Distances in Probability Space and the Statistical Complexity Setup

Kowalski, A.M.; Martín, María Teresa; Plastino, A.; Rosso, Osvaldo A.; Casas, M.

doi:10.3390/e13061055

Cited by 56 publications

(55 citation statements)

References 47 publications

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“…of (i) the normalized Shannon entropy and (ii) the so-called disequilibrium Q J , which is defined in terms of the extensive (in the thermodynamical sense) Jensen-Shannon divergence J [P, P e ] that links two PDFs [36]. The Jensen-Shannon divergence, which quantifies the difference between two (or more) probability distributions, is especially useful to compare the symbol-composition of different sequences [37].…”

Section: The Statistical Complexity and The Complexity-entropy Planementioning

confidence: 99%

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

Zanin

Zunino

Rosso

et al. 2012

Entropy

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562

440

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Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, Entropy 2012, 14 1554 as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.

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Section: The Statistical Complexity and The Complexity-entropy Planementioning

confidence: 99%

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

Zanin

Zunino

Rosso

et al. 2012

Entropy

Self Cite

562

440

View full text Add to dashboard Cite

show abstract

“…In this paper the statistical complexity is assessed through the information carried by the signal [16,12]. This approach provides a link between the entropy of the random source that generates the signal and the distance of the probability distribution of the generating source p to the uniform distribution p e .…”

Section: Statistical Complexitymentioning

confidence: 99%

Rényi Entropy Based Statistical Complexity Analysis for Gear Fault Prognostics under Variable Load

Boškoski

Juričić

2012

Condition Monitoring of Machinery in Non-Stationary Operations

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Abstract. In this paper we propose an approach for gear fault prognostics in presumably non-stationary and unknown operating conditions. The approach monitors the evolution of the statistical complexity of the generated vibrations envelope vis-à-vis its Rényi entropy. The statistical complexity is obtained through the wavelet coefficients calculated from the generated vibrations. Such an approach allows seamless estimation of the remaining useful life of the monitored drive without any prior information about the operating conditions and no a priori data regarding the physical characteristics of the monitored drive. The effectiveness of the approach was evaluated on experiments monitoring natural gear fault progress under variable load.

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“…In the following we will only employ the Hellinger divergence which is also a distance, for which h(y) = y/2, 0 ≤ y < 2 and φ(x) = ( √ x − 1) 2 . The influence of the choice of a distance when computing statistical complexities is studied in Reference [11]. Following Rosso et al [17], we work with the Hellinger distance and we define the Statistical Complexity of coordinate (i, j) in an intensity SAR image as the product…”

Section: Generalized Measure Of Statistical Complexitymentioning

confidence: 99%

Generalized Statistical Complexity of SAR Imagery

Almeida

Medeiros

Rosso

et al. 2012

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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Abstract.A new generalized Statistical Complexity Measure (SCM) was proposed by Rosso et al in 2010. It is a functional that captures the notions of order/disorder and of distance to an equilibrium distribution. The former is computed by a measure of entropy, while the latter depends on the definition of a stochastic divergence. When the scene is illuminated by coherent radiation, image data is corrupted by speckle noise, as is the case of ultrasound-B, sonar, laser and Synthetic Aperture Radar (SAR) sensors. In the amplitude and intensity formats, this noise is multiplicative and non-Gaussian requiring, thus, specialized techniques for image processing and understanding. One of the most successful family of models for describing these images is the Multiplicative Model which leads, among other probability distributions, to the G 0 law. This distribution has been validated in the literature as an expressive and tractable model, deserving the "universal" denomination for its ability to describe most types of targets. In order to compute the statistical complexity of a site in an image corrupted by speckle noise, we assume that the equilibrium distribution is that of fully developed speckle, namely the Gamma law in intensity format, which appears in areas with little or no texture. We use the Shannon entropy along with the Hellinger distance to measure the statistical complexity of intensity SAR images, and we show that it is an expressive feature capable of identifying many types of targets.

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Distances in Probability Space and the Statistical Complexity Setup

Cited by 56 publications

References 47 publications

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

Rényi Entropy Based Statistical Complexity Analysis for Gear Fault Prognostics under Variable Load

Generalized Statistical Complexity of SAR Imagery

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