An early prediction method for information cascade outbreak based on global propagation probability

Abstract

The application provides an early information cascade outbreak prediction method based on global propagation probability.The technical scheme is as follows: firstly, converting the network with known structure, regarding all the undirected edges in the network as bidirectional directed edges; then compressing the nodes in the infected state node set and the nodes in the recovered state node set into one node at a certain moment, and regarding the nodes in the susceptible state node set among all the neighbor nodes of the infected state node set as the neighbors of the compressed node, to obtain the converted network; secondly, iteratively solving the equation set to obtain the probability that all the nodes belong to the giant connected piece, which is called the global propagation probability of the node; and thirdly, calculating the probability and range of the information cascade outbreak at the moment.The application fully utilizes the network structure data and early propagation situation, proposes two equivalent relations, and can quantitatively predict the probability and range of the cascade outbreak.

Description

Technical Field

[0001] This invention belongs to the field of information processing technology, and specifically relates to an early prediction method for information cascading in a network. Background Technology

[0002] With the rapid development of radio communication and the internet, information can cascade and spread through repeated sharing. Some information can spread explosively throughout the system, much like a virus. Such cascading outbreaks exist in many scenarios, including internet information dissemination, computer virus propagation, epidemic spread, and numerous physical and chemical phase transitions. Early prediction of cascading outbreaks can help managers provide timely warnings and take appropriate proactive measures to avoid serious consequences. Therefore, early prediction of information cascading outbreaks is of great significance.

[0003] Early prediction of information cascading bursts refers to predicting the probability and scope of an information cascading burst in the early stages of information propagation. With the increasing efficiency of information transmission, much information can spread from local to global in a very short time. Making scientific predictions before this phase transition occurs is a research hotspot in the field of information science. Currently, this field typically predicts cascading bursts based on information content and time-series data. These methods are mostly applied to specific domains and require prior information such as historical data for prediction, but they neglect network structural data and propagation dynamics models, thus resulting in low prediction efficiency and only providing relatively rough estimates.

[0004] Furthermore, during information propagation, in addition to knowing the changes in the number of infected and uninfected nodes in the network, their topological positions within the network are often also known. This indicates that the input data is two-dimensional, but existing methods struggle to utilize this two-dimensional data from the early stages of propagation. Therefore, how to transform the prediction problem of cascading outbreak probability and outbreak range based on propagation dynamics models into a technical problem—analyzing and predicting the input two-dimensional data—is a highly valuable issue in this field and the focus of this invention. Summary of the Invention

[0005] This invention proposes an early prediction method for information cascading bursts based on global propagation probability. This method can make full use of the network's structural information to accurately predict information cascading bursts and their range in the early stages of propagation.

[0006] The technical solution of this invention is: a method for early prediction of cascading outbreaks based on global propagation probability, given a known network. The structure of a network. The information propagation model on the network is the SIR (Susceptible Infected Recovered) model, where each edge in the model represents the probability of information propagation. Information in the network... The confidence level α for the cascading outbreak is much less than 1. At any early time t, the set of nodes in the infected state I(t), the set of nodes in the recovered state R(t), and the set of nodes in the susceptible state S(t) are known;

[0007] Its features are:

[0008] First, regarding the network Perform the conversion. Convert the network. All undirected edges are treated as bidirectional directed edges. Then, the nodes in the infected state set I(t) and the recovered state set R(t) at time t are compressed into a single node n(t), and the nodes in the susceptible state set S(t) among all the neighbors of I(t) are taken as the neighbors of n(t), thus obtaining the transformed network G. t .

[0009] Secondly, the probability that all nodes belong to a giant connected component is obtained by iteratively solving the system of equations; this is called the global propagation probability of the nodes. That is: first, the system of equations is listed using the following relationship, and each directed edge e is iteratively calculated. vu Probability of reaching a giant connected component: network G t Each directed edge e vu The probability of reaching a giant connected component is equivalent to the directed edge e. vu At least through one of its neighboring edges e uw (w≠v) The probability of a node u belonging to a giant connected component. Then, the probability of node u belonging to a giant connected component is calculated using the following relationship: Network G t The probability p that any node u belongs to a giant connected component. u This means that node u is connected to at least one of its neighboring edges e. uv The probability of leading to a giant connected component.

[0010] Next, calculate the probability and range of the cascading information burst at time t. Then, calculate the global propagation probability p of node n(t). n(t) As a probability of information cascading explosion. Then consider network G. t The global propagation probabilities of all nodes are summed to obtain the predicted range of the information cascade outbreak. Used to predict the final total number of infected nodes s ∞ .

[0011] Furthermore, according to the following rule: if the global propagation probability is greater than 1-α, then an information cascade outbreak is predicted, and the predicted range of the outbreak is... If the global propagation probability is less than α, then an inference is made that the information has propagated locally; otherwise, the propagation situation at the next moment is observed. α represents the confidence threshold for the cascading burst of information, which is determined based on the actual situation and is usually a small value.

[0012] The innovation of this invention compared to existing technologies lies in:

[0013] (1) This invention makes full use of network structure data and early propagation information to convert the network structure at any time t into a directed network, which facilitates further analysis and calculation of cascading bursts.

[0014] (2) This invention proposes two equivalence relations. Based on these relations, the global propagation probability of all nodes in the network can be estimated efficiently and accurately by iteratively solving the system of equations.

[0015] (3) The early prediction algorithm proposed in this invention predicts the total number of infected nodes at a certain time by calculation (i.e., the predicted value). It can quantitatively predict the probability and range of cascading outbreaks. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the local structure of the network transition at three consecutive time points;

[0017] Figure 2 This is a schematic diagram illustrating an example of establishing and solving equations;

[0018] Figure 3 This is a schematic diagram illustrating the principle and flow of the present invention;

[0019] Figure 4 This is a diagram showing the early prediction results obtained using this invention. Detailed Implementation

[0020] The inventors discovered through research that the explosive spread of information in networks follows specific technical patterns, and therefore can be predicted using technical means. Information cascading explosion is a sudden phenomenon; when approaching the critical point of the explosion, there are often only a few infected nodes. Therefore, this method utilizes these few infected nodes to make effective predictions very early in the spread.

[0021] The following detailed explanation of an early prediction method based on global propagation probability provided by the present invention, in conjunction with the accompanying drawings and specific embodiments, is provided in detail.

[0022] Let's take an example of information dissemination on the Internet to illustrate this.

[0023] Figure 1 This is a schematic diagram of the local structure of the network transition at three consecutive time points. The network known in this invention... The structure of the network (including all nodes and all edges). When using this invention, firstly, the network... Perform the conversion. Convert the network. All undirected edges are treated as bidirectional directed edges. Then, the nodes in the infected state set I(t) and the recovered state set R(t) at time t are compressed into a single node n(t), and the nodes in the susceptible state set S(t) among all the neighbors of I(t) are taken as the neighbors of n(t), thus obtaining the transformed network G. t . Figure 1 (a)-(c) represent schematic diagrams illustrating the network transformation using this invention at times t=0, t=1, and t=2, respectively. The left side of the symbol "→" in each diagram represents the network at that time. The right side of the symbol "→" represents the network G after the transformation at a certain moment. t Among them, in Figure 1 In (a), at time t=0, only node 1 is infected, while nodes 2 through 14 are susceptible. Node 1 is compressed into node n(0), and its neighbors 2, 3, 10, and 11 are designated as neighbors of node n(0). Figure 1 In (b), at time t=1, nodes 2 and 3 are infected nodes, node 1 is a recovered node, and all other nodes are susceptible nodes. Nodes 1 to 3 are compressed into node n(1), and the neighboring nodes 4, 8, and 9 of nodes 2 and 3 are taken as the neighbors of n(1); Figure 1 In (c), at time t=2, node 4 is an infected node, nodes 1 to 3 are recovered nodes, and the other nodes are susceptible nodes. Nodes 1 to 4 are compressed into node n(2), and the neighboring nodes 5, 6, 7, 12, 13, and 14 of node 4 are taken as the neighboring nodes of n(2). The network is transformed using this method, and the transformed network is denoted as G. t .

[0024] Figure 2 This is a schematic diagram illustrating an example of establishing and solving the equations. The diagram shows network G. t The local structure of node u is given, where nodes v0, v1, v2, v3, and v4 are the neighbors of node u. The system of equations can be derived using the following relationships: Network G t directed edges The probability of reaching a giant connected component is equivalent to the probability of a directed edge. At least through one of its neighboring edges e uv (v≠v0) is the probability of reaching a giant connected component. Let network G be an example. t The propagation probability from node u to its neighbor node v (node ​​v in this embodiment represents nodes v0, v1, v2, v3, v4) is β. uv Directed edge The probability of leading to a giant connected component is For directed edges Then probability Equal to directed edge ev0u At least through one of its neighboring edges e uv (v≠v0) The probability p of leading to a giant connected component u→v Therefore, we have the equation:

[0025]

[0026] Where θu represents the set of neighboring nodes of node u, in this embodiment θu = {v0, v1, v2, v3, v4}. Using a similar process, for network G... t With M directed edges, we can obtain M equations. The system of M equations can be solved efficiently through iteration.

[0027] Then, use the following relationship to calculate the probability that node u belongs to a giant connected component: Network G t The probability p that node u belongs to a giant connected component. u This means that node u is connected to at least one of its neighboring edges e. uv The probability of reaching a giant connected component. Therefore, the global propagation probability p of node u can be calculated. u :

[0028]

[0029] Using a similar process, network G is calculated. t The global propagation probability p of any node m in the middle m Network G t The predicted range of the information cascade outbreak is obtained by summing the global propagation probabilities of all nodes.

[0030]

[0031] Where V(t) is the network G t The set of nodes, card(I(t)∪R(t)) represents the number of nodes contained in the set I(t)∪R(t).

[0032] The invention will be further validated below using two computer-simulated network datasets and one open-source real-world dataset. The first computer-simulated network dataset is... The first dataset used was a random network with 12,008 nodes, where the probability of an edge connecting any two nodes was 0.0003. The second computer simulation dataset was a scale-free BA (Barabasi-Albert) network with 22,470 nodes and an average degree of 3. The third dataset was an open-source real-world Deezer network, downloaded from http: / / snap.stanford.edu / data / , containing 28,281 nodes and an average degree of 3.28. We conducted information propagation experiments on these three networks using the SIR propagation model. The simulation stopped when the number of infected nodes in the network reached 0 (at which point all infected nodes became recovered nodes). We recorded the change in the total number of infected nodes over time in each simulation and denoted the total number of infected nodes at the final moment as s. ∞ The following section utilizes this invention to predict the cascading bursts of information in the early stages of propagation. For example... Figure 4 As shown, in Figure 4 In experiments (a) and (c), we set up one infected node in the network at time t=0, and the rest were susceptible nodes, with no recovering nodes. Figure 4 In experiments (b) and (d), we set up multiple infected nodes and susceptible nodes in the network at time t=0, with no recovering nodes. The three graphs in each row, from left to right, represent the experimental results in the ER, BA, and Deezer networks, respectively. In each graph, a star-shaped line represents the change in global propagation probability over time, a solid dotted line represents the change in the total number of infected nodes over time, a dashed line represents the outbreak warning line (i.e., a value of 1-α, where α = 0.01 and 1-α = 0.99 in this embodiment), and a dotted line represents the predicted outbreak range. In the coordinate system, the horizontal axis measures time, the left vertical axis measures the global propagation probability, and the right vertical axis measures the total number of infected nodes. For example... Figure 4 As shown in (a), the global transmission probability fluctuates in the early stages of transmission, and exceeds the outbreak warning line at t=29, t=8, and t=18 in the three subgraphs from left to right, respectively. This suggests a cascading outbreak, with predicted outbreak ranges of 4318, 5303, and 8318, which closely match the actual total number of infected nodes (4299, 5308, and 8164, respectively). Figure 4 As shown in (b), the global transmission probability fluctuates in the early stages of transmission, and exceeds the outbreak warning line at t=9, t=3, and t=12 in the three subgraphs from left to right, respectively. This allows for the inference of a cascading outbreak, and the predicted outbreak ranges of 4441, 5310, and 8320 closely match the actual total number of ultimately infected nodes (4292, 5318, and 8322, respectively). Figure 4As shown in (c), the global propagation probability fluctuates in the early stages of propagation, and is less than α at t=19, t=13, and t=19 in the three subgraphs from left to right, respectively. Therefore, a local propagation inference is made, and the total number of infected nodes is ultimately very small (5, 2, and 5 respectively), which matches the real scenario. Figure 4 As shown in (d), the global propagation probability fluctuates in the early stages of propagation, and is less than α at t=11, t=17, and t=21 in the three subgraphs from left to right, respectively. Therefore, a local propagation inference is made, and the total number of infected nodes is very small (2, 3, and 6 respectively), which is consistent with the real scenario. The experimental results show that although the number of infected nodes is often small in the early stages of information propagation, this invention still provides a quantitative and accurate prediction very early in the propagation process.

Claims

1. A method for early prediction of cascading outbreaks based on global propagation probability, given a known network. Structure, network The information propagation model on the network is the SIR model, where SIR stands for Susceptible Infected Recovered; information in the network... Confidence level of mid-cascade outbreak , Much less than 1; at any early time The set of nodes in the infected state is known. Node set in the recovery state and the set of nodes in the susceptible state ; Its features are: First, regarding the network Perform conversion: convert the network All undirected edges are treated as bidirectional directed edges; then, the time interval is... Infected Node Set and the set of nodes in the recovery state All nodes are compressed into one node. and will Among all neighboring nodes, the susceptible node set The node as The neighbors, obtained the converted network ; Secondly, each directed edge is calculated iteratively by listing the system of equations using the following relationship. Probability of reaching a giant connected component: network Each directed edge The probability of reaching a giant connected component is equivalent to the probability of a directed edge. At least through one of its adjacent sides ( The probability of a node leading to a giant connected component; then, the following relationship is used to calculate the node. Probability of being a giant connected fragment: network any node The probability of being a giant connected piece Equal to node At least through one of its adjacent sides The probability of leading to a giant connected component; Node global propagation probability As a probability of information cascading explosion; then the network The global propagation probabilities of all nodes are summed to obtain the predicted range of the information cascade outbreak. ; Among them, the probability that all nodes belong to a giant connected component is obtained by iteratively solving the system of equations, which is called the global propagation probability of the node; Among them, the network is used by the following formula The global propagation probabilities of all nodes are summed to obtain the predicted range of the information cascade outbreak. : in For the network The set of nodes, Represents a set The number of nodes included.

2. The method for early prediction of cascading outbreaks based on global propagation probability according to claim 1, characterized in that, Inferences are made according to the following rule: if the global propagation probability is greater than... Then, an inference is made that an information cascade outbreak will occur, and the predicted range of the outbreak is... ; If the global propagation probability is less than If so, then we can infer that the information has spread locally; otherwise, we will continue to observe the spread at the next moment. The confidence threshold for the cascading burst of information is determined based on the actual situation.

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