Tsallis Entropy, Escort Probability and the Incomplete Information Theory

Darooneh, Amir H.; Naeimi, Ghassem; Mehri, Ali; Sadeghi, Parvin

doi:10.3390/e12122497

Cited by 16 publications

(7 citation statements)

References 22 publications

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“…43 The entropy can be organized by using the axioms of the incomplete information theory as in Equation 10: In conclusion, if the axioms of the information theory are changed in order to comprise the escort probability as an indicator of incomplete knowledge, the form of Tsallis entropy is obtained but in terms of the escort probability. 45 Kraskov Entropy.…”

Section: Entropy-based Feature Extraction Methodsmentioning

confidence: 99%

Entropy: A Promising EEG Biomarker Dichotomizing Subjects With Opioid Use Disorder and Healthy Controls

et al. 2020

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Electroencephalography (EEG) signals are known to be nonstationary and often multicomponential signals containing information about the condition of the brain. Since the EEG signal has complex, nonlinear, nonstationary, and highly random behaviour, numerous linear feature extraction methods related to the short-time windowing technique do not satisfy higher classification accuracy. Since biosignals are highly subjective, the symptoms may appear at random in the time scale and very small variations in EEG signals may depict a definite type of brain abnormality it is valuable and vital to extract and analyze the EEG signal parameters using computers. The challenge is to design and develop signal processing algorithms that extract this subtle information and use it for diagnosis, monitoring, and treatment of subjects suffering from psychiatric disorders. For this purpose, finite impulse response–based filtering process was employed rather than traditional time and frequency domain methods. Finite impulse response subbands were analyzed further to obtain feature vectors of different entropy markers and these features were fed into a classifier namely multilayer perceptron. The performances of the classifiers were finally compared considering overall classification accuracies, area under receiver operating characteristic curve scores. Our results underline the potential benefit of the introduced methodology is promising and is to be treated as a clinical interface in dichotomizing substance use disorders subjects and for other medical data analysis studies. The results also indicate that entropy estimators can distinguish normal and opioid use disorder subjects. EEG data and theta frequency band have distinctive capability for almost all types of entropies while nonextensive Tsallis entropy outperforms compared with other types of entropies.

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Section: Entropy-based Feature Extraction Methodsmentioning

confidence: 99%

Entropy: A Promising EEG Biomarker Dichotomizing Subjects With Opioid Use Disorder and Healthy Controls

et al. 2020

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“…It is most frequently used in crystallography [1], chemistry [2] and physics [3,4], but also in many other very diverse areas: natural language processing [5], transportation [6], character recognition [7], image processing [8,9], economy [10]. Theoretical developments also continue [11][12][13].…”

Section: Maximum Entropy Methodsmentioning

confidence: 99%

Asymptotic Behavior of the Maximum Entropy Routing in Computer Networks

Tuba¹

2013

Entropy

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Maximum entropy method has been successfully used for underdetermined systems. Network design problem, with routing and topology subproblems, is an underdetermined system and a good candidate for maximum entropy method application. Wireless ad-hoc networks with rapidly changing topology and link quality, where the speed of recalculation is of crucial importance, have been recently successfully investigated by maximum entropy method application. In this paper we prove a theorem that establishes asymptotic properties of the maximum entropy routing solution. This result, besides being theoretically interesting, can be used to direct initial approximation for iterative optimization algorithms and to speed up their convergence.

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“…In non-extensive statistical physics, the quantity to be compared with the distribution of the observed system is not the original

but its associated escort distribution

[ 18 , 19 , 39 ]. The normalized cumulative distribution of the acoustic parameter

, expressed as a q-exponential function, is obtained by integrating the probability density function

…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Non-Extensive Statistical Analysis of Acoustic Emissions Recorded in Marble and Cement Mortar Specimens Under Mechanical Load Until Fracture

Loukidis

Triantis

2020

Entropy

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Non-extensive statistical mechanics (NESM), which is a generalization of the traditionalBoltzmann-Gibbs statistics, constitutes a theoretical and analytical tool for investigating theirreversible damage evolution processes and fracture mechanisms occurring when materials aresubjected to mechanical loading. In this study, NESM is used for the analysis of the acousticemission (AE) events recorded when marble and cement mortar specimens were subjected tomechanical loading until fracture. In total, AE data originating from four distinct loading protocolsare presented. The cumulative distribution of inter-event times (time interval between twoconsecutive AE events) and the inter-event distances (three-dimensional Euclidian distance betweenthe centers of successive AE events) were examined under the above concept and it was found thatNESM is suitable to detect criticality under the terms of mechanical status of a material. This wasconducted by evaluating the fitting results of the q-exponential function and the corresponding qindicesof Tsallis entropy qδτ and qδ r , along with the parameters τδτ and dδ r . Results supportthat qδτ + qδ r ≈ 2 for AE data recorded from marble and cement mortar specimens of this work,which is in good agreement with the conjecture previously found in seismological data and AE datarecorded from Basalt specimens.Keywords: non-extensive statistical physics

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Tsallis Entropy, Escort Probability and the Incomplete Information Theory

Cited by 16 publications

References 22 publications

Entropy: A Promising EEG Biomarker Dichotomizing Subjects With Opioid Use Disorder and Healthy Controls

Entropy: A Promising EEG Biomarker Dichotomizing Subjects With Opioid Use Disorder and Healthy Controls

Asymptotic Behavior of the Maximum Entropy Routing in Computer Networks

Non-Extensive Statistical Analysis of Acoustic Emissions Recorded in Marble and Cement Mortar Specimens Under Mechanical Load Until Fracture

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