Multi-layer network state prediction method based on multi-mode spatio-temporal data modeling

Abstract

The invention relates to a multi-layer network state prediction method based on multi-mode spatio-temporal data modeling. The method comprises the following steps: acquiring spatio-temporal multi-mode data capable of reflecting interaction of nodes in a multi-layer dynamic network; associating connectivity and attribute information of nodes with a network group through Bernoulli distribution and Poisson distribution on the basis of space-time multi-modal data, establishing a multi-layer space-time Hawkes process with a shared group so as to capture interaction between each layer of nodes from historical events to subsequent events, and constructing a multi-modal space-time model; and solving parameters of the multi-modal space-time model by using a hierarchical expectation-maximum algorithm with local convergence to obtain a network state prediction result. Compared with the prior art, the method has the advantages of accurate modeling, accurate prediction and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-layer network state prediction, and in particular to a multi-layer network state prediction method based on multi-modal spatiotemporal data modeling. Background Art

[0002] Nowadays, network data is widely used in many fields, such as transportation network systems. In modern network systems, there are interactions between entities, and these interactions often take many forms. The large number of interactions between entities can be represented as a multi-layer dynamic network, with each layer corresponding to a specific form of interaction. For example, in a modern subway system, the passenger flow at a certain time period and station, such as inflow and outflow, reflects the circulation of people between stations. In addition to the correlation between entities within each individual network layer, multi-layer dynamic networks, such as subway passenger inflow and outflow networks, also show significant correlation between layers. Comprehensively describing the interactions between entities in a multi-layer dynamic network can help provide deep insights and promote effective decision-making in network systems.

[0003] With the rapid development of information science and data collection technology, the scenarios of available network data have become more diverse and can be used to fully understand the interactions between different entities in multi-layer networks. Specifically, exploring multi-layer networks involves the collection of multimodal data, including static data, dynamic data, and other types of data from natural, artificial, and human factors. Information from multimodal data is transmitted through the network in the time and space dimensions of each layer, forming a multi-layer dynamic network as a multimodal spatiotemporal system with the following characteristics:

[0004] Multi-layer dynamic networks exhibit interactive spatiotemporal characteristics involving multimodal variables. Among them, event frequency, as a kind of multimodal data, is used to record dynamic count data at various entities, time periods, and layers of the network. In addition to the correlation between layers, the network reflected in the event frequency data also exhibits complex spatiotemporal characteristics. Due to the spatial correlation structure layout of the system, the event frequency data collected from different entities show spatial correlation, that is, the event frequency data close to each other in the spatial domain have mutual dependence. Since the events occurring in the entities evolve over time, the frequency data collected from adjacent time points show temporal autocorrelation. For example, passenger inflow and outflow are two highly correlated interactive variables that constitute the two layers of the urban subway network system. Passenger flow is the dynamic count data of adjacent stations, which has similar patterns and changes dynamically over time.

[0005] In addition to event frequency data, the network also includes attribute data that characterizes entity attributes. These attribute data belong to another type of modal data, namely static data. The collected attribute data has the diverse and multi-scale characteristics of entities, and can describe the network structure characteristics from multiple perspectives. For example, in the urban subway network system, the attribute variables of each station involve hotel service apartments, leisure shopping, major buildings, public facilities services, residential areas, schools, public transportation, etc. These attribute variables have unique characteristics of each station entity. Attribute information helps to fully reflect the interactive relationship between system entities.

[0006] Therefore, it is crucial to build multi-layer dynamic network models by fully capturing the interactive spatiotemporal characteristics between entities and layers from multimodal variables. Challenges still exist in this field: First, although data from network systems provide comprehensive information in both temporal and spatial dimensions, the count-type nature of the data and the complex spatiotemporal characteristics pose challenges to the development of modeling methods. Second, multi-layer network modeling is expected to capture the information of each layer of the network and the correlations between different layers. Specifically, for the correlations between different layers, individual entities in the network often show a tendency to form tightly knit subgroups (called groups). Entities belonging to the same group tend to interact more frequently than entities from different groups. The group structure is shared across all layers. Third, multimodal data provides deep information for network modeling, but the differences in modalities and multiple interactive characteristics between multiple variables pose challenges to network feature fusion. Summary of the invention

[0007] The purpose of the present invention is to provide a multi-layer network state prediction method based on multimodal spatiotemporal data modeling, which utilizes the relevant multimodal data reflecting the interaction of each node collected in a complex dynamic network to achieve accurate modeling and prediction of the multi-layer dynamic interaction spatiotemporal characteristics.

[0008] The purpose of the present invention can be achieved by the following technical solutions:

[0009] A multi-layer network state prediction method based on multimodal spatiotemporal data modeling includes the following steps:

[0010] S1, obtain spatiotemporal multimodal data that can reflect the interaction of each node in the multi-layer dynamic network;

[0011] S2, based on spatiotemporal multimodal data, the connectivity and attribute information of nodes are associated with network groups through Bernoulli distribution and Poisson distribution, and a multi-layer spatiotemporal Hawkes process with shared groups is established to capture the interaction between nodes in each layer from historical events to subsequent events, and to construct a multimodal spatiotemporal model;

[0012] S3, using the hierarchical expectation-maximum algorithm with local convergence to solve the parameters of the multimodal spatiotemporal model and obtain the network state prediction results.

[0013] The multi-layer dynamic network is composed of N nodes, where a certain node is represented as node i (i=1, ...N). It is assumed that there are L layers in the network, and all layers share the same group structure.

[0014] The multi-layer dynamic network is described by spatiotemporal multimodal data, including attribute data providing static attribute information of each node, and event frequency data describing the frequency of a certain event type in each layer, and both the attribute data and event frequency data have spatiotemporal dynamic characteristics.

[0015] Assume that there are R groups among all nodes in a multi-layer dynamic network, and the probability that a node i belongs to group r in the network is expressed as τ ir , where i = 1, ..., N, r = 1, ..., R and N is the number of nodes; z ir Indicates whether node i belongs to group r, that is, if node i belongs to group r, then z ir =1; otherwise z ir =0;

[0016] Assume that each node has K attributes, and the nodes in the group have the same attribute preference, with x ik Denote the attribute k of node i. Assume that node i belongs to group r and use Poisson distribution to model the relationship between discrete-valued attributes:

[0017]

[0018] Among them, φ rk represents the expected value of attribute k in group r, characterizing the preference of attributes in the group, k = 1, ..., K and r = 1, ..., R, K is the number of attributes.

[0019] The method of associating the connectivity and attribute information of nodes with network groups through Bernoulli distribution and Poisson distribution is as follows:

[0020] The connectivity between node pairs under a given group is characterized to capture the network structure, using γ ij represents the connectivity between nodes i and j, where γ ij =1 means nodes i and j are connected neighbors, otherwise γ ij =0;

[0021] Assuming that connectivity and node attributes are conditionally independent under a given group, the connectivity γ between node pair ij is calculated by Bernoulli distribution when nodes i and j belong to groups r and r′ respectively. ijModeling, that is, z ir =z jr , =1:

[0022] γ ij |z ir , z jr′ ~Bemoulli(θ rr′ )

[0023] Among them, θ rr′ represents the probability of connecting groups r and r′, Bemoulli represents Bernoulli distribution, and the connectivity matrix between nodes is

[0024] After characterizing the network structure with the connectivity matrix Γ, the event frequency is modeled as a dynamic counting process in a multi-layer network, where the dynamic counting process of the network is a random process, all layers share the network structure, and each layer l contains a spatiotemporal counting process;

[0025] Using the counting process on all nodes i and layers l To characterize the network computing process, represents the number of counts occurring on node i and layer l in the time interval [0, t], where L is the total number of layers in the network;

[0026] Using the conditional density function To model the count quantity, given the historical data but

[0027]

[0028] The number of counts that occurred at time t Modeled by a Poisson distribution:

[0029]

[0030] Wherein, Δt represents the time interval, and Poisson represents Poisson distribution.

[0031] The establishment of a multi-layer spatiotemporal Hawkes process with a shared group is specifically as follows: a spatiotemporal Hawkes process is used to count nodes i and layer l Modeling takes into account the self-excitation characteristics of the previous events on the adjacent nodes triggering the upcoming events on node i, as shown below:

[0032]

[0033]

[0034] Among them, considering that there is a time pattern caused by the network background effect on each node i, the background rate basis term that varies with time is introduced formula represents the triggering effect of the previous network events of the adjacent nodes on the upcoming event of node i before time t, represents the jump size of the counting process of node i stimulated by neighbor node j; exponential kernel Used to describe time decay, where t j represents the time before time t, It means that it occurs at time t j and the event counts of neighboring nodes j on layer l. δ is the time-dependent bandwidth, which is considered as a hyperparameter.

[0035] Write the multimodal spatiotemporal model parameters to be estimated in matrix form, including the group matrix Attribute Preference Matrix Probability matrix between groups Connectivity Matrix Background rate basis matrix And the influence incentive term α = {α l} l＝1，…，L ,in The parameter set except Γ is denoted as η = {T, Φ, Θ, μ, α}; the data used for model training includes attribute data and event frequency data, and the data set is represented as D = {x, n}.

[0036] The hierarchical expectation-maximum algorithm performs the following steps to solve the parameters of the multimodal spatiotemporal model:

[0037] Step 1) Given the connectivity matrix Γ, estimate T, Φ, Θ, μ, α;

[0038] Step 11) Given the connectivity matrix Γ, estimate T, Φ, Θ;

[0039] Given a group z, the Poisson distribution conditional probability of all node attributes x is:

[0040]

[0041] Given a group z, the Bernoulli distribution conditional probability of the connectivity matrix Γ of all nodes is:

[0042]

[0043] Since the group matrix z is unknown, it is considered as a latent variable, and the log-likelihood functions of T, Φ, and Θ based on x and Γ are

[0044] Use the EM algorithm to estimate T, Φ and Θ:

[0045] In step E, given the mth iteration T (m) , Φ (m) , Θ (m) , where m = 1, 2, ..., we get z ir The prior distribution of is as follows, where i=1,...,N and r=1,....,R:

[0046]

[0047] in, P(x i , Γ i |z ir , Φ (m) , Θ (m) )=P(x i |z ir , Φ (m) )P(Γ i |z ir , Θ (m) )and

[0048] In the M step, given z ir The prior distribution of , the expected log-posterior likelihood function of T, Φ and Θ is expressed as:

[0049]

[0050] By Q(T, Φ, Θ, T (m) , Φ (m) , Θ (m) ) Find the partial derivatives of T, Φ and Θ, and update T, Φ and Θ in the m+1th iteration round to:

[0051]

[0052]

[0053]

[0054] Step 12) Given the connectivity matrix Γ, estimate μ and α;

[0055] Suppose there are D available samples, and the samples contain time points t in the interval [0, T] 1 ,…,t T Network counting data, that is, n = {n id} i＝1，…，N，d＝1，…，D , the log-likelihood function of the multilayer spatiotemporal Hawkes process with respect to μ and α is expressed as Among them, log P(nid |Γ, μ, α) is the log-likelihood function of sample d at node i, that is:

[0056]

[0057] Use the EM algorithm to solve the log-likelihood function log P(n|Γ, μ, α):

[0058] According to the Qinsheng inequality: log P(n|Γ, μ, α) ≥ log P(n|Γ, μ, α) lower and

[0059]

[0060] Where, for sample d, d = 1, ..., D, we define is the probability of a background event occurring at node i at time t, and defines In each layer l, from the previous time point t j The probability of an event occurring at neighbor node j causing an event to occur at node i at time t;

[0061] In the E step, given the μ of the mth iteration (m) and α (m) , where m = 1, 2, ..., then and It is expressed as:

[0062]

[0063]

[0064] In the M step, the estimated and Substituting log P(n id |Γ,μ,α) lower Solve the formula to get the expected logarithmic posterior likelihood function Q about μ and α lower (μ, α, μ (m) , α (m) ); lower (μ, α, μ (m) , α (m) ) Take the derivative about μ and α, update μ and α of the m+1th iteration, and get:

[0065]

[0066]

[0067] Step 2) Given T, Φ, Θ, μ, update Γ;

[0068] The connectivity matrix Γ is related to the event frequency process n and the group z, which is determined based on T. For each node i (i = 1, ..., N), let Γ i is the i-th column of the matrix Γ, and its posterior distribution is written as:

[0069] P(Γ i |z,n i , Θ, μ i , α i )∝P(α i |n i , Γ i , μ i )P(Γ i |z,Θ)

[0070] Among them, P(α i |n i , Γ i , μ i ) is calculated as and Assume that it is a uniformly distributed probability density function, that is

[0071] based on Uniform distribution, maximizing the posterior logarithm Equivalent to maximizing To obtain

[0072] The given Γ is realized by the EM algorithm i and Maximization under the conditions

[0073] Considering There is no analytical expression for the solution of , and the solution that maximizes the posterior distribution (Γ i |z,n i , Θ, μ i , α i ) i ,Right now Complete the update of Γ.

[0074] The numerical algorithm performs the following steps:

[0075] Step 21) For each node i, i=1, ..., N, execute:

[0076] Based on Γ i and z, n i , Θ, μ i , α i Calculate ρ i =P(Γ i |z,ni , Θ, μ i , α i );

[0077] For each node j, Among them, the subset To remove the node index of node i, perform the following steps:

[0078] Step 211) Setup Keep Γ i The other elements in remain unchanged to obtain

[0079] Step 212) Using the EM algorithm, given and renew make maximum;

[0080] Step 213) Based on and z, n i , Θ, μ i , calculate

[0081] Step 214) Update Γ i ;

[0082] Step 22) By combining Get the updated

[0083] In step S3, after the multimodal spatiotemporal model parameters are solved, the group of each node i (i=1, ..., N) is represented as:

[0084]

[0085] The attribute preference of each group r (r = 1, ..., R) is represented by Φ r ={φ rk , k = 1, ..., K};

[0086] This gives the conditional density function for any node i and layer l:

[0087] Given a historical network event that occurred before time t Using the conditional density function Predict the expected event occurrence frequency at node i and layer l, where i=1,…,N and l=1,…,L.

[0088] Compared with the prior art, the present invention has the following beneficial effects:

[0089] The present invention establishes a multi-layer network model to fully capture the count properties and inter-layer interactions of spatiotemporal features. By combining the multi-layer spatiotemporal Hawkes process for event frequency modeling and the Bernoulli and Poisson distributions for attribute information modeling, a multimodal spatiotemporal model is constructed. A hierarchical EM algorithm is used to solve the constructed model, which theoretically guarantees the local convergence of the model and enables accurate modeling and prediction of multi-layer dynamic interactive spatiotemporal features. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 The figure is a flow chart of the method of the present invention.

[0091] Figure 2 A schematic diagram of a multi-layer network containing multimodal data according to the present invention.

[0092] Figure 3 It is the logical relationship between the variables in the embodiment of the present invention.

[0093] Figure 4 is the parameter estimation result related to the attributes in the embodiment of the present invention, wherein FIG. (4a) shows the group matrix The estimation results of ; Figure (4b) shows the attribute preference matrix The estimation results of ; Figure (4c) shows the probability matrix between groups The estimated results.

[0094] Figure 5 5a shows the parameter estimation result of the background rate basis term μ in the embodiment of the present invention, wherein FIG. (5a) shows the first layer time-varying background rate basis term; FIG. (5b) shows the estimation result of the second layer time-varying background rate basis term.

[0095] Figure 6 is the parameter estimation result of the connectivity matrix and the influencing excitation term in the embodiment of the present invention, wherein FIG. (6a) shows the connectivity matrix The estimation results of ; Figure (6b) shows the first layer of the impact incentive items The estimation results of ; Figure (6c) shows the second layer of the incentive term The estimated results.

[0096] Figure 7 4 is the passenger flow prediction result of the station 45 in the embodiment of the present invention, wherein the dots are actual passenger flow observation values, and the solid line, dot-dash line, and dashed line are the one-step, two-step, and three-step prediction results of the embodiment of the present invention, respectively. DETAILED DESCRIPTION

[0097] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0098] This embodiment takes a subway network system in a certain place as an example. The subway network system generates a large amount of passenger circulation data every day. The raw data of the subway network system collected automatically includes smart card identifiers, entry and exit timestamps, corresponding stations and fare amounts. This embodiment converts these records into passenger flow (entry) and passenger flow (exit) counts within 20 minutes at each station. The daily time frame for analyzing passenger flow is defined as the inflow time from 5:30 to 12:30 in the morning (the next day) and the outflow time from 6:00 to 1:00 in the morning (the next day), so the daily passenger flow profile of each station has 59 time points with equal intervals. This embodiment covers passenger flow data from January 1 to March 31 of a specific year, excluding public holidays, weekends, days affected by typhoons, and days showing significant outliers, and only focuses on the weekday operation mode of the subway system. In addition, attribute information is used to describe the natural and social characteristics of each station. Each station has 7 attribute variables, including hotel serviced apartments, leisure shopping, major buildings, public facilities services, residential areas, schools, and public transportation.

[0099] The subway system forms a two-layer network (i.e., L = 2), which depicts the passenger flow at 91 nodes (i.e., stations, N = 91). The multimodal data includes 59 time points in a day (i.e., t 1 =1,t T =59) collected passenger inflow and outflow data and 7 attributes of each station (i.e. K = 7). There are 40 days of daily passenger flow data and attribute data. This embodiment uses the data of the first 20 days for model training and the data of the last 20 days for evaluating the model prediction performance.

[0100] The following provides a multi-layer network state prediction method based on multimodal spatiotemporal data modeling. Figure 1 As shown, the following steps are included:

[0101] S1, obtain spatiotemporal multimodal data that can reflect the interaction of each node in the multi-layer dynamic network;

[0102] S2, based on spatiotemporal multimodal data, the connectivity and attribute information of nodes are associated with network groups through Bernoulli distribution and Poisson distribution, and a multi-layer spatiotemporal Hawkes process with shared groups is established to capture the interaction between nodes in each layer from historical events to subsequent events, and to construct a multimodal spatiotemporal model;

[0103] S3, using the hierarchical expectation-maximum algorithm with local convergence to solve the parameters of the multimodal spatiotemporal model and obtain the network state prediction results.

[0104] The specific implementation of this method is as follows:

[0105] 1. Establish a multimodal spatiotemporal model

[0106] Figure 2 A schematic diagram of a multi-layer network with multimodal data is shown. The multi-layer dynamic network consists of N nodes, where a node is denoted as node i (i=1,…N). Assume that there are L layers in the network, where all layers share the same group structure. The network is described by multimodal data, including attribute data that provides static attribute information for each node, and event frequency data that describes the frequency of a certain event type in each layer, both of which have spatiotemporal dynamic characteristics.

[0107] Assume that there are R groups among all nodes in the network. The probability that a node i belongs to group r in the network is expressed as τ ir , where i = 1, ..., N, r = 1, ..., R and The present invention is based on ir Indicates whether node i belongs to group r, that is, if node i's group is r, then z ir =1; otherwise z ir =0.

[0108] Assume that each node has K attributes, and the nodes in the group have the same attribute preference. ik represents the attribute k of node i. Assuming node i belongs to group r, then z ir =1, the present invention uses Poisson distribution to model the relationship between discrete value attributes:

[0109]

[0110] Among them, φ rk represents the expected value of attribute k in group r, characterizing the preference of attributes in the group, k=1,...,K and r=1,...,R.

[0111] For modeling of multivariate spatiotemporal counting processes in networks, the present invention first characterizes the connectivity between node pairs in a given group to capture the network structure. ij represents the connectivity between nodes i and j, where γ ij =1 means nodes i and j are connected neighbors, otherwise γ ij=0. The embodiment of the present invention assumes that connectivity and node attributes are conditionally independent under a given group. In addition to conditionally modeling the attributes of the node group according to formula (1), the embodiment of the present invention also uses Bernoulli distribution to distribute the connectivity γ between the node pair ij when nodes i and j belong to groups r and r′ respectively. ij Modeling, that is, z ir =z jr , =1:

[0112] γ ij |z ir , z jr′ ~Bernoulli(θ rr′ ) (2)

[0113] Among them, θ rr′ represents the probability that groups r and r′ are connected. The connectivity matrix between nodes is From formula (2), we can see that the groups can be connected to each other.

[0114] After characterizing the network structure with the connectivity matrix Γ, the embodiment of the present invention models the event frequency as a dynamic counting process in a multi-layer network. The network counting process is a random process. All layers share the network structure, and each layer l contains a spatiotemporal counting process. The embodiment of the present invention uses the counting process on all nodes i and layer l. To characterize the network computing process, represents the number of counts occurring on node i and layer l in the time interval [0, t]. The present invention uses the conditional density function To model the count quantity, given the historical data but

[0115]

[0116] The number of counts occurring at time t is modeled by a Poisson distribution:

[0117]

[0118] The embodiment of the present invention proposes to use the spatiotemporal Hawkes process to count the nodes i and the layers l. Modeling takes into account the self-excitation characteristics of the previous events on the adjacent nodes triggering the upcoming events on node i, as shown below:

[0119]

[0120]

[0121] Here, considering that there is a time pattern caused by the network background effect on each node i, the embodiment of the present invention introduces a background rate basis term that varies with time: formula It represents the triggering effect of the previous network events of the adjacent nodes on the upcoming event of node i before time t. represents the jump size of the counting process CIF of node i stimulated by neighbor node j. It is used to capture the triggering effect of adjacent nodes on node i. Its value is highly correlated with the network structure (i.e., the connectivity matrix Γ). If γ ij =1, then And if γ ij =0, then Considering that the event at the most recent time point may have a greater triggering effect on the upcoming event, the embodiment of the present invention adopts the exponential kernel g(tt j )= To describe the time decay, where t j represents the time before time t, It means that it occurs at time t j and the event counts of neighboring nodes j on layer l, while δ is the time-dependent bandwidth, which is treated as a hyperparameter. Figure 3 The logical relationship between the variables in the embodiment of the present invention is shown.

[0122] 2. Model parameter estimation

[0123] Write the model parameters to be estimated in matrix form, including the group matrix Attribute Preference Matrix Probability matrix between groups Connectivity Matrix Background rate basis matrix And the influence excitation term α={α l} l＝1，…，L ,in The parameter set except Γ is recorded as η = {T, Φ, Θ, μ, α}. The data that can be used for model training includes attribute data and event frequency data, and the data set is represented as D = {x, n}. The likelihood function log P (D, Γ|η) can be written as:

[0124] log P(D, Γ|η)=log P(x, Γ|T, Φ, Θ)+log P(n, Γ|μ, α) (6)

[0125] Among them, since Γ and η are unknown parameters to be estimated, the formula (6) cannot directly obtain a feasible solution. Therefore, the present invention proposes a hierarchical algorithm for parameter estimation. The algorithm is divided into two steps: step 1) estimates T, Φ, Θ, μ, α according to the given Γ, and step 2) updates Γ according to the estimated T, Φ, Θ, μ:

[0126] Step 1) Given Γ estimate T, Φ, Θ, μ, α

[0127] (1) Given Γ, estimate T, Φ, Θ

[0128] Given a group z, the Poisson distribution conditional probability of all node attributes x is:

[0129]

[0130] Given a group z, the Bernoulli distribution conditional probability of the connectivity matrix Γ of all nodes is:

[0131]

[0132] However, since the group matrix z is unknown, it is considered as a latent variable. The log-likelihood functions of T, Φ and Θ based on x and Γ are The embodiment of the present invention uses the EM algorithm to estimate T, Φ and Θ.

[0133] In step E, given the mth iteration T (m) , Φ (m) , Θ (m) , where m = 1, 2, ..., we get z ir The prior distribution of is as follows, where i=1,…,N and r=1,…,R:

[0134]

[0135] in, P(x i , Γ i |z ir , Φ (m) , Θ (m) )=P(x i |z ir , Φ (m) )P(Γ i |z ir , Θ (m) )and Therefore, according to formula (7) and formula (8),

[0136] In the M step, given formula (9), the expected logarithmic posterior likelihood function of T, Φ and Θ can be expressed as:

[0137]

[0138] By Q(T, Φ, Θ, T (m) , Φ (m) , Θ (m) ) Find the partial derivatives of T, Φ and Θ, and update T, Φ and Θ in the m+1th iteration round as follows:

[0139]

[0140]

[0141] (2) Given Γ, estimate μ and α

[0142] Suppose there are D available samples, which contain time points t in the interval [0, T] 1 ,…,t T Network counting data, that is, n = {n id} i＝1，…，N，d＝1，…，D The log-likelihood function of the multi-layer spatiotemporal Hawkes process with respect to μ and α can be expressed as Among them, log P(n id |Γ, μ, α) is the log-likelihood function of sample d at node i, that is:

[0143]

[0144] The embodiment of the present invention realizes solving the log-likelihood function log P(n|Γ, μ, α) by using the EM algorithm. According to the Jensen inequality, log P(n|Γ, μ, α)≥log P(n|Γ, μ, α) lower and but:

[0145]

[0146] Where, for sample d, d = 1, ..., D, we define is the probability of a background event occurring at node i at time t, and defines In each layer l, from the previous time point t j The probability that an event occurs at node i at time t due to an event occurring at neighbor node j.

[0147] In the E step, given the μ of the mth iteration (m) and α (m) , where m = 1, 2, ..., then and It can be expressed as:

[0148]

[0149] In the M step, the estimated value obtained by formulas (16) and (17) is and Substituting into formula (15), we can obtain the expected logarithmic posterior likelihood function Q for μ and α lower (μ, α, μ (m) , α (m) ). Then, by lower (μ, α, μ (m) , α (m) ) Take the derivative about μ and α, and update μ and α to the m+1th iteration to obtain:

[0150]

[0151] To simplify the calculation, the summation term in formula (14) is can be estimated as And when γ ij =1,

[0152]

[0153] Step 2) Update Γ given T, Φ, Θ, μ

[0154] The connectivity matrix Γ is related to the event frequency process n and the group z. The group z is determined based on T. For each node i (i=1,...,N), let Γ i is the i-th column of the matrix Γ, and its posterior distribution can be written as:

[0155] P(Γ i |z,n i , Θ, μ i , α i )∝P(α i |n i , Γ i , μ i )P(Γ i |z,Θ) (20)

[0156] Among them, P(α i |n i , Γ i , μ i ) can be calculated as and Since Γ i Different values ​​of will not affect Therefore, without loss of generality, we can assume that it is a probability density function of uniform distribution, that is,

[0157] To obtain The posterior logit should be maximized Also because is assumed to be uniformly distributed, so it is equivalent to maximizing First, the EM algorithm can be used to achieve a given Γ i and Maximization under the conditions Here we refer to formulas (17) and (19) to estimate As shown in formula (8),

[0158] The goal of this algorithm is to find the value that maximizes the posterior distribution (Γ i |z,n i ,Θ,μ i ,α i ) i ,Right now because There is no analytical expression for the solution of , and the embodiment of the present invention adopts a numerical algorithm, as shown in Table 1, where the subset is the node index of node i to be removed. This algorithm does not need to be repeated 2 N-1 times, and only N iterations are needed to determine the optimal Greatly reduces the computational burden.

[0159] Table 1 Numerical algorithm

[0160]

[0161] The above hierarchical EM algorithm is iteratively executed to perform overall parameter estimation until Γ converges.

[0162] 3. Prediction of online attributes and event frequency in the future

[0163] After the model parameter estimation is completed, the group of each node i (i = 1, ..., N) can be expressed as:

[0164]

[0165] The attribute preference of each group r (r = 1, ..., R) can be expressed as Φ r ={φ rk ,k=1,…,K}.

[0166] Thus, the CIF equation of any node i and layer l can be obtained. Given the network history events that occurred before time t According to formula (5), the present invention can utilize CIF Predict the expected event frequency at node i and layer l, where i=1,…,N and l=1,…,L.

[0167] 4. Parameter estimation and prediction result analysis

[0168] This embodiment compares the learned group probability matrix by taking several values ​​of R and the attribute preference matrix The number of groups is determined to be R = 3. Without loss of generality, the bandwidth value is set to δ = 1. Figure 4 The results of attribute-related parameter estimation in the embodiment of the present invention are shown, including and These attributes can provide key information between stations in the subway network. As shown in Figure (4a), group 0 contains 17 stations, such as stations 0, 1, 2, 5, 11, 12, 13, etc. Group 2 and group 3 contain 42 and 32 stations respectively. Figure (4b) shows the estimated matrix Each element φ rk Represents the expected value of attribute k in group r. Each station has 7 attribute variables. Obviously, the station in group 0 is the downtown business district, full of hotel service apartments, leisure shopping, major buildings and public facilities services. Group 2 is the main educational area with the largest number of schools among all groups, dense residential areas and sufficient public facilities services. Group 1 may be a suburb, with public facilities services, residential areas, and schools around the station, but lacking hotel service apartments, leisure shopping, and major buildings. In addition, stations within and between groups are also interconnected. In Figure (4c), stations in the same group trigger a strong interaction effect due to their common attribute preferences. Stations in different groups are not independent, and there are also connections between them, but the interactions are relatively weak compared to stations in the same group.

[0169] Figure 5 The time-varying background rate basis μ estimated by the proposed method is shown. Figures (5a) and (5b) show the estimation results of μ for the first and second layers, respectively. It can be seen that the two layers have unique time-varying patterns, and some sites have similar background rate basis terms, while other sites have different background rate basis terms.

[0170] The estimated connectivity matrix and the influence incentive terms are as follows Figure 6 The connectivity matrix Γ represents the network structure shared by all layers. The obtained network structure can provide important engineering suggestions for the system, enabling it to cross different engineering fields, such as optimizing structural layout, effective resource allocation, and complex task scheduling. and Characterize the spatial dependencies between layer 1 and layer 2 nodes and their neighboring nodes.

[0171] This embodiment uses the proposed method to predict the passenger flow of the subway network, and the performance of the model is shown in Table 2. The table shows the average values ​​of the mean absolute errors MAEs and relative mean absolute errors RMAEs of the passenger flow count prediction. In order to conduct a comprehensive evaluation, this embodiment adopts one-step, two-step and three-step predictions. The method proposed in the present invention performs well in one-step, two-step and three-step predictions. Thanks to its comprehensive consideration of spatiotemporal dynamics and inter-layer interaction patterns, the MAE and RMAE of the prediction results are small. In urban subway systems, accurate prediction of passenger flow in the next 20 minutes is crucial for resource and personnel scheduling. The RMAE of one-step prediction (i.e., 20-minute passenger flow prediction) is 0.0626, indicating that the proposed method is very effective in subway network modeling.

[0172] Table 2 Model prediction performance of the embodiment of the present invention

[0173]

[0174] Figure 7 The predicted passenger flow and outflow of station 45 (from group 1) on the 10th day in the test set are further shown. The points in the figure are the actual passenger flow observations, and the lines, dotted lines, and dashed lines are the one-step, two-step, and three-step prediction results of the embodiment of the present invention, respectively. The method proposed in the present invention achieves a good one-step prediction, which is quite close to the actual observations. Although the accuracy of the two-step prediction and the three-step prediction is not exactly the same, they can also effectively predict the trends of passenger flow inflow and passenger flow outflow.

[0175] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning, or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A multi-layer network state prediction method based on multimodal spatiotemporal data modeling, characterized in that: The following steps are involved: S1, obtain spatiotemporal multimodal data that can reflect the interaction of each node in the multi-layer dynamic network; S2, based on spatiotemporal multimodal data, the connectivity and attribute information of nodes are associated with network groups through Bernoulli distribution and Poisson distribution, and a multi-layer spatiotemporal Hawkes process with shared groups is established to capture the interaction between nodes in each layer from historical events to subsequent events, and to construct a multimodal spatiotemporal model; S3, using the hierarchical expectation-maximum algorithm with local convergence to solve the parameters of the multimodal spatiotemporal model and obtain the network state prediction results.

2. The multi-layer network state prediction method based on multimodal spatiotemporal data modeling according to claim 1 is characterized in that: The multi-layer dynamic network is composed of N nodes, where a certain node is represented as node i (i=1, ...N). It is assumed that there are L layers in the network, and all layers share the same group structure.

3. The multi-layer network state prediction method based on multimodal spatiotemporal data modeling according to claim 2 is characterized in that: The multi-layer dynamic network is described by spatiotemporal multimodal data, including attribute data providing static attribute information of each node, and event frequency data describing the frequency of a certain event type in each layer, and both the attribute data and event frequency data have spatiotemporal dynamic characteristics.

4. The multi-layer network state prediction method based on multimodal spatiotemporal data modeling according to claim 3 is characterized in that: Assume that there are R groups among all nodes in a multi-layer dynamic network, and the probability that a node i belongs to group r in the network is expressed as τ ir , where i = 1, ..., N, r = 1, ..., R and N is the number of nodes; z ir Indicates whether node i belongs to group r, that is, if node i belongs to group r, then z ir =1; otherwise z ir =0; Assume that each node has K attributes, and the nodes in the group have the same attribute preference, with x ik Denote the attribute k of node i. Assume that node i belongs to group r and use Poisson distribution to model the relationship between discrete-valued attributes: Among them, φ rk It represents the expected value of attribute k in group r, characterizing the preference of attributes in the group, k = 1,…,K and r = 1,…,R, where K is the number of attributes.

5. The multi-layer network state prediction method based on multimodal spatiotemporal data modeling according to claim 4 is characterized in that: The method of associating the connectivity and attribute information of nodes with network groups through Bernoulli distribution and Poisson distribution is as follows: The connectivity between node pairs under a given group is characterized to capture the network structure, using γ ij represents the connectivity between nodes i and j, where γ ij =1 means nodes i and j are connected neighbors, otherwise γ ij =0; Assuming that connectivity and node attributes are conditionally independent under a given group, the connectivity γ between node pair ij is calculated by Bernoulli distribution when nodes i and j belong to groups r and r′ respectively. ij Modeling, that is, z ir =z jr′ =1: γ ij |from ir ,With jr′ ~Bernoulli(θ rr′ ) Among them, θ rr′ represents the probability of groups r and r′ being connected, Bernoulli represents Bernoulli distribution, and the connectivity matrix between nodes is After characterizing the network structure with the connectivity matrix Γ, the event frequency is modeled as a dynamic counting process in a multi-layer network, where the dynamic counting process of the network is a random process, all layers share the network structure, and each layer l contains a spatiotemporal counting process; Using the counting process on all nodes i and layers l To characterize the network computing process, represents the number of counts occurring on node i and layer l in the time interval [0, t], where L is the total number of layers in the network; Using the conditional density function To model the count quantity, given the historical data but The number of counts that occurred at time t Modeled by a Poisson distribution: Wherein, Δt represents the time interval, and Poisson represents Poisson distribution.

6. A multi-layer network state prediction method based on multimodal spatiotemporal data modeling according to claim 5, characterized in that: The establishment of a multi-layer spatiotemporal Hawkes process with a shared group is specifically as follows: a spatiotemporal Hawkes process is used to count nodes i and layer l Modeling takes into account the self-excitation characteristics of the previous events on the adjacent nodes triggering the upcoming events on node i, as shown below: Among them, considering that there is a time pattern caused by the network background effect on each node i, the background rate basis term that varies with time is introduced formula represents the triggering effect of the previous network events of the adjacent nodes on the upcoming event of node i before time t, represents the jump size of the counting process of node i stimulated by neighbor node j; exponential kernel Used to describe time decay, where t j represents the time before time t, It means that it occurs at time t j and the event counts of neighboring nodes j on layer l. δ is the time-dependent bandwidth, which is treated as a hyperparameter.

7. The multi-layer network state prediction method based on multimodal spatiotemporal data modeling according to claim 6 is characterized in that: Write the multimodal spatiotemporal model parameters to be estimated in matrix form, including the group matrix Attribute Preference Matrix Probability matrix between groups Connectivity Matrix Background rate basis matrix And the impact of incentives in The parameter set except Γ is denoted as η = {T, Φ, Θ, μ, α}; the data used for model training includes attribute data and event frequency data, and the data set is represented as D = {x, n}.

8. The multi-layer network state prediction method based on multimodal spatiotemporal data modeling according to claim 7 is characterized in that: The hierarchical expectation-maximum algorithm performs the following steps to solve the parameters of the multimodal spatiotemporal model: Step 1) Given the connectivity matrix Γ, estimate T,Φ,Θ,μ,α; Step 11) Given the connectivity matrix Γ, estimate T,Φ,Θ; Given a group Z, the Poisson distribution conditional probability of all node attributes x is: Given a group z, the Bernoulli distribution conditional probability of the connectivity matrix Γ of all nodes is: Since the group matrix z is unknown, it is considered as a latent variable, and the log-likelihood function of T, Φ and Θ based on x and T is Use the EM algorithm to estimate T, Φ and Θ: In step E, given T(m), Φ(m), Θ(m) of the mth iteration, where m = 1, 2, ..., we get z ir The prior distribution of is as follows, where i = 1, ..., N and r = 1, ..., R: Among them, P(x i ,Γ i |z ir ,Φ (m) ,Θ (m) =P(x i |z ir ,Φ (m) P(Γ i |z ir ,Θ (m) and In the M step, given z ir The prior distribution of , the expected log-posterior likelihood function of T, Φ and Θ is expressed as: By taking the partial derivatives of Q(T,Φ,Θ,T(m),Φ(m),Θ(m)) with respect to T,Φ and Θ, T,Φ and Θ in the m+1th iteration round are updated as follows: Step 12) Given the connectivity matrix Γ, estimate μ and α; Suppose there are D available samples, and the samples contain time points t1,…,t in the interval [0,T] T Network counting data, that is, n = {n id } i＝1,…,N,d＝1,…,D , the log-likelihood function of the multilayer spatiotemporal Hawkes process with respect to μ and α is expressed as Among them, logP(n id |Γ,μ,α) is the log-likelihood function of sample d at node i, that is: Use the EM algorithm to solve the log-likelihood function logP(n|Γ,μ,α): According to the Qinsheng inequality: logP(n|Γ,μ,α)≥logP(n|Γ,μ,α) iower and For sample d, d = 1, ..., D, we define is the probability of a background event occurring at node i at time t, and defines In each layer l, from the previous time point t j The probability of an event occurring at neighbor node j causing an event to occur at node i at time t; In the E step, given the mth iteration μ (m) and α (m) , where m = 1, 2, ..., then and It is expressed as: In the M step, the estimated and Substituting logP(n id |Γ,μ,α) lower Solve the formula to get the expected logarithmic posterior likelihood function Q about μ and α lower (μ,α,μ (m) ,α (m) ); lower (μ,α,μ (m) ,α (m) ) Take the derivative about μ and α, update μ and α of the m+1th iteration, and get: Step 2) Given T,Φ,Θ,μ, update Γ; The connectivity matrix Γ is related to the event frequency process n and the group z, which is determined based on T. For each node i (i = 1, ..., N), let Γ i is the i-th column of the matrix Γ, and its posterior distribution is written as: P(Γ i ||z,n i ,Θ,u i ,a i )∝P(α i |n i ,C i ,u i )P(Γ i |z,Θ) Among them, P(αi|ni,Γi,μi) is calculated as and Assume that it is a uniformly distributed probability density function, that is based on Uniform distribution, maximizing the posterior logarithm Equivalent to maximizing To obtain The given Γ is realized by the EM algorithm i and Maximization under the conditions Considering There is no analytical expression for the solution of , and the solution that maximizes the posterior distribution (Γ i |z,n i ,Θ,μ i ,α i ) i ,Right now Complete the update of Γ.

9. The multi-layer network state prediction method based on multimodal spatiotemporal data modeling according to claim 8 is characterized in that: The numerical algorithm performs the following steps: Step 21) For each node i, i=1,…,N, execute: Based on Γ i and z, n i , Θ, μ i , α i Calculate ρ i = P(Γ i |z, n i , Θ, μ i , α i ); For each node j, Among them, the subset To remove the node index of node i, perform the following steps: Step 211) Setup Keep Γ i The other elements in remain unchanged to obtain Step 212) Using the EM algorithm, given and renew make maximum; Step 213) Based on and calculate Step 214) Update Γ i ; Step 22) By combining Get the updated 10. A multi-layer network state prediction method based on multimodal spatiotemporal data modeling according to claim 9, characterized in that: In step S3, after the multimodal spatiotemporal model parameters are solved, the group of each node i (i=1, ..., N) is represented as: The attribute preference of each group r (r = 1, ..., R) is represented by φ r ={φ rk ,k=1,…,K}; This gives the conditional density function for any node i and layer l: Given a historical network event that occurred before time t Using the conditional density function Predict the expected event frequency at node i and layer l, where i=1,…,N and l=1,…,L.

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