On Shannon entropy and its applications

Saraiva, Paulo

doi:10.1016/j.kjs.2023.05.004

Cited by 16 publications

(5 citation statements)

References 10 publications

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“…In the 1940s, Claude Shannon introduced the concept of information entropy by integrating statistical thermodynamics, and provided a mathematical expression for calculating specific information entropy, thereby addressing the quantification issue of information. [28] Information entropy, also known as Shannon entropy, is commonly described using probability theory to measure the uncertainty in a system.…”

Section: Information Entropymentioning

confidence: 99%

Identifying influential spreaders in complex networks based on density entropy and community structure

Su 苏,

Chen 陈,

Ai 艾

et al. 2024

Chinese Phys. B

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In recent years, exploring the relationship between community structure and node centrality in complex networks has gained significant attention from researchers, given its fundamental theoretical significance and practical implications. To address the impact of network communities on target nodes and effectively identify highly influential nodes with strong propagation capabilities, this paper therefore proposes a novel influential spreaders identification algorithm based on density entropy and community structure (DECS). The proposed method initially integrates a community detection algorithm to obtain the community partition results of the networks. It then comprehensively considers the internal and external density entropies and degree centrality of the target node to evaluate its influence. Experimental validation is conducted on eight networks of varying sizes through susceptible-infected-recovered (SIR) propagation experiments and network static attack experiments. The experimental results demonstrate that the proposed method outperforms five other node centrality methods under the same comparative conditions, particularly in terms of information spreading capability, thereby enhancing the accurate identification of critical nodes in networks.

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Section: Information Entropymentioning

confidence: 99%

Identifying influential spreaders in complex networks based on density entropy and community structure

Su 苏,

Chen 陈,

Ai 艾

et al. 2024

Chinese Phys. B

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“…The approach presented in this study seeks to automatically identify the optimal neighborhood radius using the entropy feature (E f ), which characterizes data distribution and provides insight into its structure. Entropy and data volume are closely linked: larger datasets exhibit greater disorder and entropy, whereas smaller datasets offer fewer choices, resulting in reduced entropy [83]. The aim here is to utilize this feature within a neighborhood to identify the optimal radius that enhances differentiation among the three primary geometric patterns (linearity, planarity, and scatter).…”

Section: Neighborhood Scalementioning

confidence: 99%

Hierarchical SVM for Semantic Segmentation of 3D Point Clouds for Infrastructure Scenes

Mansour,

Martens,

Blankenbach

2024

Infrastructures

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The incorporation of building information modeling (BIM) has brought about significant advancements in civil engineering, enhancing efficiency and sustainability across project life cycles. The utilization of advanced 3D point cloud technologies such as laser scanning extends the application of BIM, particularly in operations and maintenance, prompting the exploration of automated solutions for labor-intensive point cloud modeling. This paper presents a demonstration of supervised machine learning—specifically, a support vector machine—for the analysis and segmentation of 3D point clouds, which is a pivotal step in 3D modeling. The point cloud semantic segmentation workflow is extensively reviewed to encompass critical elements such as neighborhood selection, feature extraction, and feature selection, leading to the development of an optimized methodology for this process. Diverse strategies are implemented at each phase to enhance the overall workflow and ensure resilient results. The methodology is then evaluated using diverse datasets from infrastructure scenes of bridges and compared with state-of-the-art deep learning models. The findings highlight the effectiveness of supervised machine learning techniques at accurately segmenting 3D point clouds, outperforming deep learning models such as PointNet and PointNet++ with smaller training datasets. Through the implementation of advanced segmentation techniques, there is a partial reduction in the time required for 3D modeling of point clouds, thereby further enhancing the efficiency and effectiveness of the BIM process.

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“…The hyper-parameters (a, b) are selected for Bayesian computations of the parameter λ and Shannon's entropy in such a manner that the prior mean is precisely identical to the true values of the parameter, i.e., λ = a/b. Specifically, we consider (a, b) = (3, 4) and (3,2) for λ = 0.75 and 1.5, respectively. When computing Bayes estimators under the LINEX loss function, we consider the loss function parameter c = −0.5 and 0.5.…”

Section: Monte Carlo Simulation Studymentioning

confidence: 99%

“…The HPD credible intervals have smaller simulated average lengths than those frequentist confidence intervals. (3,20,8) [1] 0.8372 0.0189 0.8066 0.0174 0.7991 0.0181 0.8329 0.0024 0.8298 0.0025 [2] 0.8371 0.0185 0.8074 0.0171 0.8000 0.0178 0.8333 0.0024 0.8302 0.0025 [3] 0.8371 0.0172 0.8101 0.0160 0.8031 0.0166 0.8342 0.0023 0.8314 0.0024 (3,20,16) [4] 0.8475 0.0091 0.8305 0.0087 0.8263 0.0089 0.8413 0.0016 0.8394 0.0017 [5] 0.8475 0.0091 0.8305 0.0087 0.8263 0.0089 0.8413 0.0016 0.8394 0.0017 [6] 0.8475 0.0088 0.8312 0.0084 0.8272 0.0086 0.8416 0.0016 0.8398 0.0016 (3,50,20) [7] 0.8485 0.0074 0.8348 0.0071 0.8314 0.0073 0.8433 0.0014 0.8418 0.0014 [8] 0.8485 0.0072 0.8353 0.0070 0.8320 0.0071 0.8435 0.0014 0.8420 0.0014 [9] 0.8483 0.0066 0.8366 0.0064 0.8336 0.0065 0.8442 0.0013 0.8428 0.0013 (3,50,40) [10] 0.8496 0.0039 0.8425 0.0039 0.8407 0.0039 0.8472 0.0009 0.8463 0.0009 [11] 0.8496 0.0039 0.8425 0.0039 0.8407 0.0039 0.8472 0.0009 0.8463 0.0009 [12] 0.8495 0.0038 0.8428 0.0037 0.8411 0.0038 0.8474 0.0008 0.8465 0.0008 (5,20,8) [1] 0.8371 0.0180 0.8505 0.0124 0.8011 0.0174 0.8483 0.0023 0.8306 0.0025 [2] 0.8370 0.0177 0.8504 0.0122 0.8020 0.0171 0.8484 0.0023 0.8310 0.0024 [3] 0.8369 0.0166 0.8503 0.0117 0.8046 0.0161 0.8485 0.0022 0.8319 0.0023 (5,20,16) [4] 0.8474 0.0087 0.8536 0.0072 0.8276 0.0085 0.8511 0.0016 0.8400 0.0016 [5] 0.8474 0.0086 0.8536 0.0072 0.8276 0.0085 0.8511 0.0016 0.8400 0.0016 [6] 0.8474 0.0084 0.8536 0.0070 0.8283 0.0082 0.8511 0.0015 0.8403 0.0016 (5,50,20) [7] 0.8485 0.0070 0.8535 0.0061 0.8325 0.0069 0.8515 0.0013 0.8422 0.0014 [8] 0.8484 0.0069 0.8535 0.0060 0.8329 0.0068 0.8515 0.0013 0...…”

Section: Monte Carlo Simulation Studymentioning

confidence: 99%

See 1 more Smart Citation

On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data

Kumar,

2024

Stats

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Shannon’s entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon’s entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon’s entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon’s entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis.

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On Shannon entropy and its applications

Cited by 16 publications

References 10 publications

Identifying influential spreaders in complex networks based on density entropy and community structure

Identifying influential spreaders in complex networks based on density entropy and community structure

Hierarchical SVM for Semantic Segmentation of 3D Point Clouds for Infrastructure Scenes

On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data

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