology applications. The proposed Lyapunov exponent enhancement based chaotic maps are analyzed with Lyapunov exponents, bifurcation diagrams, entropy, correlation and some other statistical tests. The results show that excellent random features can be accomplished even with one-dimensional chaotic maps with the proposed approach.

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“…It is determined by identifying points on the trajectory in phase space that is similar to each other and not correlated with time. Divergence rate of these point pairs yields the value of KSE [60], calculated as where C m (r, N m ) is the correlation function which provides probability of two points being closer to each other than r. Higher KSE value signifies higher unpredictability. Hence KSE does not give the accurate results for signals with slightest noise.…”

Section: Kolmogorov Sinai Entropymentioning

confidence: 99%

EEG-based human emotion recognition using entropy as a feature extraction measure

2021

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Many studies on brain–computer interface (BCI) have sought to understand the emotional state of the user to provide a reliable link between humans and machines. Advanced neuroimaging methods like electroencephalography (EEG) have enabled us to replicate and understand a wide range of human emotions more precisely. This physiological signal, i.e., EEG-based method is in stark comparison to traditional non-physiological signal-based methods and has been shown to perform better. EEG closely measures the electrical activities of the brain (a nonlinear system) and hence entropy proves to be an efficient feature in extracting meaningful information from raw brain waves. This review aims to give a brief summary of various entropy-based methods used for emotion classification hence providing insights into EEG-based emotion recognition. This study also reviews the current and future trends and discusses how emotion identification using entropy as a measure to extract features, can accomplish enhanced identification when using EEG signal.

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On the Connections of Generalized Entropies With Shannon and Kolmogorov–Sinai Entropies

Cited by 14 publications

References 27 publications

Entropy and Fractal Antennas

Entropy and Fractal Antennas

Lyapunov Exponent Enhancement in Chaotic Maps with Uniform Distribution Modulo One Transformation

EEG-based human emotion recognition using entropy as a feature extraction measure

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