Jensen-Shannon Divergence Measure Research Articles

Multi-attribute group decision-making problem of medical consumption products based on extended TODIM-VIKOR approach with Fermatean fuzzy information measure

The fundamental goal of this research is to develop a MAGDM (Multi-Attribute Group Decision Making) problem of Medical Consumption Products. We propose TODIM–VIKOR approach in this paper, which combines the TODIM (an acronym in Portuguese for Interactive and Multi-criteria Decision-Making) and VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) procedures under Fermatean fuzzy information. A new Fermatean fuzzy scoring function is presented for dealing with comparison problems. In addition, we introduce a novel entropy measure for assessing the degree of fuzziness associated with an FFS. We also offer a Jensen–Shannon divergence measure for the Fermatean Fuzzy set that can be used to compare the discrimination information of two FFSs. This suggested measure meets all mathematical standards for being considered a measure. We introduced entropy and divergence measures to determine the objective weight in the TODIM–VIKOR approach. Meanwhile, to deal with multiple attribute group decision-making, a new decision procedure based on the suggested Entropy and Jensen–Shannon divergence measure was proposed in a Fermatean Fuzzy environment. In this article, TODIM has in view to find out the overall dominance degree, and VIKOR is to determine the compromise solution. Finally, we manage a supplier selection problem to verify the performance of the suggested Fermatean fuzzy TODIM–VIKOR method by comparing the ranking solution to the rankings of existing methodologies. We investigate the reliability and effectiveness of our proposed methodology.

A Novel Spherical Fuzzy VIKOR Approach Based on TODIM for Evaluating and Ranking the Opinion Polls With Shannon Entropy and Jensen-Shannon Divergence Measure

A Novel Spherical Fuzzy VIKOR Approach Based on TODIM for Evaluating and Ranking the Opinion Polls With Shannon Entropy and Jensen-Shannon Divergence Measure

A novel multidimensional trust evaluation and fusion mechanism in fog-based Internet of Things

With the fast advancement of IoT, it has gained more attention from industry and academia. However, because diverse security attacks result in the lack of trust between IoT edge devices and the network, a proper trust mechanism is necessary. To address the issue, a novel trust management approach is proposed in this work. In particular, we have proposed a multidimensional trust evaluation mechanism to comprehensively evaluate the trustworthiness of IoT edge devices, with diverse opinions formed by different network entities after observing. Next, a novel trust fusion scheme named JSDM-AHP that integrates the objective Jensen–Shannon divergence measure (JSDM) and analytic hierarchy process (AHP) is developed to fuse diverse decision factors. Theoretical analysis and simulation results show that the proposed trust strategy has high computation-efficiency, scalability, resilience, robustness, and outperforms all the other compered methods in reliability. Furthermore, with the proposed security approach, diverse cyber attacks such as flooding attacks, random attacks, conflicting behavior attacks, on–off attacks, and recommendation attacks can well be defended against, reflecting the high security of the method.

On the Discretization of Continuous Probability Distributions Using a Probabilistic Rounding Mechanism

Most existing flexible count distributions allow only approximate inference when used in a regression context. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under-, and over-dispersion). The new method, referred to as “balanced discretization”, consists of discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation (probabilistic rounding) in terms of the continuous distribution. For illustrative purposes, we develop the family of balanced discrete gamma distributions that can model equi-, under-, and over-dispersed count data. This family of count distributions is appropriate for building flexible count regression models because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we show that under the equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersions, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data are Poisson distributed.

An efficient method for building a database of diatom populations for drowning site inference using a deep learning algorithm.

Seasonal or monthly databases of the diatom populations in specific bodies of water are needed to infer the drowning site of a drowned body. However, existing diatom testing methods are laborious, time-consuming, and costly and usually require specific expertise. In this study, we developed an artificial intelligence (AI)-based system as a substitute for manual morphological examination capable of identifying and classifying diatoms at the species level. Within two days, the system collected information on diatom profiles in the Huangpu and Suzhou Rivers of Shanghai, China. In an animal experiment, the similarities of diatom profiles between lung tissues and water samples were evaluated through a modified Jensen-Shannon (JS) divergence measure for drowning site inference, reaching a prediction accuracy of 92.31%. Considering its high efficiency and simplicity, our proposed method is believed to be more applicable than existing methods for seasonal or monthly water monitoring of diatom populations from sections of interconnected rivers, which would help police narrow the investigation scope to confirm the identity of an immersed body.

A More General Information Theoretic Study of Wireless Location Verification System

In recent years, the issue of location verification system (LVS) has received significant attention in wireless communication networks, especially in Intelligent Transportation Systems (ITSs) and vehicular technology, where the location information is important for users' safety and security. In this article, we consider a vehicular network and analyze a more general Information Theoretic (ITc) study of LVS, specifically, aiming at finding an optimum decision threshold for detection a spoofed location and increasing the system ability in correctly detecting malicious users. For this purpose, we propose different information theoretic measures (Renyi divergence, Renyi mutual information, Kullback-Leibler divergence, Kullback-Leibler mutual information and Jensen-Shannon divergence) for identifying malicious user. Simulation results and comparison between proposed measures show that the optimum decision threshold can be achieved by applying the Jensen-Shannon divergence measure.

Convergence of household incomes in the European Union countries

The aim of the study is to verify the hypothesis of a tendency towards levelling of household income in the EU countries in the years 2007—2015. Convergence process of the level and the distribution of household disposable income was analysed. The basic source of information were Eurostat’s data from EU-SILC database. The convergence analysis of income levels was carried out for the mean, median and first decile of annual equivalised household disposable incomes, weighted by country population. To examine their convergence, regression models used in economic convergence analyses were adapted and the concept of absolute ß convergence was used. In the study of income distributions convergence the income distribution in households by decile groups was used, and the degree of their discrepancy was assessed using the generalised form of the Jensen-Shannon divergence measure. The study was conducted for 27 EU countries, 15 of the old EU states and 12 new member states. On the basis of the obtained results, it was concluded that there was no convergence of the distributions of income by quantiles. However, the convergence of the considered characteristics of income distributions (mean, median, first decile) was observed.

Quantification of Secrecy in Partially Observed Stochastic Discrete Event Systems

While cryptography is used to protect the content of information (e.g., a message) by making it undecipherable, behaviors (as opposed to information) may not be encrypted and may only be protected by partially or fully hiding through creation of ambiguity (by providing covers that generate indistinguishable observations from secrets). Having a cover together with partial observability does cause ambiguity about the system behaviors desired to be kept secret, yet some information about secrets may still be leaked due to statistical difference between the occurrence probabilities of the secrets and their covers. In this paper, we propose a Jensen–Shannon divergence (JSD)-based measure to quantify secrecy loss in systems modeled as partially observed stochastic discrete event systems, which quantifies the statistical difference between two distributions, one over the observations generated by secret and the other over those generated by cover. We further show that the proposed JSD measure for secrecy loss is equivalent to the mutual information between the distributions over possible observations and that over possible system status (secret versus cover). Since an adversary is likely to discriminate more if he/she observes for a longer period, our goal is to evaluate the worst case loss of secrecy as obtained in the limit over longer and longer observations. Computation for the proposed measure is also presented. Illustrative examples, including the one with side-channel attack, are provided to demonstrate the proposed computation approach.

A Fractional Entropy in Fractal Phase Space: Properties and Characterization

A two-parameter generalization of Boltzmann-Gibbs-Shannon entropy based on natural logarithm is introduced. The generalization of the Shannon-Khinchin axioms corresponding to the two-parameter entropy is proposed and verified. We present the relative entropy, Jensen-Shannon divergence measure and check their properties. The Fisher information measure, the relative Fisher information, and the Jensen-Fisher information corresponding to this entropy are also derived. Also the Lesche stability and the thermodynamic stability conditions are verified. We propose a generalization of a complexity measure and apply it to a two-level system and a system obeying exponential distribution. Using different distance measures we define the statistical complexity and analyze it for two-level and five-level system.

Segmentation of Heteropolymer Sequences Specifying Subsequences with Different Composition and Statistical Properties

AbstractWe have studied the segmentation of two‐letter AB heterosequences composed of subsequences with different composition and distribution of A and B monomer units along the chain. Our approach is based on the segmentation function S(k) introduced in the present work and on the Jensen–Shannon divergence measure determined with respect to the probabilities of the lengths of uniform blocks of A and B monomer units. It is shown that the function S(k) is extremely sensitive to the sequence statistics. Even visual analysis of S(k) allows judgment on some features of sequence statistics. In particular, function S(k) is constant for random copolymers, it is an oscillating function for random block copolymers and shows monotonic growth up to some constant value for proteinlike copolymers. However, due to significant fluctuations observed for short sequences, the function S(k) can be effectively used only for segmentation of a heterosequence composed of very long subsequences. On the other hand, we find that the Jensen–Shannon divergence measure does not allow one to judge the type of statistics, but is extremely efficient for segmentation of a heterosequence. Therefore, the two introduced functions, being mutually complementary, provide an effective approach for recognizing and segmentation of heterosequences. As an example, the methods developed are applied for concatenating sequences of different proteins.Segmentation function S(k, l, x) as a function of parameter k and starting number x of “window” for a sequence composed of elastin and ribonuclease sequences.magnified imageSegmentation function S(k, l, x) as a function of parameter k and starting number x of “window” for a sequence composed of elastin and ribonuclease sequences.

Conformation-dependent evolution of copolymer sequences.

A "toy model" of molecular evolution of sequences in copolymers is proposed and implemented using a molecular-dynamics-based algorithm. The model involves coupling of conformation-dependent and sequence-dependent properties. It is shown that this model allows the realization of two main possibilities: ascending and descending branches of evolution (in terms of information content of a sequence), depending on the interaction parameters shaping the conformation of a polymer globule. The problem of adequate description of information complexity of copolymer sequences is studied. It is shown that Shannon's entropy or compressibility of a sequence gives preference to random sequences and therefore cannot be applied for this purpose. On the other hand, the Jensen-Shannon divergence measure turns out to give the description of information complexity which corresponds to our intuitive expectations. In particular, this characteristic can adequately describe two branches of evolution mentioned above, exhibiting a singularity on the boundary of these regimes.

Delineating relative homogeneous G+C domains in DNA sequences

The concept of homogeneity of G+C content is always relative and subjective. This point is emphasized and quantified in this paper using a simple example of one sequence segmented into two subsequences. Whether the sequence is homogeneous or not can be answered by whether the two-subsequence model describes the DNA sequence better than the one-sequence model. There are at least three equivalent ways of looking at the 1-to-2 segmentation: Jensen–Shannon divergence measure, log likelihood ratio test, and model selection using Bayesian information criterion. Once a criterion is chosen, a DNA sequence can be recursively segmented into multiple domains. We use one subjective criterion called segmentation strength based on the Bayesian information criterion. Whether or not a sequence is homogeneous and how many domains it has depend on this criterion. We compare six different genome sequences (yeast S. cerevisiae chromosome III and IV, bacterium M. pneumoniae, human major histocompatibility complex sequence, longest contigs in human chromosome 21 and 22) by recursive segmentations at different strength criteria. Results by recursive segmentation confirm that yeast chromosome IV is more homogeneous than yeast chromosome III, human chromosome 21 is more homogeneous than human chromosome 22, and bacterial genomes may not be homogeneous due to short segments with distinct base compositions. The recursive segmentation also provides a quantitative criterion for identifying isochores in human sequences. Some features of our recursive segmentation, such as the possibility of delineating domain borders accurately, are superior to those of the moving-window approach commonly used in such analyses.

Entropic texture-edge detection for image segmentation

A new procedure for edge detection in textured grey-level images is outlined, using the Jensen-Shannon divergence measure between the grey-level histograms of two adjacent regions defined by a sliding window. The procedure is computationally simple and provides a basic tool for both a sharpening technique and an early texture segmentation.

A class of statistical and spectral distance measures based on Bose-Einstein statistics

A class of statistical distance measures and their spectral counterparts are presented. They have strong physical foundations since they are based on the combinatorial law leading to Bose-Einstein statistics in statistical physics. It is shown that these distance measures are very closely related to the recently introduced Jensen-Shannon divergence measure. The Kullback-Leibler information (1951) number is found to be a limit case of this class.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>