Tsallis versus Renyi entropic form for systems with q-exponential behaviour: the case of dissipative maps

Johal, Ramandeep S.; Tirnakli, Uğur

doi:10.1016/j.physa.2003.09.064

Cited by 18 publications

(9 citation statements)

References 44 publications

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“…(1) has been employed in a growing number of theoretical and empirical works on a large variety of themes. Examples include scale-free networks [10][11][12][13][14], dynamical systems [15][16][17][18][19][20][21][22][23][24][25][26][27], algebraic structures [28][29][30][31] among other topics in statistical physcics [32][33][34][35][36].…”

Section: Q-exponential Distributionmentioning

confidence: 99%

q-distributions in complex systems: a brief review

Picoli¹,

Mendes²,

Malacarne³

et al. 2009

Braz. J. Phys.

104

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The nonextensive statistical mechanics proposed by Tsallis is today an intense and growing research field. Probability distributions which emerges from the nonextensive formalism (q-distributions) have been applied to an impressive variety of problems. In particular, the role of q-distributions in the interdisciplinary field of complex systems has been expanding. Here, we make a brief review of q-exponential, q-Gaussian and q-Weibull distributions focusing some of their basic properties and recent applications. The richness of systems analyzed may indicate future directions in this field.

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Section: Q-exponential Distributionmentioning

confidence: 99%

q-distributions in complex systems: a brief review

Picoli¹,

Mendes²,

Malacarne³

et al. 2009

Braz. J. Phys.

104

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“…Maximum cross correlation is a special case of Renyi entropic thresholding (q = 2). Under maximum entropy principle implemented in the thresholding process, Renyi and Tsallis will generate the same results always [53]. As a result, of this, the discussion that follows on algorithms performance evaluation will be focusing on Shannon and Renyi entropic thresholding algorithms only.…”

Section: Resultsmentioning

confidence: 99%

Comparative Performance Evaluation of Entropic Thresholding Algorithms Based on Shannon, Renyi and Tsallis Entropy Definitions for Electrical Capacitance Tomography Measurement Systems

Mwambela¹

2018

IJISA

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Abstract-The concept of entropy as a measure of information has been extensively applied in information theory and related fields. The complex nature of information has resulted in some proposed entropy definitions. In image processing, the entropy concept has been used in developing thresholding techniques based on maximum entropy principles for image segmentation, enhancement and object detection purposes. In this article, entropy definitions are analysed to establish their relationship and after that evaluate their performance in image thresholding. Static simulated data from Electrical Capacitance Tomography measurement system for annular and stratified flows in multiphase hydrocarbons production has been used. Performance evaluation results of thresholding algorithms using Renyi entropy has shown to improve the measurements, particularly for stratified flow regimes. The improvement is solely based on the entropy definition, and it has been observed the introduced controlling parameters do not affect its performance. Renyi entropic thresholding algorithm is relatively robust as it is independent of the controlling parameter q and the grey level resolution. Therefore, there is the potential possibility of using Renyi entropic thresholding to improve measurements in hydrocarbons flow measurement using Electrical Capacitance Tomography measurement system.

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“…Furthermore, Tsallis entropy is a much more sensitive function than Rényi entropy with respect to changes in q value, which is conducive to determine the proper q parameter. Besides, Tsallis entropy has been found to possess non-extensive property, which is helpful to deal with non-extensive character of XWT transform [50]. Based on the above advantages of the Tsallis entropy, it is applied to the fault feature extraction of analog circuits in this work.…”

Section: Discussionmentioning

confidence: 99%

Analog Circuit Fault Diagnosis via Joint Cross-Wavelet Singular Entropy and Parametric t-SNE

Wei

et al. 2018

Entropy

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Abstract:In this paper, a novel method with cross-wavelet singular entropy (XWSE)-based feature extractor and support vector machine (SVM) is proposed for analog circuit fault diagnosis. Primarily, cross-wavelet transform (XWT), which possesses a good capability to restrain the environment noise, is applied to transform the fault signal into time-frequency spectra (TFS). Then, a simple segmentation method is utilized to decompose the TFS into several blocks. We employ the singular value decomposition (SVD) to analysis the blocks, then Tsallis entropy of each block is obtained to construct the original features. Subsequently, the features are imported into parametric t-distributed stochastic neighbor embedding (t-SNE) for dimension reduction to yield the discriminative and concise fault characteristics. Finally, the fault characteristics are entered into SVM classifier to locate circuits' defects that the free parameters of SVM are determined by quantum-behaved particle swarm optimization (QPSO). Simulation results show the proposed approach is with superior diagnostic performance than other existing methods.

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Tsallis versus Renyi entropic form for systems with q-exponential behaviour: the case of dissipative maps

Cited by 18 publications

References 44 publications

q-distributions in complex systems: a brief review

q-distributions in complex systems: a brief review

Comparative Performance Evaluation of Entropic Thresholding Algorithms Based on Shannon, Renyi and Tsallis Entropy Definitions for Electrical Capacitance Tomography Measurement Systems

Analog Circuit Fault Diagnosis via Joint Cross-Wavelet Singular Entropy and Parametric t-SNE

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