Entropy Measures Research Articles

A hyperspectral band selection strategy based on adjacency clustering and local structural correlation

ABSTRACT A popular strategy to reduce the spectral size of HyperSpectral Images (HSI) is to suppress all bands whose information content is largely duplicated in surviving bands. This is commonly termed Band Selection (BS). In this manuscript, a novel, unsupervised BS technique is proposed, consisting of three main steps: 1) Adjacent structural-similarity-based band partitioning, 2) for each partition, correlation-based, cluster-representative band selection, and 3) bad cluster removal using an Entropy measure. Initially, the adjacent structural similarity is measured, using Structural SIMilarity Index (SSIM); the next step is adjacency-partitioned cluster formation using a derivative-based approach. Then, a representative band with a high correlation is selected for each cluster. Finally, according to the Entropy measure, the cluster representatives are ranked to obtain the optimal subset of bands. The proposed Adjacency Clustering and Local Structural Correlation (ACLSC)-based BS is compared with other state-of-art approaches in terms of classification performance on benchmark HSI datasets. Overall Accuracy (OA), Average Accuracy (AA), and Kappa ( κ ) are computed on three datasets, namely, Indian Pines, Salinas, and Pavia University, to validate the proposed algorithm. Validation results support the use of adjacency clustering and incorporation of spatial-structural features for BS purposes.

Analyzing household income inequality in Pakistan: a subgroup decomposition of generalized entropy measures

Analyzing household income inequality in Pakistan: a subgroup decomposition of generalized entropy measures

Retracted: On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers

Retracted: On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers

Retracted: Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications

Retracted: Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications

Probabilistic Hesitant Fuzzy Evidence Theory and Its Application in Capability Evaluation of a Satellite Communication System.

Evaluating the capabilities of a satellite communication system (SCS) is challenging due to its complexity and ambiguity. It is difficult to accurately analyze uncertain situations, making it difficult for experts to determine appropriate evaluation values. To address this problem, this paper proposes an innovative approach by extending the Dempster-Shafer evidence theory (DST) to the probabilistic hesitant fuzzy evidence theory (PHFET). The proposed approach introduces the concept of probabilistic hesitant fuzzy basic probability assignment (PHFBPA) to measure the degree of support for propositions, along with a combination rule and decision approach. Two methods are developed to generate PHFBPA based on multi-classifier and distance techniques, respectively. In order to improve the consistency of evidence, discounting factors are proposed using an entropy measure and the Jousselme distance of PHFBPA. In addition, a model for evaluating the degree of satisfaction of SCS capability requirements based on PHFET is presented. Experimental classification and evaluation of SCS capability requirements are performed to demonstrate the effectiveness and stability of the PHFET method. By employing the DST framework and probabilistic hesitant fuzzy sets, PHFET provides a compelling solution for handling ambiguous data in multi-source information fusion, thereby improving the evaluation of SCS capabilities.

Exploring the Hidden Complexity: Entropy Analysis in Pulse Oximetry of Female Athletes.

This study examines the relationship between physiological complexity, as measured by Approximate Entropy (ApEn) and Sample Entropy (SampEn), and fitness levels in female athletes. Our focus is on their association with maximal oxygen consumption (VO2,max). Our findings reveal a complex relationship between entropy metrics and fitness levels, indicating that higher fitness typically, though not invariably, correlates with greater entropy in physiological time series data; however, this is not consistent for all individuals. For Heart Rate (HR), entropy measures suggest stable patterns across fitness categories, while pulse oximetry (SpO2) data shows greater variability. For instance, the medium fitness group displayed an ApEn(HR) = 0.57±0.13 with a coefficient of variation (CV) of 22.17 and ApEn(SpO2) = 0.96±0.49 with a CV of 46.08%, compared to the excellent fitness group with ApEn(HR) = 0.60±0.09 with a CV of 15.19% and ApEn(SpO2) =0.85±0.42 with a CV of 49.46%, suggesting broader physiological responses among more fit individuals. The larger standard deviations and CVs for SpO2 entropy may indicate the body's proficient oxygen utilization at higher levels of physical demand. Our findings advocate for combining entropy metrics with wearable sensor technology for improved biomedical analysis and personalized healthcare.

A Novel Trigonometric Entropy Measure Based on the Complex Proportional Assessment Technique for Pythagorean Fuzzy Sets

The extension of intuitionistic fuzzy sets (IFS) to Pythagorean fuzzy sets (PFS) is a significant advancement, addressing the inherent limitations of IFS. This study introduces a novel entropy measure specifically designed for Pythagorean fuzzy sets, establishing its axiomatic definition and presenting key properties. Decision making guided by entropy is advantageous, as it effectively mitigates ambiguity with increasing entropy values. Furthermore, a numerical example is provided to facilitate a comparative assessment of our newly introduced entropy measure in contrast to existing PFS entropy measures. The validation of our findings is achieved through the application of the COPRAS method, which determines decision outcomes based on a multitude of influencing factors. Notably, the determination of weights in this method is underpinned by the utilization of our innovative entropy measure.

Measures of Distance in Quantum Mechanics

Combining gravity with quantum theory is still a work in progress. On the one hand, classical gravity is the geometry of space-time determined by the energy–momentum tensor of matter and the resulting nonlinear equations; on the other hand, the mathematical description of a quantum system is Hilbert space with linear equations describing evolution. In this paper, various measures in Hilbert space will be presented. In general, distance measures in Hilbert space can be divided into measures determined by energy and measures determined by entropy. Entropy measures determine quasi-distance because they do not satisfy all the axioms defining distance. Finding a general rule to determine such a measure unambiguously seems to be fundamental.

Topological characterization of cove-edged graphene nanoribbons with applications to NMR spectroscopies

Graphene nanoribbons (GNRs) have recently garnered significant attention due to their potential applications in transistors, photovoltaics, and quantum electronic devices. Cove-edged graphene nanoribbons (CGNRs) are particularly intriguing due to their unique electromagnetic properties. These nanoribbons, characterized by asymmetric edges composed of alternating hexagons, exhibit exceptional electronic properties. In this study, we employed a variety of degree and degree-sum-based topological descriptors (TDs) to calculate the topological entropy measures of CGNRs. The explicit mathematical formulae of the TDs for the CGNRs were derived using the edge partition method. Additionally, we determined the spectral diameters, delocalization energies, resonance energies, and HOMO-LUMO gaps to assess these compounds' thermodynamic and kinetic stabilities. We also utilized NEWGRAPH and MATLAB software to predict the NMR patterns for the CGNRs. The shallow HOMO-LUMO gaps in these calculations suggest that CGNRs are promising candidates for topological spintronics applications.

Confidence Levels Measurement of Mobile Phone Selection Using a Multiattribute Decision-Making Approach with Unknown Attribute Weight Information Based on T-Spherical Fuzzy Aggregation Operators

Advancement in mobile phone (MP) technology has revolutionized the lifestyle. In recent years, we observed that MP technology had been involved in almost all aspects of life, such as communication purposes, e-commerce, mobile baking, and social media connectivity. So, it becomes a hot research topic to select the best MP that fulfills the desired feathers requirement. In this paper, the expert’s familiarity with the examined objects is factored into the initial judgments under the T-spherical fuzzy sets (T-SFSs) environment. The T-SFS is the extension of the picture fuzzy (PF) set (PFS), which gives wider scope for finding the most precise options than existing fuzzy frameworks. The multiattribute decision-making (MADM) is a common and valuable method for aggregating information. For MADM, various aggregation operators (AOs) have been created over the years. The article introduces the newly proposed approach T-spherical fuzzy (T-SF) confidence level weighted averaging T−SFWAc and T-SF confidence level weighted geometric T−SFWGc. Also, some desired properties of AOs are discussed, and the T-SF entropy measure is introduced for selecting the weight criteria. A MADM framework is introduced, on the behalf of proposed operators. The proposed MADM framework is applied to solve the real-life example of consumers’ preferences to show effectiveness and practicality. Lastly, the developed framework is set side by side with other prevailing approaches to demonstrate the superiority and significance of other existing AOs.

Informational separability and entropy

Informational separability occurs when information decreases as the result of suppressing information that differentiates a subset of states in experiments. With multiple states, informational separability leads to entropy measures. Its implications in multiple different contexts are discussed, including segregation measurement, inference with partial information, and rational inattention.

Daily Streamflow of Argentine Rivers Analysis Using Information Theory Quantifiers.

This paper analyzes the temporal evolution of streamflow for different rivers in Argentina based on information quantifiers such as statistical complexity and permutation entropy. The main objective is to identify key details of the dynamics of the analyzed time series to differentiate the degrees of randomness and chaos. The permutation entropy is used with the probability distribution of ordinal patterns and the Jensen-Shannon divergence to calculate the disequilibrium and the statistical complexity. Daily streamflow series at different river stations were analyzed to classify the different hydrological systems. The complexity-entropy causality plane (CECP) and the representation of the Shannon entropy and Fisher information measure (FIM) show that the daily discharge series could be approximately represented with Gaussian noise, but the variances highlight the difficulty of modeling a series of natural phenomena. An analysis of stations downstream from the Yacyretá dam shows that the operation affects the randomness of the daily discharge series at hydrometric stations near the dam. When the station is further downstream, however, this effect is attenuated. Furthermore, the size of the basin plays a relevant role in modulating the process. Large catchments have smaller values for entropy, and the signal is less noisy due to integration over larger time scales. In contrast, small and mountainous basins present a rapid response that influences the behavior of daily discharge while presenting a higher entropy and lower complexity. The results obtained in the present study characterize the behavior of the daily discharge series in Argentine rivers and provide key information for hydrological modeling.

The sex effect on balance control while standing on vestibular-demanding tasks with/without vestibular simulations: implication for sensorimotor training for future space missions.

Background: Anatomical differences between sexes in the vestibular system have been reported. It has also been demonstrated that there is a sex difference in balance control while standing on vestibular-demanding tasks. In 2024, NASA expects to send the first female to the Moon. Therefore, to extend the current knowledge, this study attempted to examine whether different sexes respond differently to vestibular-disrupted and vestibular-demanding environments. Method: A total of fifteen males and fifteen females participated in this study. The vestibular function was quantified through different SOT conditions (SOT1: baseline; SOT5: vestibular demanding by standing with blindfolded and sway reference surface). The vestibular stimulation (VS) was applied either unilaterally or bilaterally to vestibular system to induce the sensory-conflicted and challenging tasks. Thus, a total of 6 conditions (2 SOT conditions X 3 VSs: no-VS, unilateral VS, and bilateral VS) were randomly given to these participants. Three approaches can be quantified the balance control: 1) the performance ratio (PR) of center of gravity trajectories (CoG), 2) the sample entropy measure (SampEn) of CoG, and 3) the total traveling distance of CoG. A mixed three-way repeated ANOVA measure was used to determine the interaction among the sex effect, the effect of SOT, and the effect of VS on balance control. Results: A significant sex effect on balance control was found in the PR of CoG in the anterior-posterior (AP) direction (p = 0.026) and in the SampEn of CoG in both AP and medial-lateral (ML) directions (p = 0.025, p < 0.001, respectively). Also, a significant interaction among the sex effect, the effect of SOT, and the effect of VS on balance control was observed in PR of CoG in the ML direction (p < 0.001), SampEn of CoG in the AP and ML directions (p = 0.002, p < 0.001, respectively), and a traveling distance in AP direction (p = 0.041). Conclusion: The findings in the present study clearly revealed the necessity to take sex effect into consideration while standing in vestibular-perturbed or/and vestibular demanding tasks. Also, the results in the present study could be a fundamental reference for future sensorimotor training.

On degree-based entropy measure for zero-divisor graphs

Let [Formula: see text] be a commutative ring with [Formula: see text] A zero-divisor graph [Formula: see text] is an undirected graph on the vertex set [Formula: see text] such that any two nonzero elements [Formula: see text] are adjacent whenever [Formula: see text] The concept of entropy measure is fundamental and has been the subject of interest in various fields. The purpose of this paper is to calculate the entropy measure of [Formula: see text] for various rings. We take into consideration the ring [Formula: see text] for [Formula: see text] where [Formula: see text] and [Formula: see text] are distinct prime numbers. Moreover, we also discussed the entropy measure of the zero-divisor graph for the rings [Formula: see text] and [Formula: see text] This study will help us further understand the algebraic structure of the commutative rings.

Randomness-Enhanced Expressivity of Quantum Neural Networks.

As a hybrid of artificial intelligence and quantum computing, quantum neural networks (QNNs) have gained significant attention as a promising application on near-term, noisy intermediate-scale quantum devices. Conventional QNNs are described by parametrized quantum circuits, which perform unitary operations and measurements on quantum states. In this Letter, we propose a novel approach to enhance the expressivity of QNNs by incorporating randomness into quantum circuits. Specifically, we introduce a random layer, which contains single-qubit gates sampled from a trainable ensemble pooling. The prediction of QNN is then represented by an ensemble average over a classical function of measurement outcomes. We prove that our approach can accurately approximate arbitrary target operators using Uhlmann's theorem for majorization, which enables observable learning. Our proposal is demonstrated with extensive numerical experiments, including observable learning, Rényi entropy measurement, and image recognition. We find the expressivity of QNNs is enhanced by introducing randomness for multiple learning tasks, which could have broad application in quantum machine learning.

On distance dependent entropy measures of poly propylene imine and zinc porphyrin dendrimers

AbstractA key paradigm in contemporary research is the use of graphs to represent physical systems, molecular structures, or particularly metal frameworks. Graphs are increasingly widely used in a variety of fields, including the study of quantum and molecular systems, macromolecules and their interactions, socioeconomic and ecological systems, and technical and infra‐structural systems. Understanding how these systems function, are robust, and are stable begins with structural characterization. The use of entropies and entropy‐like measurements of graphs/structures of molecules/networks is crucial from both a mathematical and physical standpoint. Several entropy measures of graphs have been defined and studied extensively during the last few decades. The current paper is devoted to investigation of distance dependent entropy measures of Poly Propylene Imine (PPI) dendrimers and Zinc Porphyrin dendrimers. The analytical formulae of distance dependent entropy measures have been developed and their patterns have been presented through graphical tools.

Comparative analysis of modified reverse degree topological indices for certain carbon nanosheets using entropy measures and multi criteria decision‐making analysis

AbstractThe diverse applications of various carbon nanostructures have sparked significant research interest. The potential significance of carbon nanosheets lies in their exceptional mechanical, electrical, and thermal properties, enabling advancements in various technological applications such as energy storage, electronics, and engineering, playing important roles in material science and nanotechnology. In the field of mathematical chemistry, topological indices play a crucial role by providing numerical insights into molecular structures. These insights facilitate predictive correlations with chemical properties and reactivity, ultimately finding utility in areas like drug design and material sciences. Expanding on this, the study delves into the application of entropy‐based methodologies that originates from the arrangement of chemical structures. By assessing the complexity and other features of these structures, graph entropies are translated into information‐theoretic metrics. This article examines modified reverse degree‐based topological indices with its universal applicability to all degree‐based indices. The standout feature is the adaptable parameter “” effectively shaping the molecular graphs degree sequence to best fit each dataset with their unique physicochemical properties, distinguishing it from conventional fixed degree methodologies. Additionally, we investigate graph entropies and examine the impact of varying the parameter “” on entropy measures across a range of nanosheet structures. The research focuses on characterizing carbon nanosheets, employing effective (MCDM) multiple criteria decision‐making methods like VIKOR, TOPSIS, and SAW. Through these techniques, a comprehensive comparative analysis of the nanosheets is conducted with the aim of establishing optimized rankings for each type based on their unique attributes and characteristics.

Information Measures for Continuous Function-Valued q-Rung Orthopair Fuzzy Sets and an Extended TOPSIS

The concept of continuous function-valued [Formula: see text]-rung orthopair fuzzy set (CFV[Formula: see text]ROFS) represents an innovative framework within fuzzy set theory, where the assessment of an element’s membership and nonmembership degrees is accomplished through continuous functions. This paper introduces a novel entropy measure for CFV[Formula: see text]ROFS, employing the Riemann integral. Furthermore, it outlines a theoretical framework for constructing a similarity measure based on entropy and presents a distance measure. The newly introduced entropy measure is used for weighting criteria and measuring the distance of the alternatives in decision-making processes. To illustrate the practical utility of these concepts, an extended Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is proposed and is employed to tackle a real-world problem previously addressed in the literature. The outcomes of this extended TOPSIS are compared with those given in existing studies, and a sensitivity analysis is performed concerning the variable [Formula: see text].

Correlation dimension and entropy in the assessment of sex differences based on human gait data.

It is proved that there are differences between gait performed by females and males, which appear in movements of selected body parts. Despite numerous state-of-the-art studies related to the discriminative analysis of motion capture data, the question of whether measures of signal complexity and uncertainty can extract valuable features for the problem of sex distinction still remains open. It is the subject of the paper. Correlation dimension, as well as approximate and sample entropies, are selected to describe motion data. In the numerical experiments, the collected dataset with 884 samples of 25 females and 30 males was used. The measurements took place in the Human Motion Laboratory (HML), equipped with a highly precise motion capture system. Two variants of data representation were investigated-time series that contain joint rotations of taken skeleton model as well as positions of the markers attached to the human body. Finally, a comparative analysis between the populations of females and males using descriptive statistics, non-parametric estimation, and statistical hypotheses verification was carried out. There are statistically significant sex differences extracted by the taken measures. In general, the movements of lower limbs result in greater values of correlation dimension and entropies for females, while selected upper body parts play a similar role for males. The dissimilarities are mainly observed in hip, ankle, shoulder, and head movements. Correlation dimension and entropy measures provide robust and explainable features of motion capture data with a valuable description of the human locomotion system. Thus, beyond the importance of discovered differences between females and males, their interpretation and understanding are also known.

On some new fuzzy entropy measure of Pythagorean fuzzy sets for decision-making based on an extended TOPSIS approach

Fuzzy entropy measures are valuable tools in decision-making when dealing with uncertain or imprecise information. There exist many entropy measures for Pythagorean Fuzzy Sets (PFS) in the literature that fail to deal with the problem of providing reasonable or consistent results to the decision-makers. To deal with the shortcomings of the existing measures, this paper proposes a robust fuzzy entropy measure for PFS to facilitate decision-making under uncertainty. The usefulness of the measure is illustrated through an illustration of decision-making in a supplier selection problem and compared with existing fuzzy entropy measures. The Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) approach is also explored to solve the decision-making problem. The results demonstrate that the proposed measure can effectively capture the degree of uncertainty in the decision-making process, leading to more accurate decision outcomes by providing a reliable and robust ranking of alternatives.