Volume 31 Issue 5
Sep.  2022
Turn off MathJax
Article Contents
SONG Zhanjie and ZHANG Jiaxing, “A Note for Estimation About Average Differential Entropy of Continuous Bounded Space-Time Random Field,” Chinese Journal of Electronics, vol. 31, no. 5, pp. 793-803, 2022, doi: 10.1049/cje.2021.00.213
Citation: SONG Zhanjie and ZHANG Jiaxing, “A Note for Estimation About Average Differential Entropy of Continuous Bounded Space-Time Random Field,” Chinese Journal of Electronics, vol. 31, no. 5, pp. 793-803, 2022, doi: 10.1049/cje.2021.00.213

A Note for Estimation About Average Differential Entropy of Continuous Bounded Space-Time Random Field

doi: 10.1049/cje.2021.00.213
Funds:  This work was supported by the National Key R&D Program of China (2020YFC1522602) and the Shenzhen Sustainable Development Project (KCXFZ20201221173013036).
More Information
  • Author Bio:

    was born in Hebei Province, China. He received the Ph.D. degree in Nankai University. He is currently a Professor of Georgia Tech Shenzhen Institute, Tianjin University, and Tianjin Key Laboratory of Brain-Inspired Intelligence Technology, Tianjin University. His research interests include sampling approximation and reconstruction of random signals. (Email: zhanjiesong@tju.edu.cn)

    (corresponding author) was born in Hebei Province, China. He is currently working toward the Ph.D. degree with the School of Mathematics, Tianjin University. His research interests include space-time random field and entropy. (Email: zhangjiaxing2017@tju.edu.cn)

  • Received Date: 2021-06-18
  • Accepted Date: 2022-02-27
  • Available Online: 2022-04-24
  • Publish Date: 2022-09-05
  • In this paper, we mainly study the discrete approximation about average differential entropy of continuous bounded space-time random field. The estimation of differential entropy on random variable is a classic problem, and there are many related studies. Space-time random field is a theoretical extension of adding random variables to space-time parameters, but studies on discrete estimation of entropy on space-time random field are relatively few. The differential entropy forms of continuous bounded space-time random field and discrete estimations are discussed, and three estimation forms of differential entropy in the case of random variables are generated in this paper. Furthermore, it is concluded that under the condition that the entropy estimation formula after space-time segmentation converges with probability 1, the average entropy in the bounded space-time region can also converge with probability 1, and three generalized entropies are verified respectively. In addition, we also carried out numerical experiments on the convergence of average entropy estimation based on parameters, and the numerical results are consistent with the theoretical results, which indicting further study of the average entropy estimation problem of space-time random fields is significant in the future.
  • loading
  • [1]
    A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Doklady Akademii nauk SSSR, vol.30, pp.299–303, 1941.
    [2]
    A. N. Kolmogorov, “On the degeneration of isotropic turbulence in an incompressible viscous flu,” Doklady Akademii nauk SSSR, vol.31, pp.538–542, 1941.
    [3]
    A. N. Kolmogorov, “Dissipation of energy in isotropic turbulence,” Doklady Akademii nauk SSSR, vol.32, pp.19–21, 1941.
    [4]
    A. M. Yaglom, “Some classes of random fields in n-dimensional space, related to stationary random processes,” Theory of Probability and Its Applications, vol.2, no.3, pp.273–320, 1957. doi: 10.1137/1102021
    [5]
    A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions. Volume I: Basic results, Springer, New York, vol.131, 1987.
    [6]
    A. M. Yaglom, Correlation Theory of Stationary and Related Random Functions. Volume Ⅱ: Supplementary Notes and References, Springer-Velag, Berlin, 1987.
    [7]
    J. Sun, “Tail probabilities of the maxima of Gaussian random fields,” Annals of Probability, vol.21, no.1, pp.34–71, 1993.
    [8]
    R. Basu, V. Sidoravicius, and A. Sly, “Lipschitz embeddings of random fields,” Probability Theory and Related Fields, vol.171, pp.1121–1179, 2018.
    [9]
    Z. Song and S. Zhang, “An almost sure result on approximation of homogeneous random field from local averages,” Chinese Journal of Electronics, vol.28, no.1, pp.93–99, 2019. doi: 10.1049/cje.2018.11.001
    [10]
    L. Wu and G. Samorodnitsky, “Regularly varying random fields,” Stochastic Processes and Their Applications, vol.130, no.7, pp.4470–4492, 2020. doi: 10.1016/j.spa.2020.01.005
    [11]
    G. Cleanthous, A. G. Georgiadis, A. Lang, and E. Porcu, “Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces,” Stochastic Processes and Their Applications, vol.130, no.8, pp.4873–4891, 2020. doi: 10.1016/j.spa.2020.02.003
    [12]
    E. Koch, C. Dombry, and C. Y. Robert, “A central limit theorem for functions of stationary max-stable random fields on $\mathbb{R}^{d}$,” Stochastic Processes and Their Applications, vol.129, no.9, pp.3406–3430, 2020.
    [13]
    Z. Ye, “On entropy and $\varepsilon$-entropy of random fields,” Ph.D. Thesis, Cornell University, Ithaca, NY, USA, 1989.
    [14]
    Z. Ye and T. Berger, “A new method to estimate the critical distortion of random fields,” IEEE Transactions on Information Theory, vol.38, no.1, pp.152–157, 1992. doi: 10.1109/18.108261
    [15]
    Z. Ye and T. Berger, Information Measures for Discrete Random Fields, Science Press, Beijing/New York, 1998.
    [16]
    P. Fan, Y. Dong, J. lu, and S. Liu, “Message importance measure and its application to minority subset detection in big data,” 2016 IEEE Globecom Workshops (GC Wkshps), Washington, DC, USA, pp.1–5, 2016.
    [17]
    R. She, S. Liu, Y. Dong, and P. Fan, “Focusing on a probability element: Parameter selection of message importance measure in big data,” 2017 IEEE International Conference on Communications, Alberta, Canada, pp.1–6, 2017.
    [18]
    D. Wang and F. Shao, “Research of neural network structural optimization based on information entropy,” Chinese Journal of Electronics, vol.29, no.4, pp.632–638, 2020. doi: 10.1049/cje.2020.05.006
    [19]
    Z. Zhang, J. Luo, and M. Jin, “Application of maximum entropy theorem in channel estimation,” Chinese Journal of Electronics, vol.29, no.2, pp.361–370, 2020. doi: 10.1049/cje.2020.01.015
    [20]
    S. Zhu, W. Xi, and L. Fan, “Sequence-oriented stochastic model of RO-TRNGs for entropy evaluation,” Chinese Journal of Electronics, vol.29, no.2, pp.371–377, 2020. doi: 10.1049/cje.2019.12.010
    [21]
    W. Lin, H. Wang, and Z. Deng, “State machine with tracking tree and traffic allocation scheme based on cumulative entropy for satellite network,” Chinese Journal of Electronics, vol.29, no.1, pp.183–189, 2020. doi: 10.1049/cje.2019.06.024
    [22]
    J. Cai, Y. Li, and W. Li, “Two entropy-based criteria design for signal complexity measures,” Chinese Journal of Electronics, vol.28, no.6, pp.1139–1143, 2019. doi: 10.1049/cje.2019.07.008
    [23]
    K. Li and Y. Gao, “Fuzzy clustering with the structural $\alpha$-entropy,” Chinese Journal of Electronics, vol.27, no.6, pp.1118–1125, 2018. doi: 10.1049/cje.2018.04.004
    [24]
    Y. Zuo, J. Li, and Y. Tang, “A value classification of electronic product reviews based on maximum entropy,” Chinese Journal of Electronics, vol.25, no.6, pp.1071–1078, 2016. doi: 10.1049/cje.2016.06.014
    [25]
    Z. Dai, X. Zhang, and H. Fang, “High accuracy velocity measurement based on keystone transform using entropy minimization,” Chinese Journal of Electronics, vol.25, no.4, pp.774–778, 2016. doi: 10.1049/cje.2016.06.009
    [26]
    C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal, vol.27, no.3, pp.379–423, 1948. doi: 10.1002/j.1538-7305.1948.tb01338.x
    [27]
    L. Györfi and E. C. van der Meulen, “Density-free convergence properties of various estimators of entropy,” Computational Statistics and Data Analysis, vol.5, no.4, pp.425–436, 1987. doi: 10.1016/0167-9473(87)90065-X
    [28]
    L. Györfi and E. C. van der Meulen, “On the nonparametric estimation of entropy functional,” Nonparametric Functional Estimation and Related Topics, NATO ASI Series, Springer, Dordrecht, vol.335, pp.81–95, 1990.
    [29]
    B. Forte and W. Hughes, “The maximum entropy principle: a tool to defne new entropies,” Reports on Mathematical Physics, vol.26, no.2, pp.227–235, 1988. doi: 10.1016/0034-4877(88)90025-0
    [30]
    S. Lee, I. Vonta, and A. Karagrigoriou, “A maximum entropy type test of fit,” Computational Statistics and Data Analysis, vol.55, no.9, pp.2635–2643, 2011. doi: 10.1016/j.csda.2011.03.012
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(4)

    Article Metrics

    Article views (981) PDF downloads(157) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return