基于稀疏贝叶斯算法的演化博弈网络重构

计算机与现代化 ›› 2022, Vol. 0 ›› Issue (04): 72-78.

基于稀疏贝叶斯算法的演化博弈网络重构

(长安大学理学院，陕西西安710064)

出版日期:2022-05-07 发布日期:2022-05-07
作者简介:赵丽娜(1997—)，女，山西长治人，硕士研究生，研究方向：复杂网络，E-mail: 2304613460@qq.com; 张亚楠（1992—），女，河南商丘人，硕士研究生，研究方向：深度学习，人工智能，E-mail: 3086057318@qq.com; 肖玉柱（1980—），男，辽宁大石桥人，副教授，硕士生导师，博士，研究方向：深度学习，复杂网络，E-mail: yuzhuxiao@chd.edu.cn。
基金资助:
中央高校基本科研业务费专项资金资助项目(310812163504, 300102129202)

Reconfiguration of Evolutionary Game Network Based on Sparse Bayesian Algorithm

(School of Sciences, Chang’an University, Xi’an 710064, China)

Online:2022-05-07 Published:2022-05-07

摘要/Abstract

摘要： 演化博弈是自然和社会系统中一种常见的互动类型，探知演化博弈网络的拓扑结构是理解其功能和集体行为的基础。对于演化博弈网络，个体的博弈行为通常难以用动力学方程进行描述，而且相关的时序信息一般数量有限并且是离散的，因此在有限的个体博弈信息下重构网络的结构有着重要的研究意义。本文基于稀疏贝叶斯学习方法进一步发展了演化博弈网络的重构方法，通过在随机网络和小世界网络上的数值模拟验证该方法的有效性。与先前的基于L1范数的方法相比，该方法同样能够在较少的个体博弈信息下实现网络的重构，并且具有更高的重构效率和更强的噪声鲁棒性。

关键词: 演化博弈网络, 稀疏贝叶斯, 网络重构

Abstract: Evolutionary game is a common type of interaction model in natural and social systems. Exploring the topological structure of an evolutionary game network is the basis for understanding its functions and collective behaviors. For evolutionary game networks, the individual game behavior is usually difficult to be described by dynamic equations, and the related time series information is generally limited and discrete, so it is important to reconstruct the network structure under the limited individual game information. This paper develops the reconstruction method of evolutionary game network based on the sparse Bayesian learning method. The validity of this method is verified by numerical simulation on random networks and small-world networks. Compared with previous L1 norm-based methods, this method can also reconstruct networks with less individual game information, and has higher reconstructing efficiency and stronger noise robustness.

Key words: evolutionary game network, sparse Bayes, network reconstruction

赵丽娜, 张亚楠, 肖玉柱. 基于稀疏贝叶斯算法的演化博弈网络重构[J]. 计算机与现代化, 2022, 0(04): 72-78.

ZHAO Li-na, ZHANG Ya-nan, XIAO Yu-zhu. Reconfiguration of Evolutionary Game Network Based on Sparse Bayesian Algorithm[J]. Computer and Modernization, 2022, 0(04): 72-78.

参考文献［29］

［1］	WANG L Z, CHEN Y Z, WANG W X, et al. Physical controllability of complex networks［J］. Scientific Reports, 2017,7(1). DOI: 10.1038/srep40198.
［2］	ANGULO M T, MORENO J A, LIPPNER G, et al. Fundamental limitations of network reconstruction from temporal data［J］. Journal of the Royal Society, Interface, 2017,14(127). DOI: 10.1098/rsif.2016.0966.
［3］	LINDMARK G, ALTAFINI C. Minimum energy control for complex networks［J］. Scientific Reports, 2018,8(1). DOI: 10.1038/s41598-018-21398-7.
［4］	BOF N, BAGGIO G, ZAMPIERI S. On the role of network centrality in the controllability of complex networks［J］. IEEE Transactions on Control of Network Systems, 2017,4(3):643-653.
［5］	WANG W X, LAI Y C, GREBOGI C, et al. Network reconstruction based on evolutionary-game data via compressive sensing［J］. Physical Review X, 2011,1(2). DOI: 10.1103/PhysRevX.1.021021.
［6］	MENARA T, BAGGIO G, BASSETT D S, et al. A framework to control functional connectivity in the human brain［C］// Proceedings of the 2019 IEEE 58th Conference on Decision and Control (CDC). 2019:4697-4704.
［7］	RAZA K, ALAM M. Recurrent neural network based hybrid model for reconstructing gene regulatory network［J］. Computational Biology and Chemistry, 2016,64:322-334.
［8］	WANG W X, YANG R, LAI Y C, et al. Time-series-based prediction of complex oscillator networks via compressive sensing［J］. Europhysics Letters, 2011,94(4). DOI: 10.1209/0295-5075/94/48006.
［9］	MANTEGNA R N. Hierarchical structure in financial markets［J］. The European Physical Journal B: Condensed Matter and Complex Systems, 1999,11(1):193-197.
［10］	LUO Q, LIU X, YI D Y. Reconstructing gene networks from microarray time-series data via Granger causality［C］// Proceedings of the 2009 International Conference on Complex Sciences. 2009:196-209.
［11］	HU Y, WANG Z Y, LI X L. Impact of policies on electric vehicle diffusion: An evolutionary game of small world network analysis［J］. Journal of Cleaner Production, 2020,265. DOI: 10.1016/j.jclepro.2020.121703.
［12］	KE M L, GAO Z, WU Y P, et al. Compressive sensing-based adaptive active user detection and channel estimation: Massive access meets massive MIMO［J］. IEEE Transactions on Signal Processing, 2020,68:764-779.
［13］	ZHANG C C, SONG S T, WEN X T, et al. Improved sparse decomposition based on a smoothed L0 norm using a Laplacian kernel to select features from fMRI data［J］. Journal of Neuroscience Methods, 2015,245:15-24.
［14］	TROPP J A, GILBERT A C. Signal recovery from random measurements via orthogonal matching pursuit［J］. IEEE Transactions on Information Theory, 2007,53(12):4655-4666.
［15］	TIPPING M E. Sparse Bayesian learning and the relevance vector machine［J］. Journal of Machine Learning Research, 2001,1:211-244.
［16］	FENG J C, JIA K B, LI Z, et al. Bayesian sparse-based reconstruction in bioluminescence tomography improves localization accuracy and reduces computational time［J］. Journal of Biophotonics, 2018,11(4). DOI: 10.1002/jbio.201700214.
［17］	包学志. 基于贝叶斯原理的4D-CT图像肝脏呼吸运动预测方法研究［D］. 深圳:中国科学院大学, 2020.
［18］	JI Y Z, YUAN S Y, WANG S X, et al. Frequency-domain sparse Bayesian learning inversion of AVA data for elastic parameters reflectivities［J］. Journal of Applied Geophysics, 2016,133:1-8.
［19］	ZHANG Z L, JUNG T P, MAKEIG S, et al. Compressed sensing of EEG for wireless telemonitoring with low energy consumption and inexpensive hardware［J］. IEEE Transactions on Biomedical Engineering, 2013,60(1):221-224.
［20］	郑月龙,张卫国. 多人演化雪堆博弈的合作动态研究［J］. 管理工程学报, 2016,30(4):112-116.
［21］	BONGARD J, LIPSON H. Automated reverse engineering of nonlinear dynamical systems［J］. Proceedings of the National Academy of Sciences of the United States of America, 2007,104(24):9943-9948.
［22］	蔡霞,马社祥,孟鑫. 启发式重构算法在压缩传感中的应用研究［J］. 计算机应用研究, 2012,29(11):4232-4234.
［23］	FORNASIER M, RAUHUT H. Compressive sensing［M］// Handbook of Mathematical Methods in Imaging. Springer, 2011:187-228.
［24］	〖KG-*3〗CANDES E, ROMBERG J. L1-MAGIC: Recovery of Sparse Signals via Convex Programming［DB/OL］. (2005-10-30)［2021-03-29］. http://brainimaging.waisman.wisc.edu/~chung/BIA/download/matlab.v1/l1magic-1.1/l1magic_notes.pdf.
［25］	WIPF D P, RAO B D. Sparse Bayesian learning for basis selection［J］. IEEE Transactions on Signal Processing, 2004,52(8):2153-2164.
［26］	BRENNAN M, BRESLER G, NAGARAJ D. Phase transitions for detecting latent geometry in random graphs［J］. Probability Theory and Related Fields, 2020,178(3-4):1215-1289.
［27］	WATTS D J, STROGATZ S H. Collective dynamics of ‘small-world’ networks［J］. Nature, 1998,393(6684):440-442.
［28］	薛晓斐. 基于小世界网络的新冠肺炎疫情谣言传播仿真研究［J］. 图书情报研究, 2021,14(1):51-59.
［29］	AMIN F, ABBASI R, REHMAN A, et al. An advanced algorithm for higher network navigation in social Internet of Things using small-world networks［J］. Sensors, 2019,19(9). DOI: 10.3390/s19092007.