Nonlinear spread function based graph-vector autoregressive disease propagation prediction method and system

Abstract

The application discloses a graph-vector autoregressive disease propagation prediction method and system based on a nonlinear extension function. Firstly, disease propagation data is modeled as a graph and a graph signal. A graph-vector autoregressive model is used to describe the correlation between time-varying graph signals. A nonlinear extension function is used to map the signals from a low-dimensional space to a high-dimensional space. Then, an optimization problem is proposed to estimate the parameters of the graph-vector autoregressive model based on the nonlinear extension function. Finally, numerical experiments are performed on different data sets using the optimized prediction model to verify the performance of the prediction model. This method can describe the nonlinear spatiotemporal correlation between time-varying graph signals and thus make predictions. The model is suitable for predicting problems of disease propagation data with spatiotemporal characteristics. The method can better describe the nonlinear spatiotemporal correlation characteristics of time-varying data and has good prediction ability.

Description

Technical Field

[0001] This invention relates to the fields of disease transmission prediction, graphical models, and graphical signal processing, specifically a graph-vector autoregressive method for disease transmission prediction based on a nonlinear spread function. Background Technology

[0002] Predicting multivariate processes is a key problem in signal processing and has been widely applied in disease transmission prediction. Predicting the spread of diseases based on historical data and implementing corresponding countermeasures can significantly reduce the harm of infectious diseases. However, accurately predicting irregular, time-varying disease transmission data—characterized by high dimensionality and irregularities—requires a challenging approach to describing the intrinsic correlations of time series data, representing their underlying structure, and ultimately making accurate predictions.

[0003] Disease transmission data is a typical type of spatiotemporal data, exhibiting correlation characteristics in both time and space. Temporally, the number of infected individuals is influenced by the infection situation at previous moments; spatially, the incidence rate and transmission characteristics of a region are highly correlated with its neighboring regions and regions with similar related factors, and vice versa. Classical signal processing prediction methods primarily focus on the temporal evolution characteristics of disease transmission, neglecting its spatial correlation and nonlinear correlation.

[0004] Therefore, a method is needed that can predict disease transmission data. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a graph-vector autoregressive method for predicting disease transmission based on a nonlinear spread function. This method is applicable to the prediction problem of disease transmission data with spatiotemporal characteristics. This method can better describe the nonlinear spatiotemporal correlation characteristics of time-varying data and has good predictive ability.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] The graph-vector autoregressive disease transmission prediction method based on a nonlinear spread function provided by this invention includes the following steps:

[0008] 1) Acquire disease transmission data and perform graph and graph signal modeling on the disease transmission data;

[0009] 2) Construct a graph-vector autoregressive model;

[0010] 3) Use nonlinear spreading functions to map graph signals from low-dimensional space to high-dimensional space;

[0011] 4) Construct a graph-vector autoregressive model based on a nonlinear spread function;

[0012] 5) Estimate the parameters of the graph-vector autoregressive model based on the nonlinear spread function to obtain an optimized disease transmission prediction model.

[0013] Furthermore, the disease transmission data is modeled as graphs and graph signals in the following manner:

[0014] set up Region Time-varying disease transmission data at consecutive moments are ;

[0015] in, , For the region exist The number of infected cases at any given time;

[0016] The region is modeled as graph nodes, and the nodes are connected by edges based on the characteristics of the data to construct the graph. ,in, For the set of graph nodes, Let be the set of edges. This is a weight matrix, where each element represents the correlation and adjacency between corresponding nodes. If there are no edges connecting nodes, the weight is 0.

[0017] at this time, As a time-varying graph signal, its internal elements represent the graph signal at graph nodes at different times.

[0018] Furthermore, the graph-vector autoregressive model is established in the following manner:

[0019] set up The signal value at a given time is represented as the value before. The signal at each time point is a function of the time-varying graph signal. The graph-vector autoregressive model is used to model the time-varying graph signal as shown in formula (1):

[0020] (1)

[0021] in, express An estimate of the number of infected cases at any given time; express The actual number of infected cases at any given time; For the error vector, It is a graph Laplace matrix. Representing the Laplace matrix Power of 1 for The coefficients of the order-highest Laplace matrix are... Degree matrix It is a diagonal matrix whose internal elements are The lines and;

[0022] Furthermore, the mapping of the signal from the low-dimensional space to the high-dimensional space using the nonlinear spreading function is performed in the following manner:

[0023] From formula (1), we can know It contains information about historical moments.

[0024] Therefore, the extended function in trigonometric form will Mapping to higher dimensions, the extended function takes the form shown in equation (2):

[0025] (2)

[0026] in, and To expand the indicators, It is the order of the extension function. and The definition is shown in formula (3):

[0027] (3)

[0028] make This indicates that the function has been expanded to... High-dimensional signals;

[0029] in, It contains information about historical moments; Representing the Laplace matrix Power; express The graphical signal at time; Indicates related The One extension function; , , This represents a parameter related to the order of the extended function.

[0030] Furthermore, the graph-vector autoregressive model based on the nonlinear spread function is constructed as follows:

[0031] The definition of the graph-vector autoregressive model based on the nonlinear spread function is shown in equation (4):

[0032] (4)

[0033] in, for A coefficient vector of dimension, The coefficients represent the high-dimensional signal after being expanded by the spread function;

[0034] Based on the minimum mean square error criterion, the coefficient vector of the prediction model The estimation problem is shown in Equation (5):

[0035] (5)

[0036] The theoretical solution to this least squares optimization problem is shown in equation (6):

[0037] (6)

[0038] in, , The definition is shown in formula (7):

[0039] (7)

[0040] in, This represents the coefficient vector obtained by solving the optimization problem; Indicates the number of days of known data required for the prediction; Representation matrix The false rebellion.

[0041] Furthermore, it also includes the following steps:

[0042] The optimized disease transmission prediction model was used to predict the transmission data of different types of diseases. The normalized minimum mean square error (rNMSE) formula was used to quantify the error and evaluate the model performance. The error formula is shown in formula (8):

[0043] (8)

[0044] in, for The actual number of cases at any given time point. For the predicted number of cases, This indicates the number of prediction steps, which is the number of days for forward prediction of disease transmission data.

[0045] The present invention provides a graph-vector autoregressive disease transmission prediction system based on a nonlinear expansion function, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-mentioned method.

[0046] The beneficial effects of this invention are as follows:

[0047] This invention provides a graph-vector autoregressive (GAR) disease transmission prediction method based on a nonlinear spread function. The method involves: 1) modeling disease transmission data into graphs and graph signals; 2) using a GAR model to characterize the correlation between time-varying graph signals; 3) using a nonlinear spread function to map the signals from a low-dimensional space to a high-dimensional space; 4) proposing an optimization problem to estimate the parameters of the GAR model based on the nonlinear spread function; and 5) conducting numerical experiments on different datasets to verify the performance of the optimized prediction model. This method can characterize the nonlinear spatiotemporal correlation between time-varying graph signals for prediction. This model combines a nonlinear spread module with a GAR model, optimizes the parameters of the nonlinear prediction model, and finally uses the optimized nonlinear prediction model to predict disease transmission data. This method is suitable for predicting disease transmission data with spatiotemporal characteristics, effectively describing the nonlinear spatiotemporal correlation characteristics of time-varying data, and exhibiting good predictive ability.

[0048] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0049] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0050] Figure 1 This is a flowchart of a graph-vector autoregressive method for predicting disease transmission based on a nonlinear spread function.

[0051] Figure 2 This is a comparison chart of the prediction errors of the 6-step SEIRS data in the example, which is susceptible-infected but not yet ill-infected-recovered-susceptible.

[0052] Figure 3 This is a comparison chart of the 6-step prediction errors for novel coronavirus data in the example. Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0054] In this embodiment, graph signal processing serves as a powerful tool for processing irregular domain data. Within the graph signal processing framework, irregular structures are modeled as graphs, and irregular time-varying data are modeled as graph signals—that is, time-varying graph signals on graph nodes. This allows for flexible characterization of the temporal and spatial correlations of data. A graph-based vector autoregression model is used to predict the evolution of time series, modeling the linear relationship between each time signal and its preceding time signals, but neglecting the nonlinear relationships. Therefore, a nonlinear expansion function can be added to the graph prediction model to nonlinearly expand the signal to a higher dimension. The expanded signal contains both linear and nonlinear projections of the original signal, thus effectively characterizing the nonlinear spatiotemporal correlations between data.

[0055] like Figure 1 As shown, the graph-vector autoregressive disease transmission prediction method based on a nonlinear spread function provided in this embodiment includes the following steps:

[0056] 1) Graph and graph signal modeling of disease transmission data: Assumptions Region Time-varying disease transmission data at consecutive moments are ,in , For the region exist The number of infected cases at any given time. The region is modeled as graph nodes, with edges connecting the nodes based on the characteristics of the data, thus constructing a graph. ,in For the set of graph nodes, Let be the set of edges. This is a weight matrix, where each element represents the correlation and adjacency between corresponding nodes. If there is no edge connecting nodes, the weight is 0. It is also a degree matrix. It is a diagonal matrix whose internal elements are The lines and. At this time, As a time-varying graph signal, its internal elements represent the graph signal at graph nodes at different times.

[0057] 2) Using a graph-vector autoregressive model to characterize the correlation between time-varying graph signals: Assumptions The signal value at a given time is represented as the value before. The signal at each time point is a function of the time-varying graph signal. The graph-vector autoregressive model is used to model the time-varying graph signal as shown in formula (1):

[0058] (1)

[0059] in, express An estimate of the number of infected cases at any given time; express The actual number of infected cases at any given time; For the error vector, It is a graph Laplace matrix. Representing the Laplace matrix Power of 1 for The coefficients of the order-highest Laplace matrix are... Degree matrix It is a diagonal matrix whose internal elements are The lines and;

[0060] 3) Using a nonlinear spreading function to map graph signals from low-dimensional space to high-dimensional space:

[0061] From formula (1), we can know It contains information about historical moments.

[0062] Therefore, the extended function in trigonometric form will Mapping to higher dimensions, the extended function takes the form shown in equation (2):

[0063] (2)

[0064] in, and To expand the indicators, It is the order of the extension function. and The definition is shown in formula (3):

[0065] (3)

[0066] make This indicates that the function has been expanded to... High-dimensional signals;

[0067] in, It contains information about historical moments; Representing the Laplace matrix Power; express The graphical signal at time; Indicates related The One extension function; , , This represents a parameter related to the order of the extended function.

[0068] 4) An optimization problem is proposed to estimate the parameters of the graph-vector autoregressive model based on the nonlinear spread function:

[0069] The definition of the graph-vector autoregressive model based on the nonlinear spread function is shown in equation (4):

[0070] (4)

[0071] in, for A coefficient vector of dimension, The coefficients represent the high-dimensional signal after being expanded by the spread function;

[0072] Based on the minimum mean square error criterion, the coefficient vector of the prediction model The estimation problem is shown in Equation (5):

[0073] (5)

[0074] The theoretical solution to this least squares optimization problem is shown in equation (6):

[0075] (6)

[0076] in, , The definition is shown in formula (7):

[0077] (7)

[0078] in, This represents the coefficient vector obtained by solving the optimization problem; Indicates the number of days of known data required for the prediction; Representation matrix The false rebellion.

[0079] 5) Conduct numerical experiments on different datasets using the optimized prediction model to verify its performance:

[0080] The optimized prediction model is used to predict the spread of different types of disease data. The normalized minimum mean square error (rNMSE) formula is used to quantify the error and evaluate the model performance. The error formula is shown in formula (8):

[0081] (8)

[0082] in, for The actual number of cases at any given time point. For the predicted number of cases, This indicates the number of prediction steps, which is the number of days for forward prediction of disease transmission data.

[0083] Simulation Example

[0084] This example uses data generated by the simulated Susceptible-Infected-Infected-Recovered-Susceptible (SEIRS) model and novel coronavirus infection data for simulation:

[0085] First, graph models were built for different data based on geographical location: for simulated SEIRS data based on the flight network of 125 international airports over 487 days, a graph with 125 nodes was constructed; for novel coronavirus infection data containing the number of infected persons in 100 regions over 507 days, a 6-nearest neighbor graph with 100 nodes was constructed.

[0086] Secondly, the different datasets are divided into two parts along the time dimension: in-sample data and out-of-sample data. The in-sample data is further divided into training data and test data. Model parameters are determined using cross-validation on the in-sample data. , The value;

[0087] Then, based on the obtained parameters, predictions are made for out-of-sample data, and the prediction results are continuously used as new historical data to make predictions for the next moment.

[0088] Finally, this example method is compared with the Graph-VAR (Graphical-Vector Autoregressive Moving Average) and Graph Multinomial-VAR (Graphical-Various-Vector Autoregressive) models proposed by Isufi et al. Six-step predictions are performed on different data, and the prediction results for each data point are visualized as follows: Figure 2 , Figure 3 As shown, observe the predictive effects of different data;

[0089] The graph-vector autoregressive method for predicting disease transmission based on a nonlinear spread function in this example outperforms the methods mentioned above. This is because the method in this example characterizes the nonlinear correlation between signals and makes better use of the internal correlation of the data, thereby reducing the prediction error.

[0090] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A graph-vector autoregressive method for predicting disease transmission based on a nonlinear spread function, characterized by: Includes the following steps: 1) Acquire disease transmission data and perform graph and graph signal modeling on the disease transmission data; 2) Construct a graph-vector autoregressive model; 3) Use nonlinear spreading functions to map graph signals from low-dimensional space to high-dimensional space; 4) Construct a graph-vector autoregressive model based on a nonlinear spread function; 5) Estimate the parameters of the graph-vector autoregressive model based on the nonlinear spread function to obtain an optimized disease transmission prediction model; The graph-vector autoregressive model is established as follows: set up The signal value at a given time is represented as the value before. The signal at each time point is a function of the time-varying graph signal. The graph-vector autoregressive model is used to model the time-varying graph signal as shown in formula (1): (1) in, express An estimate of the number of infected cases at any given time; express The actual number of infected cases at any given time; For the error vector, It is a graph Laplace matrix. Representing the Laplace matrix Power of 1 for The coefficients of the order-highest Laplace matrix are... Degree matrix It is a diagonal matrix whose internal elements are The lines and; The mapping of signals from low-dimensional space to high-dimensional space using a nonlinear spread function is performed in the following manner: make From formula (1), we can know It contains information about historical moments. Therefore, the extended function in trigonometric form will Mapping to higher dimensions, the extended function takes the form shown in equation (2): (2) in, and To expand the indicators, It is the order of the spread function. and The definition is shown in formula (3): (3) make This indicates that the function has been expanded to... High-dimensional signals; in, Representing the Laplace matrix Power; express The graphical signal at time; Indicates related The One extension function; , , This represents a parameter related to the order of the extended function; The disease transmission data is modeled as graphs and graph signals in the following manner: set up Region Time-varying disease transmission data at consecutive moments are ; in, , For the region exist The number of infected cases at any given time; The region is modeled as graph nodes, and the nodes are connected by edges based on the characteristics of the data to construct the graph. ,in, For the set of graph nodes, Let be the set of edges. This is a weight matrix, where each element represents the correlation and adjacency between corresponding nodes. If there are no edges connecting nodes, the weight is 0. at this time, As a time-varying graph signal, its internal elements represent the graph signal at graph nodes at different times.

2. The graph-vector autoregressive disease transmission prediction method based on a nonlinear spread function as described in claim 1, characterized in that: The graph-vector autoregressive model based on the nonlinear spread function is constructed as follows: The definition of the graph-vector autoregressive model based on the nonlinear spread function is shown in equation (4): (4) in, for A coefficient vector of dimension, The coefficients represent the high-dimensional signal after being expanded by the spread function; Based on the minimum mean square error criterion, the coefficient vector of the prediction model The estimation problem is shown in Equation (5): (5) The theoretical solution to this least squares optimization problem is shown in equation (6): (6) in, , The definition is shown in formula (7): (7) in, This represents the coefficient vector obtained by solving the optimization problem; Indicates the number of days of known data required for the prediction; Representation matrix The false rebellion.

3. The graph-vector autoregressive disease transmission prediction method based on a nonlinear spread function as described in claim 1, characterized in that: It also includes the following steps: The optimized disease transmission prediction model was used to predict the transmission data of different types of diseases. The normalized minimum mean square error (rNMSE) formula was used to quantify the error and evaluate the model performance. The error formula is shown in formula (8): (8) in, for The actual number of cases at any given time point. For the predicted number of cases, This indicates the number of prediction steps, which is the number of days for forward prediction of disease transmission data.

4. A graph-vector autoregressive disease transmission prediction system based on a nonlinear spread function, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method of any one of claims 1-3.

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