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浙江大学学报(工学版)
浙江大学学报(工学版)  2022, Vol. 56 Issue (5): 1017-1024    DOI: 10.3785/j.issn.1008-973X.2022.05.019
计算机与控制工程     
基于图信号处理的传染病传播预测方法
李文娟1(),邓洪高1,*(),马谋1,蒋俊正1,2
1. 桂林电子科技大学 信息与通信学院，广西壮族自治区 桂林 541004
2. 桂林电子科技大学 卫星导航定位与位置服务国家地方联合工程研究中心，广西壮族自治区 桂林 541004
Prediction method of infectious disease transmission based on graph signal processing
Wen-juan LI1(),Hong-gao DENG1,*(),Mou MA1,Jun-zheng JIANG1,2
1. School of Information and Communication, Guilin University of Electronic Technology, Guilin 541004, China
2. State and Local Joint Engineering Research Center for Satellite Navigation and Location Service, Guilin University of Electronic Technology, Guilin 541004, China
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摘要：

针对现有传染病传播预测模型存在未充分考虑数据的内在关联性的问题,采用图多项式-向量自回归(GP-VAR)模型对传染病的传播进行预测, 并提出新的用于模型参数估计的优化方法. 将传染病发病地区建模为图节点, 并根据地区间的距离信息和人群流动情况确定节点间的边及其权重, 以反映传染病传播过程中的空间关联性. 将不同时刻的感染疾病人数建模为时变图信号, 使用GP-VAR模型对时变图信号在图上的演变过程进行预测, 并设计一种最小二乘(LS)优化方法对GP-VAR模型的参数进行估计. 仿真实验结果表明, 与现有的预测方法相比，所提方法能够更好地考虑到数据在空间维的相关性和时间维的演变特性, 更加准确地刻画传染病的传播特性, 且具有普适性, 预测效果更好.
关键词： 传染病预测;  图信号处理;  时间序列;  时变图信号;  最小二乘    
Abstract:

The existing spread predicting models of infectious diseases have not sufficiently considered the intrinsic correlation of the data. To solve this problem, graph polynomial-vector autoregressive (GP-VAR) model was used to predict the spread of infectious diseases, and a new optimization method for estimating model parameters was proposed. The regions where infectious diseases occur were modeled as nodes on the graph, and edges and weights between nodes were determined by the distance information of the regions and the flow of people, so as to reflect the spatial relevance in the transmission process of infectious diseases. The number of cases at different times was modeled as the time-varying graph signal, the GP-VAR model was used to predict the evolution process of the time-varying graph signal on the graph, and a least squares (LS) optimization method was designed to estimate the parameters of the GP-VAR model. Experimental results show that the proposed method can better consider the correlation of data in spatial dimension and the evolution of data in time dimension, and characterize the transmission characteristics of infectious diseases more accurately, which has universality and better prediction effect compared with the existing prediction methods.
Key words: infectious disease prediction    graph signal processing    time series    time-varying graph signal    least squares
收稿日期: 2021-09-13 出版日期: 2022-05-31
CLC:  TN 911  
基金资助: 国家自然科学基金资助项目（62171146）；广西创新驱动发展专项（桂科AA21077008）；广西科技基地和人才专项（桂科AD21220112）；广西自然科学杰出青年基金资助项目（2021GXNSFFA220004）
通讯作者: 邓洪高     E-mail: 20022201022@mails.guet.edu.cn;dhg@guet.edu.cn
作者简介: 李文娟（1999—），女，硕士生，从事图信号处理理论与应用研究. orcid.org/0000-0002-3386-3828. E-mail: 20022201022@mails.guet.edu.cn
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引用本文:

李文娟,邓洪高,马谋,蒋俊正. 基于图信号处理的传染病传播预测方法[J]. 浙江大学学报(工学版), 2022, 56(5): 1017-1024.

Wen-juan LI,Hong-gao DENG,Mou MA,Jun-zheng JIANG. Prediction method of infectious disease transmission based on graph signal processing. Journal of ZheJiang University (Engineering Science), 2022, 56(5): 1017-1024.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2022.05.019    或    https://www.zjujournals.com/eng/CN/Y2022/V56/I5/1017

图 1  社交网络图及图上信号
图 2  有向周期时间序列图
图 3  欧洲125个主要城市的连接图
图 4  德国412个地区的连接图
图 5  不同类型的传染病数据下本研究方法连续50 d的一步预测结果
图 6  不同方法在SI、SEIRS、COVID-19数据下的6步预测误差对比
图 7  不同参数下本研究方法的第5步预测误差对比
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