Information propagation network deduction method based on clustering fast deduction and submodule maximization

Abstract

The present invention discloses an information propagation network deduction method based on clustering rapid deduction and submodule maximization, comprising: obtaining propagation time data and the number of propagation relationships between users to be deduced; constructing a data model according to the propagation time data; constructing all potential edge sets in an information cascade set according to the reception time of the node; constructing a clustering index of the reception time and reception state of a fusion node; calculating the clustering index value of each potential edge; clustering the clustering index values ​​of all potential edges using a clustering algorithm to obtain a clustering result; obtaining a threshold for screening the clustering index value of each potential edge according to the clustering result; comparing the clustering index value of each potential edge with the threshold to deduce a valid potential edge, and obtaining a cluster structure of the node according to the valid potential edge; constructing a likelihood function of the observation cascade according to the information cascade set or information propagation, iteratively deducing the propagation edge using a greedy algorithm, and completing the deduction.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural deduction of information propagation networks, and in particular relates to an information propagation network deduction method based on clustering rapid deduction and submodule maximization. Background Art

[0002] Information dissemination network deduction involves inferring the underlying network structure underlying information dissemination based on observed data after information dissemination on mainstream social networks like Weibo and WeChat. This data typically focuses on the more readily observable time at which a user disseminates (forwards or sends) a piece of information. In complex networks, users can be abstracted as nodes, and the dissemination relationships between users—who disseminates information to whom—can be abstracted as directed edges between nodes in the network. Therefore, abstracting real-world social relationships among people into networks makes it more convenient and efficient to study the deduction of these dissemination relationships.

[0003] Existing methods for inferring communication networks can be broadly divided into two categories: those that infer only communication relationships between users and those that infer both communication relationships and the strength of these relationships. The main idea behind methods that infer only communication relationships between users is to assume that users share a common tendency or willingness to spread information. They then construct a likelihood function for the observed communication data and maximize this likelihood function to infer the most likely communication network structure on which the cascade data was observed. Methods that infer both communication relationships and the strength of these relationships aim to use the strength of the communication relationship between users as the independent variable, construct a likelihood function for the observed communication data, and then maximize this likelihood function. The common point between these two methods is that if, in multiple observed communication data, user A is always infected after user B (or user B sends a message that user A then comments on or reposts), then there is a high probability that a directed communication relationship exists from user A to user B. As early as 2010 to 2013, Gomez-Rodriguez, Myers, and others proposed several systematic methods for inferring communication networks. Assuming that the propagation trajectory of information or disease resembles a tree, the NetInf algorithm, while considering only the most likely propagation spanning tree for each cascade (i.e., the most likely propagation scenario), utilizes a greedy algorithm to iteratively deduce propagation edges, taking into account the submodularity of the log-likelihood of the observed cascade. The MulTree algorithm, on the other hand, considers all possible propagation spanning trees for each cascade (i.e., all possible propagation scenarios). Assuming that the strength of the relationships between nodes varies, the ConNIe and NetRate algorithms, respectively, use the conditional propagation probability and propagation rate between nodes as independent variables to construct likelihood functions for the observed propagation cascade data (the NetRate algorithm is based on survival analysis theory). Because the logarithm of the likelihood function for the observed cascade is convex, both algorithms utilize convex optimization methods to deduce the propagation probability and propagation rate between nodes. In recent years, scholars have proposed a number of improved methods. To more accurately characterize the heterogeneity of information dissemination between users, Zhao et al. in 2018 considered the changes in information popularity during dissemination and proposed dividing the dissemination process into different life stages. They then used the product of the information popularity in different life stages and the relationship strength between users as the apparent influence strength between users, thereby improving the inference accuracy of existing algorithms. Although motifs, a simple network building block, are crucial for describing the structure and function of networks, existing methods have not utilized them. Therefore, in 2020, Tan et al. mined motifs, the basic components of complex networks, from node observation data and incorporated them into existing inference algorithms as structural priors, thereby improving the inference performance of existing algorithms.However, the aforementioned propagation network inference methods still have some issues: when the network is slightly larger, or the average length of the observed cascade data is longer (i.e., when a large number of people are observed spreading a particular message at a time), the total number of potential edges will be at least 10 times the actual number of edges. Because existing methods infer a small number of propagation edges from all possible potential edges, the inference efficiency is low, meaning that the method runs unacceptably slow. When the time when a user forwards or becomes infected is observable, it is also easy to determine the user's infection status. However, existing methods mostly only consider the node's time factor, and less research considers both the node's time factor and the node's state factor. Moreover, existing methods rarely consider both the node's propagation time information and the node's state information to preprocess all possible potential edges to improve the algorithm's inference efficiency and accuracy. Summary of the Invention

[0004] The purpose of the present invention is to propose an information propagation network deduction method based on clustering rapid deduction and submodule maximization, which pre-processes the observed cascade data by fusing the reception time information and reception status information of the nodes, so that the algorithm can be faster and more accurate when deducing network structures of a slightly larger scale.

[0005] To achieve the above objectives, the present invention provides an information propagation network deduction method based on clustering rapid deduction and submodule maximization, comprising the following steps:

[0006] A data model is constructed based on the collected propagation time data and the number of propagation relationships between users to be deduced. Abstraction is performed based on the data model to obtain an information cascade set in the field of network propagation dynamics, nodes in the information propagation network to be deduced, the number of propagation edges in the information propagation network to be deduced, the reception time of the node, and the reception status of the node;

[0007] According to the reception time of the node, all potential edges are constructed in the information cascade set, a clustering index is constructed that integrates the reception time and reception state of the node, and the clustering index value of each potential edge is calculated;

[0008] Clustering the clustering index value of each potential edge using a 2-means clustering algorithm to obtain a clustering result, and obtaining a threshold for screening the clustering index value of each potential edge according to the clustering result;

[0009] Comparing the clustering index value of each potential edge with the threshold, deducing a valid potential edge, and obtaining a cluster structure of nodes according to the valid potential edge;

[0010] According to the information cascade set and information propagation, the likelihood function of the observation cascade is constructed in a tree-like manner; the cluster structure of the node is integrated into the likelihood function of the observation cascade, and a greedy algorithm is used to iteratively deduce a number of propagation edges to complete the propagation network deduction.

[0011] Optionally, building a data model based on the collected propagation time data and the number of propagation relationships between users to be deduced specifically includes:

[0012] A sequence consisting of each user and the time at which each user spreads information is abstracted as an information cascade, and a set consisting of multiple pieces of spread data is converted into an information cascade set;

[0013] Each cascade c k Node v in i Abstraction is the node in the information dissemination network to be deduced;

[0014] The communication relationship between users, in which users spread information to each other, is abstracted as the communication edge in the information communication network to be deduced;

[0015] Each cascade c k User v in i Time to disseminate information Abstracted as the receiving time of the node, each cascade c k User v in i The state of whether the information is propagated is abstracted as the node's receiving state X i .

[0016] Optionally, all potential edges are constructed in the information concatenation set according to the reception time of the node, specifically including:

[0017] According to the reception time of the node, all potential edges are constructed based on the information cascade set;

[0018] In each observed information cascade, if any node v i The receiving time of any node v is less than j The receiving time of the node pair (v i ,v j ) is derived as a potential edge or a node v i There is a directed edge pointing to node v j .

[0019] Optionally, a clustering index is constructed that integrates the receiving time and receiving status of the node, specifically including:

[0020] Calculating the final propagation likelihood on the potential edge and the positive correlation between the receiving states of the two nodes on the potential edge using the receiving time and receiving state of the node respectively;

[0021] The clustering index is constructed by utilizing the multiplication principle and fusing the implicit information of the receiving time and receiving state of the nodes.

[0022] Optionally, obtaining a threshold for screening the clustering index value of each potential edge according to the clustering result specifically includes:

[0023] After performing 2-means clustering on the clustering index values ​​of all potential edges, the potential edges are divided into two categories according to the index values, including a category with a large clustering index value and a category with a small clustering index value, wherein the minimum value of the category with a large clustering index value is greater than the maximum value of the category with a small clustering index value;

[0024] The clustering index values ​​of a class with a smaller clustering index value are calculated to obtain an average value, which is used as a threshold.

[0025] Optionally, constructing a likelihood function of an observation cascade in a tree-like manner according to the information cascade set and information propagation specifically includes:

[0026] Based on information cascade collection and information propagation, the probability distribution of cascade data observed on a potential network is constructed in a tree-like manner.

[0027] Optionally, the likelihood function of the observation cascade is expressed as:

[0028]

[0029] Among them, c k represents the kth cascade data, C represents the set of all cascade data, G * represents a potential unknown propagation network, f(c k |G * ) represents the likelihood function of the k-th observation cascade.

[0030] Optionally, the method of integrating the cluster structure of the node into the likelihood function of the observation cascade is:

[0031]

[0032] in, Corresponding to the k-th observed node v i and propagation time The sequence data composed of Indicates the kth cascade data c k Midpoint v i The receiving time, Indicates the kth cascade data c k Midpoint v j The receiving time, G * represents a potentially unknown propagation network, CSj Represents node v j The cluster structure of a ij represents the potential edge (v i ,v j ) on the information transmission rate, Indicates that in the propagation data of the kth observation, the potential edge (v i ,v j ) on the propagation likelihood.

[0033] Technical effect of the invention: The present invention discloses an information propagation network deduction method based on clustering fast deduction and submodule maximization, and proposes an effective clustering index, which integrates the twice normalized propagation possibility between nodes (node ​​reception time information) and the positive correlation between node reception status (node ​​reception status information), and can better distinguish a large number of invalid potential edges from valid edges in the initial potential edges; an efficient preprocessing method is proposed, which mainly performs clustering based on an effective clustering index, and then takes the average value of a class with a small clustering index value in the potential edge as a threshold, and uses this threshold to separate the large potential edges from the valid edges. The invalid potential edges are pruned (at least about 50% of the invalid potential edges can be pruned, and at most about 90% of the invalid potential edges can be pruned), and the more likely or valid potential parent nodes of the nodes can be accurately captured; the preprocessing method proposed in the present invention can be integrated as a component into the front of most methods that rely on node reception time information, so as to improve the deduction efficiency of subsequent algorithms; the preprocessing method of the present invention is integrated into an existing algorithm and it is found that after the integration, the running time of the algorithm is reduced by at least about 30% and at most about 85%, and the deduction accuracy is better than the original algorithm on most data sets. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0035] Figure 1 Schematic diagram of the flow of the information propagation network deduction method based on clustering rapid deduction and submodule maximization according to an embodiment of the present invention;

[0036] Figure 2 Illustration of the different roles played by the same potential edge in different cascades provided by embodiments of the present invention;

[0037] Figure 3 A diagram of a cascade of multiple propagation spanning trees provided by an embodiment of the present invention;

[0038] Figure 4A complete diagram of an information propagation network deduction method based on clustering rapid deduction and submodule maximization provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0040] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0041] like Figure 1-4 As shown, this embodiment provides an information propagation network deduction method based on clustering rapid deduction and submodule maximization, including the following steps:

[0042] A data model is constructed based on the collected propagation time data and the number of propagation relationships between users to be deduced. Abstraction is performed based on the data model to obtain an information cascade set in the field of network propagation dynamics, nodes in the information propagation network to be deduced, the number of propagation edges in the information propagation network to be deduced, the reception time of the node, and the reception status of the node;

[0043] According to the reception time of the node, all potential edges are constructed in the information cascade set, a clustering index is constructed that integrates the reception time and reception state of the node, and the clustering index value of each potential edge is calculated;

[0044] Clustering the clustering index value of each potential edge using a 2-means clustering algorithm to obtain a clustering result, and obtaining a threshold for screening the clustering index value of each potential edge according to the clustering result;

[0045] Comparing the clustering index value of each potential edge with the threshold, deducing a valid potential edge, and obtaining a cluster structure of nodes according to the valid potential edge;

[0046] According to the information cascade set and information propagation, the likelihood function of the observation cascade is constructed in a tree-like manner; the cluster structure of the node is integrated into the likelihood function of the observation cascade, and a greedy algorithm is used to iteratively deduce a number of propagation edges to complete the propagation network deduction.

[0047] like Figure 1 As shown, the present invention provides an information propagation network deduction method based on clustering rapid deduction and submodule maximization. The following will take the deduction of the microblog propagation network structure on the microblog social network as an example to illustrate the practical application of this method, including:

[0048] S1, input the observed propagation data C and the number of propagation relationships K between the users to be deduced: input the observed Weibo users and their time data of posting or commenting on Weibo after the propagation of multiple Weibo posts on the Weibo social network C = {c1, c2, ..., c m} (specifically observed m = 200 times), and the total number of user relationships K that need to be deduced, where each piece of propagation data The Weibo user v corresponding to the k-th observed post or comment on the Weibo i and the time when they posted or commented on the Weibo The sequence data composed of i If the user has not posted or commented on a Weibo post, the time when the user posted or commented on the Weibo post |C|=m represents the total number of observations;

[0049] S2, build a data model based on the observed dissemination data: a sequence of the "footprints" left by each Weibo user, that is, the time when each user posted or commented on the Weibo. Abstracted as a cascade, the set of multiple propagation data C={c1,c2,…,c m} is transformed into a set of multiple cascades, each cascade c k Weibo user v i The nodes in the microblog propagation network to be deduced are abstracted, and the propagation relationship between microblog users, who spreads microblogs to whom, is abstracted as the propagation edge in the microblog propagation network to be deduced. Each cascade c k Weibo user v i Time of posting or commenting on the Weibo Abstracted as the receiving time of the node, each cascade c k Weibo user v i The state of whether a microblog is published or commented is abstracted as the node's receiving state X i , if a Weibo user posts or comments on a Weibo (i.e. ), then the receiving state of the node is the receiving state (i.e. X i =1), if the Weibo user has not posted or commented on the Weibo (i.e. ), the receiving state of the node is the unreceived state (i.e. X i =0), then |C|=m is the number of cascades, and the number K of propagation relationships between users to be deduced is abstracted as the number of propagation edges to be deduced.

[0050] S3, construct the initial potential edge set E-initial: According to the receiving time of the microblog user, construct all possible potential edge sets from the cascade set C, that is, in each observed cascade In the example, if user vi Receiving time Less than user v j Receiving time Then the user's (v i ,v j ) is derived as a possible potential edge or the user v i There may be a directed edge pointing to user v j ;

[0051] S4, construct a clustering indicator Cluster-Metric (v i ,v j ): In terms of user reception time, on the one hand, we consider not only the propagation possibility implied by the reception time difference between two Weibo users, but also the influence of other users during the propagation process. Therefore, we normalize the propagation possibility between users. On the other hand, we consider that the sum of the probability that a user will propagate a Weibo to all its neighboring nodes is 100%, so we further normalize the propagation possibility between users and calculate the final propagation possibility between users. In terms of user reception status, we use the propagation mutual information formula to measure the positive correlation between the reception status of two users. It can be seen that this clustering indicator can more comprehensively and quantitatively measure the propagation possibility between two users or the possibility of the existence of a directed edge.

[0052] S5, calculate the clustering index value Cluster-Metric (v i ,v j ): For each potential edge or each user pair (v i ,v j ), calculate the corresponding clustering index value Cluster-Metric (v according to the observed cascade data C i ,v j );

[0053] S6, using the 2-means clustering algorithm to calculate the clustering index value Cluster-Metric (v i ,v j ) for clustering;

[0054] S7, obtain the appropriate threshold τ from the clustering results: Cluster-Metric (v i ,v jAfter clustering, the clustering index can be divided into a class with large clustering index values ​​and a class with small clustering index values. Although the propagation probability of most user pairs in the class with small values ​​is not as high as that of user pairs in the class with large values, there are inevitably a few user pairs with real edges that are classified into the class with small values ​​due to the small number of simultaneous observations in the limited number of observations. Therefore, in order to reduce the error of the division and remove or prune the potential edges that are least likely to exist as much as possible, the average value of the class with small clustering index values ​​is selected as the threshold;

[0055] S8, obtain the cluster structure CS of the node: first, the clustering index value Cluster-Metric (v i ,v j ) The initial potential edges that are smaller than the threshold are removed, and the remaining potential edges are automatically inferred as valid potential edges. Then, each user v is obtained from the valid potential edges. j Cluster structure CS j Specifically, it is to find the set of potential parent users or effective potential parent users for each user (the potential parent user set of a user is the set of other users who may spread the microblog to the user);

[0056] S9, establish the likelihood function of observing the cascade: from the cascade or microblog propagation, according to the tree modeling, the probability distribution of the most likely observation of the cascade data on a certain potential network;

[0057] S10, the cluster structure CS of the node is integrated into the likelihood function of the observation cascade. Specifically, the cluster structure of each user is integrated into the propagation likelihood function of the potential edge whose terminal node is the user.

[0058] S11. Use the greedy algorithm to iteratively deduce K propagation edges: According to the submodular property of the log-likelihood of the cascade that you want to maximize, use the greedy algorithm to iteratively deduce the K edges that need to be deduced. Specifically, the number of iterations is set to K, which means that the propagation relationship between all users who have posted or commented on Weibo in the propagation data C is finally deduced.

[0059] Furthermore, in S3, the initial potential edge set E-initial includes the following potential edges:

[0060]

[0061] in, Represents the kth cascade data, and Respectively represent the observation c k Or in the kth cascade, user v i and user v j The receiving time.

[0062] Furthermore, in S4, a clustering indicator Cluster-Metric (v i ,v j ) comprises the following steps:

[0063] S41: Calculate the potential edge (v i ,v j ) on the final propagation likelihood and potential edge (v i ,v j ) between the two user receiving states (propagation mutual information), the calculation formulas are as follows:

[0064]

[0065] in, Represents the kth cascade data, and Respectively represent the observation data c k Or in the kth cascade, user v i , user v j and user v l The receiving time, E-initial represents the initial potential edge set, Represents the propagation data c observed at the kth time k In the potential edge (v i ,v j ) on the propagation likelihood or user v i Spread the information to user v j The possibility of a ij represents the potential edge (v i ,v j ) (the default value is 1 during deduction), Indicates that in the propagation data of the kth observation, the potential edge (v i ,v j ) is a normalized operation of the propagation likelihood, so fs(v i ,v j ) means that among all the propagation data, the potential edge (v i ,v j ), and similarly, For all users v i is the potential edge of the starting node (v i ,v p ) corresponding to fs(v i ,v p ), so Indicates that in the entire observed propagation data, for the potential edge (v i ,vj ) is the result of the total normalization operation, and its value is used as the potential edge (v i ,v j ) on the final propagation likelihood fn(v i ,v j );

[0066] IMI(X i ,X j )=MI(X i =1,X j =1)+MI(X i =0,X j =0)-|MI(X i =1,X j =0)|-|MI(X i =0,X j =1)|(3)

[0067] Among them, X i and X j Represents user v i and user v j The variable of the receiving state has a value range of {0,1}, X i =0 means user v i In the unreceived state, X i =1 means user v i In receiving state (X j Similar), MI(X i =1,X j =1) indicates user v i and user v j All are receiving state (X i =1,X j =1), user v i and user v j The correlation size of the receiving state in all observation cascade data, and the rest are similar;

[0068] S42: Using the multiplication principle to fuse the information implied by the user's receiving time and receiving status, the calculation formula of the constructed clustering index is shown in formula (4):

[0069] Cluster-Metric(v i ,v j )=fn(v i ,v j )*IMI(X i ,X j ) (4)

[0070] Among them, fn(v i ,v j) represents a user pair or potential edge (v i ,v j )The final propagation likelihood, IMI(X i ,X j ) indicates the user's (v i ,v j ) positive correlation between receiving states.

[0071] Furthermore, in said S8, each user v j Cluster structure CS j The elements include:

[0072] CS j ={v i |(v i ,v j )∈E initial ∧Cluster-Metric(v i ,v j )≥τ} (5)

[0073] Wherein, E-Einitial represents the initial potential edge set, τ is the threshold value obtained in S7, specifically the clustering index value Cluster-Metric (v i ,v j )The average value of the class with the smaller median value;

[0074] Furthermore, in S9, establishing the likelihood function of the observation cascade includes the following steps:

[0075] S91: From the perspective that Weibo propagation is like a tree, for each observed cascade c k Data, consider all possible propagation scenarios or propagation trees that may produce the observed data (examples of multiple propagation spanning trees for each cascade are shown in the attached figure of the specification) Figure 4 As shown), establish the likelihood function f(c k |G * ), and its calculation formula is shown in formula (6):

[0076]

[0077] in, Represents the kth cascade data, Indicates that when observing c k or user v in the kth cascade i The receiving time, G * represents a potentially unknown propagation network, Represents a potential unknown propagation network G *On the other hand, a set of all possible propagation trees for the k-th observation data is generated, and T represents an element in the set, that is, a tree. * ) represents a given latent network G * The probability that tree T is a subgraph of it. k |T) means that on a given tree T, a cascade c is observed k possibility.

[0078] For the convenience of modeling, it is assumed that the propagation probability on each edge in the tree is known and equal. k The likelihood function f(c k |G * ) satisfies formula (7):

[0079] in, Represents the kth cascade data, Indicates that when observing c k or user v in the kth cascade i The receiving time, G * represents a potentially unknown propagation network, Represents a potential unknown propagation network G * On the top, generate the kth observation data c k The set of all possible propagation trees, T represents an element in the set, that is, a tree, f(c k |T) means that on a given tree T, a cascade c is observed k The possibility of E T represents the set of potential edges in the tree T, Indicates that in the propagation data of the kth observation, the potential edge (v i ,v j ) on the propagation likelihood, a ij represents the potential edge (v i ,v j ) on the microblog (the default value is 1 during deduction).

[0080] According to Kirchhoff's matrix tree theorem for directed weighted graphs, formula (7) can be reformulated as:

[0081]

[0082] in, Represents the kth cascade data, Indicates that when observing c k or user v in the kth cascade i The receiving time, Indicates the jth cascade data c k Medium User vj The receiving time, G * represents a potentially unknown propagation network, a ij represents the potential edge (v i ,v j ) on the microblog propagation rate (the default value is 1 during deduction), Indicates that in the propagation data of the kth observation, the potential edge (v i ,v j ) on the propagation likelihood.

[0083] S92: Since the observations of each set of propagation data are independent of each other, the likelihood function of the observed cascade data C can be expressed as the joint likelihood of all cascades f(c1,c2,…,c m |G * ), and is defined as:

[0084]

[0085] in, Represents the kth cascade data, Indicates that when observing c k or user v in the kth cascade i The receiving time, C represents the collection of all cascaded data, G * represents a potential unknown propagation network, f(c k |G * ) represents the likelihood function of the k-th observation cascade.

[0086] Therefore, the objective function of network deduction can be designed as:

[0087]

[0088] in, represents the deduced communication network, G * represents a potential unknown propagation network, K represents the number of network edges to be deduced, f(c1,c2,…,c m |G * ) represents the joint likelihood of all observation cascades, F C (c1,c2,…,c m |G * ) represents the logarithm of the joint likelihood, Represents the kth cascade data, Indicates that when observing c k or user v in the kth cascade i The receiving time, C represents the set of all cascaded data, f(c k |G * ) represents the likelihood function of the k-th observation cascade.

[0089] Furthermore, in the S10, each user v j Cluster structure CS j The specific situation of integrating into the likelihood function of the observation cascade (specifically integrating into the propagation likelihood function of some potential edges) is:

[0090]

[0091] in, Represents the kth cascade data, Indicates that when observing c k or user v in the kth cascade i The receiving time, Indicates the kth cascade data c k Medium User v j The receiving time, G * represents a potentially unknown propagation network, CS j Indicates user v j The cluster structure (ie user v j A set of very likely potential parent users), a ij represents the potential edge (v i ,v j ) on the microblog propagation rate (the default value is 1 during deduction), Indicates that in the propagation data of the kth observation, the potential edge (v i ,v j ) on the propagation likelihood.

[0092] Figure 2 The diagram shows the problem that the first normalization in the step of constructing clustering indexes in the present invention aims to solve (i.e., the problem of ignoring the influence of other nodes in the propagation process). Based on the receiving time of the node, from these three cascades, we can preliminarily deduce that (v i ,v j )、(v i ,v k ) and (v k ,v j ) these three potential transmission edges. Among them, the potential edge (v i ,v j ) appears in three cascades, and the reception time differences between the two nodes are 4, 6, and 4 respectively. According to the propagation time model in Table 2, the smaller the reception time difference of the nodes, the greater the propagation possibility between the two nodes. Therefore, in the k1 and k3 cascades, the potential edge (v i ,v j ) is equal to and greater than the propagation possibility in the k2th cascade. From the propagation data of the third cascade, we see that node vk and node v i The receiving time difference between nodes is less than j and node v i Therefore, in the k3th propagation cascade, the potential edge (v i ,v k ) is more likely to spread on the potential edge (v i ,v j ) on the transmission possibility. It can be seen that in these three cascades, even if the potential edge (v i ,v j ) has the same time difference between the two nodes at both ends of the first and third cascades, and they play different roles in the propagation of the two cascades. Obviously, the potential edge (v i ,v j ) plays a slightly larger role in the first cascade than in the third cascade. To this end, we propose a new method for calculating propagation likelihood, namely normalized propagation likelihood, which takes into account the influence of other nodes in the same propagation process (the calculation formula is shown in formula (2) fs(v i ,v j ), can well distinguish the role of potential edges in different cascades. In this example, the potential edge (v i ,v j ) The normalized propagation likelihood in the third cascade is equal to where f ij (4) represents the potential edge (v) calculated according to a transmission time model in Table 2 i ,v j ) on the propagation likelihood, f ik (2) represents the potential edge (v) calculated based on the same transmission time model in Table 2 i ,v k ). The potential edges (v i ,v j ) is 1, because in these two propagation processes, the node v is not observed. i By spreading information to other nodes, their role in these two cascades is to completely facilitate the generation of these two cascades, and their role is 100%.

[0093] Figure 3 The figure shows a diagram of a cascade of multiple propagation spanning trees in a specific embodiment of the present invention. Assume that in subgraph (a) there is a given network G *On the network G, we observe a cascade c = {(v0, t0), (v1, t1), (v2, t2), (v3, t3), (v4, t4)}. Assuming that the information propagates like a tree, in this given network G * All the possible propagation spanning trees that can generate this cascade are T1, T2, T3, and T4 in subgraph (b). Take T1 as an example to explain why tree T1 can generate cascade c. Because the receiving time of node v0 is less than that of node v1 and node v2, it can be preliminarily inferred that it is possible that node v0 spread the information to node v1 and node v2, and the receiving time of node v2 is closest to node v3 and earlier than that of node v3, so it can be preliminarily inferred that it is possible that node v2 spread the information to node v3, and although the receiving time of node v3 is closest to node v4 and earlier than that of node v4, in the given network G * In the figure, node v3 has no edge pointing to node v4, so it is unlikely that node v3 propagated information to node v4, and the receiving time of node v2 is the second closest to node v4 and earlier than node v4. Then node v2 has an edge pointing to node v4, so the preliminary inference is that node v2 may have propagated information to node v4, thus obtaining the propagation tree T1 that can generate the cascade.

[0094] Figure 4The complete diagram of the information propagation network deduction method based on clustering fast deduction and submodule maximization provided by an embodiment of the present invention is shown. Specifically, the execution process of the present invention can be divided into four modules: (a) inputting the cascade data observed after the propagation of multiple pieces of information on a potential network and the number of network edges K required to be deduced, each cascade consists of the nodes that propagate information and the time when it propagates information (this step includes the construction of the data model, that is, the set composed of multiple pieces of propagation data is abstracted as a set composed of multiple information cascades, the users of the propagation information in each cascade are abstracted as nodes in the information propagation network to be deduced, the time when the users in each cascade propagate information is abstracted as the receiving time of the nodes, the propagation relationships between users are abstracted as propagation edges in the information propagation network to be deduced, and the number of propagation relationships between users required to be deduced is abstracted as the number of propagation edges to be deduced), (b) clustering fast deduction, which is an effective preprocessing method provided by the patent of the present invention. As shown in the figure, all possible initial potential edges are first constructed based on the input cascade data, specifically the node's reception time. Then, all initial potential edges are clustered based on a carefully designed clustering index value that integrates the node's reception time and reception status. Effective or very likely potential edges are deduced for this purpose. These effective potential edges are specifically screened using a threshold—the average value of the smaller clustered value. Finally, based on the deduced effective potential edges, the cluster structure of each node is captured. This module preprocesses a large number of initial potential edges, removing a large number of invalid potential edges while efficiently obtaining the most likely potential parent node set for each node, saving a significant amount of time for subsequent algorithms. (c) Submodule maximization deduction: This module improves the efficiency of network deduction without compromising the accuracy of network deduction by integrating the node cluster structure obtained in module (b) into a submodule function. First, the likelihood function of the cascade data input in module (a) is solved based on the matrix tree theorem and converted into an objective function equivalent to the network inference problem. Then, the node cluster structure obtained in module (b) is integrated into this submodular objective function. Finally, a greedy algorithm is used to iteratively deduce the final propagation edges. (d) The output is a network containing K edges derived from the deduction. In the figure, the black solid line edge (i) represents the correctly deduced propagation edge, the black dashed line edge (ii) represents the undeduced propagation edge, and the black dotted line edge (iii) represents the incorrectly deduced propagation edge. Table 1 shows the size of the test dataset.

[0095] Table 1

[0096]

[0097]

[0098] Table 1 shows the network datasets containing the observed cascade data used in the test. The number of cascades observed in each network dataset under the three different transmission time models listed in Table 2 is 200. The first three networks (G1, G2, and G3) are generated by the well-known social network model, the Kronecker graph model. The last two networks (G4 and G5) are real networks, with G4 being a blog network and G5 being a friend relationship network.

[0099] Table 2 shows three common distributions of node reception times in the tested cascade data;

[0100] Table 2

[0101]

[0102] Table 2 shows the sampled distributions or distributions satisfied by the positive reception time difference between any two nodes during the propagation process. Three common classical distributions are shown in Table 2: exponential distribution, power-law distribution, and Rayleigh distribution. The first two are applicable to information propagation, while the latter is applicable to disease transmission.

[0103] Table 3 Comparison of the inference accuracy of various methods on the three artificial datasets (G1, G2 and G3) and two real datasets (G4, G5) in Table 1.

[0104] Table 3

[0105]

[0106] Table 3 compares the network inference accuracy of various comparison methods and the method proposed in this invention on the five datasets containing artificial and real networks in Table 1 (and the three transmission time distribution combinations in Table 2). The inference results are primarily evaluated using the F-Score (the harmonic mean of precision and recall). The bolded items in each row indicate that the method performed best on the corresponding dataset. This shows that the method proposed in this invention outperforms other methods in terms of network inference accuracy in most cases.

[0107] Table 4 Comparison of running time (unit: minutes m + seconds s) of various methods on the three artificial datasets (G1, G2 and G3) and two real datasets (G4, G5) in Table 1.

[0108] Table 4

[0109]

[0110]

[0111] Table 4 shows a comparison of the network deduction algorithm running time of various comparison methods and the method proposed in the present invention on the five data sets containing artificial networks and real networks in Table 1 (and the three transmission time distributions in Table 2). The running time units include minutes and seconds. The bold items in each row indicate that the method has the shortest running time on the data set in the corresponding row, that is, it runs the fastest. The items with an * symbol in the upper right corner indicate that the method has the second shortest running time on the data set in the corresponding row, that is, it runs the second fastest. It can be seen from this that the method proposed in the present invention is second only to the Dani method in terms of network deduction efficiency in most cases, but is better than the remaining methods. Nevertheless, it can be seen from Table 3 that the deduction accuracy of the Dani method is not optimal in most cases, while the method proposed in the present invention is the optimal.

[0112] In summary, the present invention relates to an information propagation network deduction method based on cluster rapid deduction and submodule maximization, which can improve the execution efficiency of the deduction module without affecting the submodule properties of the submodule maximization module through an effective preprocessing method of the cluster rapid deduction module. It can also achieve higher accuracy and shorter running time when the observed cascade data is small. In addition, the present invention utilizes the independent cascade model that has been widely used in the medical field from the beginning to study the spread of information. Therefore, research in fields such as infectious diseases can also refer to and draw lessons from the method proposed by the present invention.

[0113] The above description is merely a preferred embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. An information propagation network deduction method based on clustering rapid deduction and submodule maximization, characterized by: The following steps are involved: A data model is constructed based on the collected propagation time data and the number of propagation relationships between users to be deduced. Abstraction is performed based on the data model to obtain an information cascade set in the field of network propagation dynamics, nodes in the information propagation network to be deduced, the number of propagation edges in the information propagation network to be deduced, the reception time of the node, and the reception status of the node; According to the reception time of the node, all potential edges are constructed in the information cascade set, a clustering index is constructed that integrates the reception time and reception state of the node, and the clustering index value of each potential edge is calculated; Clustering the clustering index value of each potential edge using a 2-means clustering algorithm to obtain a clustering result, and obtaining a threshold for screening the clustering index value of each potential edge according to the clustering result; Comparing the clustering index value of each potential edge with the threshold, deducing a valid potential edge, and obtaining a cluster structure of nodes according to the valid potential edge; According to the information cascade set and information propagation, the likelihood function of the observation cascade is constructed in a tree-like manner; the cluster structure of the node is integrated into the likelihood function of the observation cascade, and a greedy algorithm is used to iteratively deduce a number of propagation edges to complete the propagation network deduction.

2. The information propagation network deduction method based on clustering rapid deduction and submodule maximization according to claim 1, characterized in that: The data model is constructed based on the collected propagation time data and the number of propagation relationships between users to be deduced. Specifically, the following steps are involved: A sequence consisting of each user and the time at which each user spreads information is abstracted as an information cascade, and a set consisting of multiple pieces of spread data is converted into an information cascade set; Each cascade c k Node v in i Abstraction is the node in the information dissemination network to be deduced; The communication relationship between users, in which users spread information to each other, is abstracted as the communication edge in the information communication network to be deduced; Each cascade c k User v in i Time to disseminate information Abstracted as the receiving time of the node, each cascade c k User v in i The state of whether the information is propagated is abstracted as the node's receiving state X i .

3. The information propagation network deduction method based on clustering rapid deduction and submodule maximization according to claim 1, characterized in that: According to the reception time of the node, all potential edges are constructed in the information cascade set, specifically including: According to the reception time of the node, all potential edges are constructed based on the information cascade set; In each observed information cascade, if any node v i The receiving time of any node v is less than j The receiving time of the node pair (v i ,v j ) is derived as a potential edge or a node v i There is a directed edge pointing to node v j .

4. The information propagation network deduction method based on clustering rapid deduction and submodule maximization according to claim 1, characterized in that: Construct a clustering index that integrates the receiving time and receiving status of the node, specifically including: Calculating the final propagation likelihood on the potential edge and the positive correlation between the receiving states of the two nodes on the potential edge using the receiving time and receiving state of the node respectively; The clustering index is constructed by utilizing the multiplication principle and fusing the implicit information of the receiving time and receiving state of the nodes.

5. The information propagation network deduction method based on clustering rapid deduction and submodule maximization according to claim 1, characterized in that: Obtaining a threshold for screening the clustering index value of each potential edge according to the clustering result, specifically including: After performing 2-means clustering on the clustering index values ​​of all potential edges, the potential edges are divided into two categories according to the index values, including a category with a large clustering index value and a category with a small clustering index value, wherein the minimum value of the category with a large clustering index value is greater than the maximum value of the category with a small clustering index value; The clustering index values ​​of a class with a smaller clustering index value are calculated to obtain an average value, which is used as a threshold.

6. The information propagation network deduction method based on clustering rapid deduction and submodule maximization according to claim 1, characterized in that: The likelihood function of the observation cascade is constructed in a tree-like manner according to the information cascade set and information propagation, specifically including: Based on information cascade collection and information propagation, the probability distribution of cascade data is observed on a potential network in a tree-like manner.

7. The information propagation network deduction method based on clustering rapid deduction and submodule maximization according to claim 6, characterized in that: The likelihood function of the observation cascade is expressed as: Among them, c k represents the kth cascade data, C represents the set of all cascade data, G * represents the potential unknown propagation network, f(c k |G * ) represents the likelihood function of the k-th observation cascade.

8. The information propagation network deduction method based on clustering rapid deduction and submodule maximization according to claim 1, characterized in that: The method of integrating the cluster structure of the nodes into the likelihood function of the observation cascade is: in, Corresponding to the k-th observed node v i and propagation time The sequence data composed of Indicates the kth cascade data c k Midpoint v i The receiving time, Indicates the kth cascade data c k Midpoint v j The receiving time, G * represents a potentially unknown propagation network, CS j Represents node v j The cluster structure of a ij represents the potential edge (v i ,v j ) on the information transmission rate, Indicates that in the propagation data of the kth observation, the potential edge (v i ,v j ) on the likelihood of propagation.

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