User location inference method and system based on loop coupling

By building a user social relationship diagram on a social media platform and performing cyclical iterative updates in the graph, the correlation and integration of user text information and network information is achieved, solving the problems of low accuracy and coverage of position in the existing technology, and improving the effect of user location inference.

CN114819157BActive Publication Date: 2025-03-25Chinese People's Liberation Army Cyberspace Force Information Engineering University
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Patent Information

Application Number
CN202210259419.3
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-03-16
Publication Date
2025-03-25
Estimated Expiration
2042-03-16

AI Technical Summary

Technical Problem

When the existing social media user location inference method integrates user text information and network information, it lacks the mining of the characteristics of social relationships itself, resulting in low accuracy and coverage of location inference.

Method used

A user position inference method based on circular coupling is proposed. By constructing a user social relationship diagram, the user's initial attribute value is calculated, and the social diagram is updated cyclically iteratively, so as to realize the correlation and fusion of user text information and network information.

Benefits of technology

By mining the structural characteristics of the user's social relationship diagram, the accuracy and coverage of user position inference are improved, and the error of position inference is reduced.

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Abstract

The present invention discloses a method and system for user location inference based on cyclic coupling. The method first constructs a collapsed network according to the user's mention relationship to reduce the number of isolated nodes; then assigns two attributes to each user, and calculates the structural features of the user in the social network graph based on graph theory, and calculates the user's text features according to the user's generated text as the iterative initial value of the user attribute; in the user's social graph, the two attributes are cyclically cross-iterated to achieve information association fusion through mutual enhancement; finally, the most likely location is inferred according to the user's attribute value in the network convergence state. On a public data set, the experimental results of the proposed method and four existing algorithms show that the city-level location inference accuracy of the proposed method is 37%, and the accuracy@161 is 64%, which are 6%, 3%, 6%, and 2% higher than the existing methods, respectively, and the average error and median error are also better than the existing methods.
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Description

Technical Field

[0001] The present invention belongs to the technical field of social media user location inference, and in particular relates to a user location inference method and system based on cyclic coupling. Background Art

[0002] With the popularity of mobile Internet and the growing number of social media users, social media data has become a focus of the data analysis industry. Among them, geographic location information can map data in the virtual network to the real world. Social media user location inference can provide key information for disaster monitoring, disease transmission control, political analysis, regional analysis of social behavior, and precise advertising, which is of great practical significance.

[0003] The earliest work was to infer the user's location through information such as the user's IP address and GPS. However, this information is difficult to obtain and involves user privacy issues. Later, a large number of scholars and literature analyzed the user's geographic location from public data on social media platforms. There are currently many studies on user location inference on social platforms such as Facebook, foursquare, Twitter, and Flickr. Among them, Twitter is often used in user location inference research, which is determined by the characteristics of the Twitter platform: on the one hand, Twitter users can fill in their home location when registering an account, and can add geotags when posting tweets. This information can be used as GroundTruth to help evaluate the effectiveness of location inference research; on the other hand, Twitter contains a lot of information that can be used to infer the user's location, such as the user's tweet text, the interaction relationship between users, timestamps, time zones, and participating topics.

[0004] However, due to the increasing awareness of privacy protection, location data is very sparse in the massive social media data. Cheng et al. found that only 26% of Twitter users filled in the city-level location in their profiles, and only 0.42% of tweets were geotagged with GPS; Ryoo et al. reported that only 34% of Twitter users filled in meaningful location information in their profiles, and less than 1% of tweets were attached with GPS location tags.

[0005] Existing methods for inferring the location of social media users can be divided into three categories: text-based location inference methods, network-based location inference methods, and location inference methods based on the fusion of multiple data sources. Users can mention geographical location nouns around them in their tweets; tweets from users in different regions also have great differences in terms of content and word usage habits; therefore, text-based methods use the probability distribution of words in different locations to infer the user's location. In addition to user-generated text, another major behavior of users on social media platforms is to interact with other users, including following, mentioning, liking, commenting, and forwarding. Network-based methods believe that friends with closer relationships on social media platforms are closer in the real world, and thus infer the user's location based on the location of the user's friends. Methods based on the fusion of multiple data sources combine multiple data such as user text information, social relationships, and metadata (such as time zone, topic, timestamp, etc.) to infer the user's location. However, due to the influence of factors such as noisy text content and ambiguous geographical location in social network data, it is quite difficult to achieve key technologies such as accurate location indicator word extraction, user social feature characterization, and potential correlation mining of multi-source information, resulting in low accuracy and coverage of existing methods.

[0006] The text-based method takes into account the differences in the statistical distribution of words in different geographical locations and can solve the problem of location inference for isolated users. However, the location indicators extracted by the existing methods are still mixed with non-location indicators that have similar distribution characteristics to the location indicators, resulting in a large amount of noise in the selected text features, which interferes with the user location inference effect.

[0007] Network-based methods use the interaction between users to calculate the similarity of users, but lack the ability to infer the location of isolated users without neighboring nodes. In addition, most of these algorithms do not fully analyze the second-order social relationships of users, resulting in inaccurate characterization of user social characteristics, affecting the accuracy of user location inference.

[0008] Methods based on multi-source data fusion integrate multiple information such as text, network, and metadata, improving the effect of location inference. However, such methods usually extract user text and location features from the network sequentially for fusion, without fully exploring the potential location correlation between different data sources. In addition, existing methods do not consider the structure of user social relationships themselves, which affects the accuracy and coverage of user location inference. Summary of the invention

[0009] In view of the problem that existing social media user location inference methods often fuse user text information and network information by transmitting user text features in social graphs, lack of mining the characteristics of social relationships themselves, and affecting the accuracy of location inference, the present invention proposes a user location inference method and system based on circular coupling.

[0010] In order to achieve the above object, the present invention adopts the following technical solutions:

[0011] On one hand, the present invention proposes a user location inference method based on cyclic coupling, comprising:

[0012] Step 1: Build a user social relationship graph; including:

[0013] First, extract the @ relationship from the user's historical blog text and construct the user mention relationship graph G0, which includes the marked user V L , Unmarked user V U and other users V O ; Then, V O The number of neighbors in exceeds f c Celebrity users are directly removed from graph G0; finally, V O The marked users and unmarked users connected to the remaining users in G0 are directly connected, and all other users V in G0 are removed. O , get the collapsed mention relationship graph G′0 as the user’s social relationship graph G=G′0;

[0014] Step 2: Calculate the initial attribute values ​​of the user, the initial attribute values ​​including the initial locality value and the initial aggregation value; including:

[0015] For a labeled user v∈V L , the initial locality value and the initial clustering value are determined by their true location L v Decision; and for unlabeled user v∈V U , at each candidate position L x ∈L, L is the candidate position set, based on the user's historical blog text T v And the user mention relationship subgraph of that location Calculate the user's initial locality value and initial aggregation value;

[0016] Step 3: Iteratively update user attribute values ​​based on the social graph; including:

[0017] At each candidate position L x ∈L, use the initial attribute value of the user at that position respectively, and iterate in the social relationship graph G until the network converges; in each round of iteration, cross-update the two attribute values ​​of the unmarked users in the graph according to the attribute information of the user's neighbors, and perform normalization;

[0018] Step 4: Infer user location; including:

[0019] When the network iterations in all candidate regions have reached convergence, for each unlabeled user v∈V U , and place it at each candidate position Lx ∈L, and the candidate location with the highest user locality value is taken as the user's inferred location

[0020] Furthermore, in step 2, the initial locality value and aggregation value of the marked user are calculated as follows:

[0021] First, the set of labeled users V L Divide the user into multiple subsets according to their actual location, as shown in formula (1):

[0022]

[0023] Among them, L x ∈L represents the candidate position, Indicates that the real position is at L x The set of tagged users;

[0024] Then, at each candidate position L x ∈L, respectively for all labeled users v∈V L Assign initial locality and clustering values, if the marked user v is located at the candidate location L x , then the user is placed at the candidate location L x The initial attribute values ​​of are all set to 1; otherwise, they are all set to 0, as shown in formula (2) and formula (3):

[0025]

[0026]

[0027] in, Indicates that user v is at candidate location L x The initial locality value of Indicates that user v is at candidate location L x The initial aggregation value of .

[0028] Furthermore, in step 2, the initial locality value of the unlabeled user is calculated as follows:

[0029] At each candidate position L x ∈L, according to the unlabeled user v∈V U Historical blog text of T v , calculate the probability that the user is located at the candidate location according to the following formula as its initial locality value;

[0030]

[0031] in, Indicates that user v is at candidate location L xThe initial locality value of card() is the number of elements in the collection, T v is all the historical tweets of user v, card(T v ) is the number of tweets posted by the user, T′ v ={t i |t i ∈T v and t i is in L x} is the user in L x A collection of tweets that were published.

[0032] Furthermore, in step 2, the initial aggregation value of the unlabeled user is calculated as follows:

[0033] Based on the user social relationship graph G, for each candidate location L, x ∈L generates a social relationship subgraph, denoted as The real position is not in L x The marked users are removed from the graph G, and only the real location is kept in L x Tagged users and all unlabeled users V U , the obtained subgraph is the position L x User social relationship subgraph

[0034] Then in the subgraph Based on graph theory, the local clustering coefficient CC of all nodes is calculated, that is, the closeness of the neighbor relationship around the user. The clustering coefficient of the unlabeled user is the initial clustering value of the user. The user v is at the candidate position L x The initial aggregation value of is shown in formula (4):

[0035]

[0036] in, Indicates that user v is at candidate location L x The initial aggregation value of Indicates that user v is at candidate location L x The local clustering coefficient, N v is the first-order neighbor set of user v, represents the set of edges between the first-order neighbors of user v.

[0037] Furthermore, the step 3 comprises:

[0038] During the iteration process, the two attribute values ​​of the marked users remain unchanged. For unmarked users, the attribute information of their neighbors is cross-aggregated in each iteration;

[0039] In the nth iteration, the unlabeled user v∈V U The locality value of is updated to the sum of the aggregation values ​​of all the first-order neighbors of the user, as shown in formula (6); the aggregation value of the user is updated to the sum of the locality values ​​of all the first-order neighbors of the user, as shown in formula (7):

[0040]

[0041]

[0042] Among them, N v represents the first-order user neighbor set of user v; and Respectively represent the candidate positions L x In the network cycle iteration, the locality value and aggregation value of user v in the nth iteration;

[0043] The normalization formula is as follows:

[0044]

[0045]

[0046] At each candidate position L x , and iterate according to the above formulas until the sum of the changes in the attribute values ​​of all nodes is less than the set threshold, or the number of iterations reaches the maximum number of rounds, as shown in formula (11). At this time, it is determined that the network iteration converges and the loop ends:

[0047] Loop termination condition: Δ n <f Δ or n>f max (11)

[0048] Among them, f Δ is the set change value threshold, f max is the maximum number of iterations set, Δ n is the sum of the attribute value changes of all nodes in round n, as shown in formula (12):

[0049]

[0050] Another aspect of the present invention provides a user location inference system based on loop coupling, comprising:

[0051] The social relationship graph construction module is used to construct the user social relationship graph; it includes:

[0052] First, extract the @ relationship from the user's historical blog text and construct the user mention relationship graph G0, which includes the marked user V L , Unmarked user V Uand other users V O ; Then, V O The number of neighbors in exceeds f c Celebrity users are directly removed from graph G0; finally, V O The marked users and unmarked users connected to the remaining users in G0 are directly connected, and all other users V in G0 are removed. O , get the collapsed mention relationship graph G′0 as the user’s social relationship graph G=G′0;

[0053] The initial attribute value calculation module is used to calculate the initial attribute value of the user, wherein the initial attribute value includes an initial locality value and an initial aggregation value; and comprises:

[0054] For a labeled user v∈V L , the initial locality value and the initial clustering value are determined by their true location L v Decision; and for unlabeled user v∈V U , at each candidate position L x ∈L, L is the candidate position set, based on the user's historical blog text T v And the user mention relationship subgraph of that location Calculate the user's initial locality value and initial aggregation value;

[0055] The loop iteration module is used to update the user attribute value based on the social graph loop iteration; including:

[0056] At each candidate position L x ∈L, use the initial attribute value of the user at that position respectively, and iterate in the social relationship graph G until the network converges; in each round of iteration, cross-update the two attribute values ​​of the unmarked users in the graph according to the attribute information of the user's neighbors, and perform normalization;

[0057] The user location inference module is used to infer the user location; it includes:

[0058] When the network iterations in all candidate regions have reached convergence, for each unlabeled user v∈V U , and place it at each candidate position L x ∈L, and the candidate location with the highest user locality value is taken as the user's inferred location

[0059] Furthermore, in the initial attribute value calculation module, the initial locality value and aggregation value of the marked user are calculated as follows:

[0060] First, the set of labeled users V L Divide the user into multiple subsets according to their actual location, as shown in formula (1):

[0061]

[0062] Among them, L x ∈L represents the candidate position, Indicates that the real position is at L x The set of tagged users;

[0063] Then, at each candidate position L x ∈L, respectively for all labeled users v∈V L Assign initial locality and clustering values, if the marked user v is located at the candidate location L x , then the user is placed at the candidate location L x The initial attribute values ​​of are all set to 1; otherwise, they are all set to 0, as shown in formula (2) and formula (3):

[0064]

[0065]

[0066] in, Indicates that user v is at candidate location L x The initial locality value of Indicates that user v is at candidate location L x The initial aggregation value of .

[0067] Furthermore, in the initial attribute value calculation module, the initial locality value of the unlabeled user is calculated as follows:

[0068] At each candidate position L x ∈L, according to the unlabeled user v∈V U Historical blog text of T v , calculate the probability that the user is located at the candidate location according to the following formula as its initial locality value;

[0069]

[0070] in, Indicates that user v is at candidate location L x The initial locality value of card() is the number of elements in the collection, T v is all the historical tweets of user v, card(T v ) is the number of tweets posted by the user, T′ v ={t i |t i ∈T v and t i is in L x} is the user in L x A collection of tweets that were published.

[0071] Furthermore, in the initial attribute value calculation module, the initial aggregation value of the unlabeled user is calculated as follows:

[0072] Based on the user social relationship graph G, for each candidate location L, x ∈L generates a social relationship subgraph, denoted as The real position is not in L x The marked users are removed from the graph G, and only the real location is kept in L x Tagged users and all untagged users V U , the obtained subgraph is the position L x User social relationship subgraph

[0073] Then in the subgraph Based on graph theory, the local clustering coefficient CC of all nodes is calculated, that is, the closeness of the neighbor relationship around the user. The clustering coefficient of the unlabeled user is the initial clustering value of the user. The user v is at the candidate position L x The initial aggregation value of is shown in formula (4):

[0074]

[0075] in, Indicates that user v is at candidate location L x The initial aggregation value of Indicates that user v is at candidate location L x The local clustering coefficient, N v is the first-order neighbor set of user v, represents the set of edges between the first-order neighbors of user v.

[0076] Furthermore, the loop iteration module is specifically used for:

[0077] During the iteration process, the two attribute values ​​of the marked users remain unchanged. For unmarked users, the attribute information of their neighbors is cross-aggregated in each iteration;

[0078] In the nth iteration, the unlabeled user v∈V U The locality value of is updated to the sum of the aggregation values ​​of all the first-order neighbors of the user, as shown in formula (6); the aggregation value of the user is updated to the sum of the locality values ​​of all the first-order neighbors of the user, as shown in formula (7):

[0079]

[0080]

[0081] Among them, N v represents the first-order user neighbor set of user v; and Respectively represent the candidate positions L x In the network cycle iteration, the locality value and aggregation value of user v in the nth iteration;

[0082] The normalization formula is as follows:

[0083]

[0084]

[0085] At each candidate position L x , and iterate according to the above formulas until the sum of the changes in the attribute values ​​of all nodes is less than the set threshold, or the number of iterations reaches the maximum number of rounds, as shown in formula (11). At this time, it is determined that the network iteration converges and the loop ends:

[0086] Loop termination condition: Δ n <f Δ orn>f max (11)

[0087] Among them, f Δ is the set change value threshold, f max is the maximum number of iterations set, Δ n is the sum of the attribute value changes of all nodes in round n, as shown in formula (12):

[0088]

[0089] Compared with the prior art, the present invention has the following beneficial effects:

[0090] (1) A universal feature for measuring the association between users and locations is proposed: clustering. Starting from the structural characteristics of the user social relationship network itself, the clustering coefficient of the target user in the social graph composed of users with known locations is calculated based on graph theory. This can more directly mine the location information hidden in the social relationship and improve the accuracy of user location inference.

[0091] (2) A user location inference method and system based on cyclic coupling is proposed. The two attributes of the user are given iterative initial values ​​based on the user's text features and network features, and the two attributes are cyclically cross-iterated in the social graph to achieve the association and fusion of user text information and network information, thereby reducing the error of user location inference. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1This is an algorithm framework diagram of a user location inference method based on cyclic coupling according to an embodiment of the present invention;

[0093] Figure 2 A schematic diagram of a calculation process of an iterative initial value of a user attribute according to an embodiment of the present invention;

[0094] Figure 3 This is an example diagram of cross-iterative updating of user attribute values ​​according to an embodiment of the present invention;

[0095] Figure 4 The user location distribution and statistics of the GeoText dataset in the embodiment of the present invention;

[0096] Figure 5 The influence of the number of iterations on the position inference result in the embodiment of the present invention;

[0097] Figure 6 The present invention is a schematic diagram of the architecture of a user location inference system based on loop coupling according to an embodiment of the present invention. DETAILED DESCRIPTION

[0098] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:

[0099] In order to facilitate reading and understanding of the method proposed in the present invention, some symbols and definitions used as well as the problems to be solved are described as follows.

[0100] Definition 1: User social relationship graph. The user social relationship graph is represented as G = (V, E). Where V is the set of user nodes, and V = V L ∪V U ; V L represents the set of users whose locations are known, called marked nodes; V U represents a set of users whose locations are unknown, called unlabeled nodes. E is a set of undirected edges in the graph. i ,v j The edge between ∈V is denoted as e(v i ,v j ).

[0101] Definition 2: First-order neighbors. For a user v∈V, its first-order neighbors are represented as N v The first-order neighbors of a user refer to the set of users directly connected to the user in the social graph G, that is, N v = {v j |v j ∈V and e(v,v j )∈E}.

[0102] Definition 3: Candidate positions. The candidate position set is represented as L = {L1, L2, ..., L |L|}. The candidate location is determined by the specified location inference granularity, which can be province, city or grid. For user v∈V U , and its true position is represented by L v , the inferred position is expressed as

[0103] Definition 4: User text. For a user v∈V, the user text is represented as T v ={t1, t2, ...}. User text refers to the set of historical blog posts published by the user, t i ∈T v Represents a single historical blog post text.

[0104] User location inference problem: For each user v∈V, given a set of historical texts T published by user v v , which contains the user's mention relationship; given the candidate location set L, and all the marked users V L The real geographic location of the unlabeled user v∈V U Calculate the L at each candidate position x ∈L, inferring the most likely location of user v

[0105] The symbols used in the present invention are shown in Table 1.

[0106] Table 1 Symbols

[0107]

[0108] The present invention proposes a user location inference method based on cyclic coupling, the framework is as follows Figure 1 As shown. The method constructs a user collapsed mention graph, and assigns iterative initial values ​​to the two attributes of the user according to the user's generated text and mention relationship network; then the two attributes are cyclically cross-iterated in the social relationship graph until the network converges, and finally the candidate position with the highest user attribute value is selected as the inference result. The main steps of the present invention are as follows:

[0109] Step 1: Build a user social relationship graph

[0110] First, extract the @ relationship from the user's historical blog text and construct the user mention relationship graph G0. Because there are many users who do not belong to V among the mentioned users, G0 contains all the users except the marked user V. L and unlabeled user V U , and some other user nodes, denoted as V O Then, V O The number of neighbors in exceeds f c Celebrity users are directly removed from graph G0. Finally, V OThe marked users and unmarked users connected to the remaining users in G0 are directly connected, and all other users V in G0 are removed. O , and obtain the collapsed mention relationship graph G′0 as the user’s social relationship graph G=G′0.

[0111] Step 2: Calculate the initial value of user attribute iteration

[0112] Each user is assigned two attribute values: locality and cluster. L , the local initial value and the clustered iterative initial value are determined by their true location L v Decision; and for unlabeled user v∈V U , at each candidate position L x ∈L, based on the user's historical blog text T v And the user mention relationship subgraph of that location Calculate the initial locality and aggregation values ​​for the user.

[0113] Step 3: Update user attribute values ​​based on the social graph loop

[0114] At each candidate position L x ∈L, use the initial value of the user attribute at that position respectively, and iterate in the social relationship graph G until the network converges. In each iteration, the two attribute values ​​of the unlabeled users in the graph are cross-updated according to the attribute information of the user's neighbors, and normalized.

[0115] Step 4: Infer user location

[0116] When the network iterations in all candidate regions have reached convergence, for each unlabeled user v∈V U , and place it at each candidate position L x ∈L, and the candidate location with the highest user locality value is taken as the user's inferred location

[0117] In the above steps, step 2 "calculating the initial value of the user attribute iteration" and step 3 "iteratively updating the user attribute value based on the social graph" are the key links of the algorithm. The following is a detailed explanation of these two steps.

[0118] (I) Calculate the user's initial score

[0119] In the social relationship graph G, each user has two attributes, namely locality and cluster.

[0120] · Locality of the user at the candidate location: Use the location information in the user's text to characterize the possibility that the user is located at the candidate location. The larger the locality value of a user at a candidate location, the more relevant the text posted by the user is to the location, and the more likely the user is to be located at this candidate location.

[0121] Clustering of users at candidate locations: Use the structural information of user social relationships to characterize the possibility of users being located at candidate locations. The larger the cluster value of a user at a candidate location, the closer the relationship between the user and the tagged users at the candidate location, and the more reasonable it is for the user to receive location information from the tagged users at the location.

[0122] The calculation method of the iterative initial values ​​of the two attributes of the user is as follows Figure 2 shown.

[0123] (1) Calculate the initial locality and aggregation values ​​of the marked users

[0124] First, the set of labeled users V L Divide the user into multiple subsets according to their actual location, as shown in formula (1):

[0125]

[0126] Among them, L x ∈L represents the candidate position, Indicates that the real position is at L x The collection of tagged users.

[0127] Then, at each candidate position L x ∈L, respectively for all labeled users v∈V L Assign initial values ​​to locality and aggregation. If the marked user v is located in this candidate location (city), the initial attribute values ​​of the user in this candidate location are all set to 1; otherwise, they are all set to 0, as shown in formula (2) and formula (3).

[0128]

[0129]

[0130] in, Indicates that user v is at candidate location L x The initial locality value of (initial locality value), Indicates that user v is at candidate location L x The initial aggregation value (initial aggregation value) of .

[0131] (2) Calculate the initial locality value of unlabeled users

[0132] At each candidate position Lx ∈L, according to the unlabeled user v∈V U Historical blog text of T v , calculate the probability that the user is located at the candidate location as its initial locality value.

[0133] The present invention uses local text probability to characterize the location of user v at the candidate location L x The local text probability is defined as the percentage of the latest tweets posted by the user that are located in the candidate area. x The local initial value of is shown in formula (4):

[0134]

[0135] Among them, card() is the number of elements in the set, T v is all the historical tweets of user v, card(T v ) is the number of tweets posted by the user, T′ v ={t i |t i ∈T v and t i is in L x} is the user in L x A collection of tweets that were published.

[0136] (3) Calculate the initial aggregation value of unlabeled users

[0137] At each candidate position L x ∈L, calculate the unlabeled user v∈V according to the mention relationship between users U With known users at this location The probability of the same position is used as the initial value of its clustering.

[0138] In step 1, the user social relationship graph G is constructed. On this basis, for each candidate location L x ∈L generates a social relationship subgraph, denoted as The real position is not in L x The marked users are removed from the graph G, and only the real location is kept in L x Tagged users and all untagged users V U , the obtained subgraph is the position L x The user social relationship subgraph.

[0139] Then in the subgraph Based on graph theory, the local clustering coefficient CC (Clustering Coefficient) of all nodes is calculated, that is, the closeness of the neighbor relationship around the user. The clustering coefficient of the unlabeled user is the initial value of the user's clustering. x The initial value of aggregation is shown in formula (4):

[0140]

[0141] Among them, N v is the first-order neighbor set of user v, represents the set of edges between the first-order neighbors of user v.

[0142] (II) Iteratively updating user attribute values ​​based on social graph

[0143] After obtaining the initial attribute values ​​of all users at all candidate locations, the user attribute values ​​are iterated in a loop in the social relationship graph G for each candidate location, and the locality and aggregation values ​​of the users are updated until the network reaches a convergence state.

[0144] (1) Cross-update of user attribute values

[0145] Since the relationship between the marked users and the candidate locations is fixed, the two attribute values ​​of the marked users remain unchanged during the iteration process. For the unmarked users, the attribute information of their neighbors is cross-aggregated in each iteration.

[0146] In the nth iteration, the unlabeled user v∈V U The locality value of the user is updated to the sum of the cluster values ​​of all the user's first-order neighbors, as shown in formula (6); the cluster value of the user is updated to the sum of the locality values ​​of all the user's first-order neighbors, as shown in formula (7).

[0147]

[0148]

[0149] Among them, N v represents the first-order user neighbor set of user v; and Respectively represent the candidate positions L x In the network cycle iteration, the locality value and aggregation value of user v in the nth iteration.

[0150] For ease of understanding, the present invention is described in detail in Figure 3 The example describes the iteration process of user attributes. Figure 3(a) is the user social relationship graph G, and the blue labels in G are the attribute values ​​of all users at the candidate position L1 in this round. In the next round of iteration, the attribute value update of the unlabeled user v9 is as follows Figure 3 As shown in (b).

[0151]

[0152] The normalized formula is as follows:

[0153]

[0154]

[0155] (2) Judgment conditions for network iteration convergence

[0156] At each candidate position L x , and iterate according to the above formulas until the sum of the changes in the attribute values ​​of all nodes is less than the set threshold, or the number of iterations reaches the maximum number of rounds. As shown in formula (11). At this time, it is determined that the network iteration has converged and the loop ends.

[0157] Loop termination condition: Δ n <f Δ or n>f max (11)

[0158] Among them, f Δ is the set change value threshold, f max is the maximum number of iterations set, Δ n is the sum of the attribute value changes of all nodes in the nth round, as shown in formula (12).

[0159]

[0160] After the cross-update of the user attribute values, the user location is inferred:

[0161] Finally, according to the unlabeled user v∈V U Sort the locality value of each candidate location and select the candidate location with the highest user score as the user's inferred location As shown in formula (13).

[0162]

[0163] in, In the converged state, user v is at the candidate position L x The locality value of .

[0164] In order to verify the feasibility and effectiveness of the present invention, this section conducts user location inference experiments on two public datasets, and compares and analyzes the experimental results of the method of the present invention with four existing typical algorithms.

[0165] 1.1 Experimental Data

[0166] The present invention uses the existing public Twitter dataset for experiments: GeoText (Eisenstein et al., 2010). This dataset is widely used in existing user location inference research. The users are mainly distributed in the continental United States. The distribution is as follows: Figure 4 As shown in (a). Each user has a set of historical tweet texts and a longitude and latitude coordinate. The number of users is 9.4k and the number of tweets is 377.6k. The present invention uses the city categories established by Han [Han B, Cook P, and Baldwin T. Geolocation prediction in social media data by finding location-indicative words [C]. Proceedings of the 24th International Conference on Computational Linguistics, 2012: 1045–1062.] to assign a GroundTruth city to each user based on the longitude and latitude coordinates of the user. The statistics of the number of users in each city are shown in Figure 4 As shown in (b).

[0167] 1.2 Experimental Setup

[0168] 1.2.1 Parameter settings

[0169] The experimental parameters related to the present invention are set as shown in Table 2:

[0170] Table 2 Experimental parameter settings

[0171]

[0172] 1.2.2 Evaluation indicators

[0173] When the present invention infers the user's location, the city is used as the category label. The user's inferred longitude and latitude are defined as Corresponding to the longitude and latitude, the user's inference error is the distance between the user's real longitude and latitude and the inferred longitude and latitude.

[0174] This paper uses the five evaluation indicators commonly used in previous social media user location inference articles: coverage, city-level inference accuracy, 161km inference accuracy@161, mean error, and median error. Given an unlabeled user set V U , where each user is denoted as v and the user’s real city is L v , inferring that the city is Error is error v The definitions and calculation formulas of the above evaluation indicators are as follows.

[0175] Coverage: The proportion of user location inference results obtained among all unlabeled users.

[0176]

[0177] City-level inference accuracy: The percentage of users whose inferred locations are correct among all unlabeled users.

[0178]

[0179] Accuracy@161: The proportion of unlabeled users whose inferred longitude and latitude are within 161 km of their true longitude and latitude.

[0180]

[0181] Mean Error: The average of the errors of all unlabeled users.

[0182]

[0183] Median Error: The median error of all unlabeled users.

[0184]

[0185] 1.3 Experimental results of position inference

[0186] This section conducts user location inference experiments on the public dataset GeoText. The experimental results of the proposed algorithm are compared with the existing four typical methods MADCEL-W [Afshin Rahimi, Trevor Cohn, Timothy Baldwin. Twitter User Geolocation Using a Unified Text and Network Prediction Model [A]. Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing of the Asian Federation of Natural Language Processing [C], 2015: 630-636.], GEOCEL [Mohammad Ebrahimi, Elaheh Shafei Bavani, Raymond Wong, and Fang Chen. 2018. Twitter user geolocation by filtering of highly mentioned users. Journal of the Association for Information Science and Technology 69 (02 2018), 879–889. Issue 69]. 7. https: / / doi.org / 10.1002 / asi.24011], MLP-TXT+NET[AfshinRahimi,Trevor Cohn,Timothy Baldwin.Semi-Supervised User Geolocation via GraphConvolutional Networks[A].Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics[C],2018:2009-2019.], ReLP[Tian H, Zhang M, Luo X, et al.Twitter User Location Inference Based on Representation Learning and Label Propagation.International World Wide Web Conference Committee, April 20–24, 2020, Taipei, Taiwan, China] were compared with the results on the same dataset, and the results are shown in Table 3. .

[0187] Table 3 Comparison of the results of the proposed method and four baseline methods

[0188]

[0189] The bold part in the table is the optimal value of the indicator in the result, and "-" indicates that there is no result for this indicator. It can be seen from the table that the method proposed in the present invention is superior to the existing four baseline methods in most indicators. The average error of the proposed method is only lower than that of the GEOCEL method. This is mainly because the coverage of GEOCEL is low, and the position inference is only performed when there is more inference evidence, and the error result is relatively low.

[0190] This is because the existing methods only transfer features through the user's social relationship network when using the user's network information, while the method proposed in the present invention also mines the structural information of the user's social relationship graph itself based on graph theory. The proposed method uses unlabeled users and labeled users at candidate locations to construct a social subgraph, and then calculates the clustering coefficient of unlabeled users in the graph. This feature reflects the closeness of the relationship between the user and the users in different candidate locations, which can well reflect the connection between the user and the candidate location. In addition, when fusing text information and network information, the existing methods often only pass the user's text features in the network, or vectorize the two features. The cyclic coupling method proposed in the present invention allows the two features to influence and enhance each other in each round of network iteration, and the degree of fusion is deeper, thereby improving the accuracy of user location inference.

[0191] 1.4 Impact of the number of iterations and change value threshold on position inference results

[0192] This section uses different numbers of iterations and different change value thresholds to control the loop termination, and analyzes the impact of different numbers of iterations and change value thresholds on the position inference results of the proposed method. The results are shown in the figure. Figure 5 shown.

[0193] Figure 5 The left vertical axis in the middle represents the accuracy within 161km of error, and the right vertical axis represents the number of users whose locations are correctly inferred within 161km. Figure 5 (a) shows the experimental results of changing the number of iterations from 0 to 30 in steps of 2. Figure 5 (b) shows the attribute change threshold from 1000 to 1×10 -7 The experimental results of the changes, the horizontal axis is -ln(f Δ ). As can be seen from the figure, multiple rounds of cross iteration can improve the accuracy of user location inference and eventually reach convergence. According to the experimental results, the number of iterations is set to 17 and the attribute iteration change value threshold is set to 1.

[0194] In view of the problem that the existing user location inference research does not fully explore the potential association between user text information and network information, fails to utilize the characteristics of user social relationships themselves, and leads to large errors in location inference results, the present invention proposes a user location inference method based on graph theory and cyclic cross-iteration. This method mines the structural characteristics of user social relationships themselves based on graph theory, calculates the clustering coefficient of the user in the social relationship subgraph of each candidate location, and cyclically cross-iterates in the social graph together with the user's text features to infer the user's most likely location. Experimental results on public datasets show that the city-level location inference accuracy of the proposed method is 37%, and the Accuracy@161 is 64%, which are 6%, 3%, 6%, and 2% higher than the existing methods, respectively. The average error and median error are also better than the existing methods.

[0195] Based on the above embodiments, Figure 6 As shown, the present invention also proposes a user location inference system based on loop coupling, comprising:

[0196] The social relationship graph construction module is used to construct the user social relationship graph; it includes:

[0197] First, extract the @ relationship from the user's historical blog text and construct the user mention relationship graph G0, which includes the marked user V L , Unmarked user V U and other users V O ; Then, V O The number of neighbors in exceeds f c Celebrity users are directly removed from graph G0; finally, V O The marked users and unmarked users connected to the remaining users in G0 are directly connected, and all other users V in G0 are removed. O , get the collapsed mention relationship graph G′0 as the user’s social relationship graph G=G′0;

[0198] The initial attribute value calculation module is used to calculate the initial attribute value of the user, wherein the initial attribute value includes an initial locality value and an initial aggregation value; and comprises:

[0199] For a labeled user v∈V L , the initial locality value and the initial clustering value are determined by their true location L v Decision; and for unlabeled user v∈V U , at each candidate position L x ∈L, L is the candidate position set, based on the user's historical blog text T v And the user mention relationship subgraph of that location Calculate the user's initial locality value and initial aggregation value;

[0200] The loop iteration module is used to update the user attribute value based on the social graph loop iteration; including:

[0201] At each candidate position L x ∈L, use the initial attribute value of the user at that position respectively, and iterate in the social relationship graph G until the network converges; in each round of iteration, cross-update the two attribute values ​​of the unmarked users in the graph according to the attribute information of the user's neighbors, and perform normalization;

[0202] The user location inference module is used to infer the user location; it includes:

[0203] When the network iterations in all candidate regions have reached convergence, for each unlabeled user v∈V U , and place it at each candidate position L x ∈L, and the candidate location with the highest user locality value is taken as the user's inferred location

[0204] Furthermore, in the initial attribute value calculation module, the initial locality value and aggregation value of the marked user are calculated as follows:

[0205] First, the set of labeled users V L Divide the user into multiple subsets according to their actual location, as shown in formula (1):

[0206]

[0207] Among them, L x ∈L represents the candidate position, Indicates that the real position is at L x The set of tagged users;

[0208] Then, at each candidate position L x ∈L, respectively for all labeled users v∈V L Assign initial locality and clustering values, if the marked user v is located at the candidate location L x , then the user is placed at the candidate location L xThe initial attribute values ​​of are all set to 1; otherwise, they are all set to 0, as shown in formula (2) and formula (3):

[0209]

[0210]

[0211] in, Indicates that user v is at candidate location L x The initial locality value of Indicates that user v is at candidate location L x The initial aggregation value of .

[0212] Furthermore, in the initial attribute value calculation module, the initial locality value of the unlabeled user is calculated as follows:

[0213] At each candidate position L x ∈L, according to the unlabeled user v∈V U Historical blog text of T v , calculate the probability that the user is located at the candidate location according to the following formula as its initial locality value;

[0214]

[0215] in, Indicates that user v is at candidate location L x The initial locality value of card() is the number of elements in the collection, T v is all the historical tweets of user v, card(T v ) is the number of tweets posted by the user, T′ v ={t i |t i ∈T v and t i is in L x} is the user in L x A collection of tweets that were published.

[0216] Furthermore, in the initial attribute value calculation module, the initial aggregation value of the unlabeled user is calculated as follows:

[0217] Based on the user social relationship graph G, for each candidate location L, x ∈L generates a social relationship subgraph, denoted as The real position is not in L x The marked users are removed from the graph G, and only the real location is kept in L x Tagged users and all untagged users V U, the obtained subgraph is the position L x User social relationship subgraph

[0218] Then in the subgraph Based on graph theory, the local clustering coefficient CC of all nodes is calculated, that is, the closeness of the neighbor relationship around the user. The clustering coefficient of the unlabeled user is the initial clustering value of the user. The user v is at the candidate position L x The initial aggregation value of is shown in formula (4):

[0219]

[0220] in, Indicates that user v is at candidate location L x The initial aggregation value of Indicates that user v is at candidate location L x The local clustering coefficient, N v is the first-order neighbor set of user v, represents the set of edges between the first-order neighbors of user v.

[0221] Furthermore, the loop iteration module is specifically used for:

[0222] During the iteration process, the two attribute values ​​of the marked users remain unchanged. For unmarked users, the attribute information of their neighbors is cross-aggregated in each iteration;

[0223] In the nth iteration, the unlabeled user v∈V U The locality value of is updated to the sum of the aggregation values ​​of all the first-order neighbors of the user, as shown in formula (6); the aggregation value of the user is updated to the sum of the locality values ​​of all the first-order neighbors of the user, as shown in formula (7):

[0224]

[0225]

[0226] Among them, N v represents the first-order user neighbor set of user v; and Respectively represent the candidate positions L x In the network cycle iteration, the locality value and aggregation value of user v in the nth iteration;

[0227] The normalization formula is as follows:

[0228]

[0229]

[0230] At each candidate position L x , and iterate according to the above formulas until the sum of the changes in the attribute values ​​of all nodes is less than the set threshold, or the number of iterations reaches the maximum number of rounds, as shown in formula (11). At this time, it is determined that the network iteration converges and the loop ends:

[0231] Loop termination condition: Δ n <f Δ or n>f max (11)

[0232] Among them, f Δ is the set change value threshold, f max is the maximum number of iterations set, Δ n is the sum of the attribute value changes of all nodes in round n, as shown in formula (12):

[0233]

[0234] In summary, the present invention proposes a universal feature for measuring the association between users and locations: clustering. Starting from the structural characteristics of the user social relationship network itself, the clustering coefficient of the target user in the social graph composed of the known users at the location is calculated based on graph theory, which can more directly mine the location information hidden in the social relationship and improve the accuracy of user location inference. A user location inference method and system based on cyclic coupling is proposed. The method first constructs a collapsed network according to the user's mention relationship to reduce the number of isolated nodes; then two attributes are assigned to each user, and the structural characteristics of the user in the social network graph are calculated based on graph theory, and the user's text features are calculated according to the user's generated text as the iterative initial value of the user attribute; in the user's social graph, the two attributes are cyclically cross-iterated, and the information association fusion is realized through mutual enhancement; finally, the most likely location is inferred according to the attribute value of the user in the network convergence state. The present invention assigns iterative initial values ​​to the two attributes of the user based on the user's text features and network features respectively, and cyclically cross-iterates the two attributes in the social graph to realize the association fusion of user text information and network information, thereby reducing the error of user location inference.

[0235] The above is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements and modifications without departing from the principle of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A user location inference method based on loop coupling, characterized in that: include: Step 1: Build a user social relationship graph; including: First, extract the @ relationship from the user's historical blog text and construct the user mention relationship graph G0, which includes the marked user V L , Unmarked user V U and other users V O ; Then, V O The number of neighbors in exceeds f c Celebrity users are directly removed from graph G0; finally, V O The marked users and unmarked users connected to the remaining users in G0 are directly connected, and all other users V in G0 are removed. O , get the collapsed mention relationship graph G′0 as the user’s social relationship graph G=G′0; Step 2: Calculate the initial attribute values ​​of the user, the initial attribute values ​​including the initial locality value and the initial aggregation value; including: For a labeled user v∈V L , the initial locality value and the initial clustering value are determined by their true location L v Decision; and for unlabeled user v∈V U , at each candidate position L x ∈L, L is the candidate position set, based on the user's historical blog text T v And the user mention relationship subgraph of that location Calculate the user's initial locality value and initial aggregation value; Step 3: Iteratively update user attribute values ​​based on the social graph; including: At each candidate position L x ∈L, use the initial attribute value of the user at that position respectively, and iterate in the social relationship graph G until the network converges; in each round of iteration, cross-update the two attribute values ​​of the unmarked users in the graph according to the attribute information of the user's neighbors, and perform normalization; Step 4: Infer user location; including: When the network iterations in all candidate regions have reached convergence, for each unlabeled user v∈V U , and place it at each candidate position L x ∈L, and the candidate location with the highest user locality value is taken as the user's inferred location 2. The user position inference method based on cyclic coupling according to claim 1, characterized in that: In step 2, the initial locality value and aggregation value of the marked user are calculated as follows: First, the set of labeled users V L Divide the user into multiple subsets according to their actual location, as shown in formula (1): Among them, L x ∈L represents the candidate position, Indicates that the real position is at L x The set of tagged users; Then, at each candidate position L x ∈L, respectively for all labeled users v∈V L Assign initial locality and clustering values, if the marked user v is located at the candidate location L x , then the user is placed at the candidate location L x The initial attribute values ​​of are all set to 1; otherwise, they are all set to 0, as shown in formula (2) and formula (3): in, Indicates that user v is at candidate location L x The initial locality value of Indicates that user v is at candidate location L x The initial aggregation value of .

3. The user position inference method based on cyclic coupling according to claim 1, characterized in that: In step 2, the initial locality value of the unlabeled user is calculated as follows: At each candidate position L x ∈L, according to the unlabeled user v∈V U Historical blog text of T v , calculate the probability that the user is located at the candidate location according to the following formula as its initial locality value; in, Indicates that user v is at candidate location L x The initial locality value of card() is the number of elements in the collection, T v is all the historical tweets of user v, card(T v ) is the number of tweets posted by the user, T′ v ={t i |t i ∈T v andt i is in L x } is the user in L x A collection of tweets that were published.

4. The user position inference method based on cyclic coupling according to claim 1, characterized in that: In step 2, the initial aggregation value of the unlabeled user is calculated as follows: Based on the user social relationship graph G, for each candidate location L, x ∈L generates a social relationship subgraph, denoted as The real position is not in L x The marked users are removed from the graph G, and only the real location is kept in L x Tagged users and all untagged users V U , the obtained subgraph is the position L x User social relationship subgraph Then in the subgraph Based on graph theory, the local clustering coefficient CC of all nodes is calculated, that is, the closeness of the neighbor relationship around the user. The clustering coefficient of the unlabeled user is the initial clustering value of the user. The user v is at the candidate position L x The initial aggregation value of is shown in formula (5): in, Indicates that user v is at candidate location L x The initial aggregation value of Indicates that user v is at candidate location L x The local clustering coefficient, N v is the first-order neighbor set of user v, represents the set of edges between the first-order neighbors of user v.

5. The user position inference method based on cyclic coupling according to claim 1, characterized in that: The step 3 comprises: During the iteration process, the two attribute values ​​of the marked users remain unchanged. For unmarked users, the attribute information of their neighbors is cross-aggregated in each iteration; In the nth iteration, the unlabeled user v∈V U The locality value of is updated to the sum of the aggregation values ​​of all the first-order neighbors of the user, as shown in formula (6); the aggregation value of the user is updated to the sum of the locality values ​​of all the first-order neighbors of the user, as shown in formula (7): Among them, N v represents the first-order user neighbor set of user v; and Respectively represent the candidate positions L x In the network cycle iteration, the locality value and aggregation value of user v in the nth iteration; The normalization formula is as follows: At each candidate position L x , and iterate according to the above formulas until the sum of the changes in the attribute values ​​of all nodes is less than the set threshold, or the number of iterations reaches the maximum number of rounds, as shown in formula (11). At this time, it is determined that the network iteration converges and the loop ends: Loop termination condition: Δ n <f Δ or n>f max (11) Among them, f Δ is the set change value threshold, f max is the maximum number of iterations set, Δ n is the sum of the attribute value changes of all nodes in round n, as shown in formula (12):

6. A user location inference system based on loop coupling, characterized in that: include: The social relationship graph construction module is used to construct the user social relationship graph; it includes: First, extract the @ relationship from the user's historical blog text and construct the user mention relationship graph G0, which includes the marked user V L , Unmarked user V U and other users V O ; Then, V O The number of neighbors in exceeds f c Celebrity users are directly removed from graph G0; finally, V O The marked users and unmarked users connected to the remaining users in G0 are directly connected, and all other users V in G0 are removed. O , get the collapsed mention relationship graph G′0 as the user’s social relationship graph G=G′0; The initial attribute value calculation module is used to calculate the initial attribute value of the user, wherein the initial attribute value includes an initial locality value and an initial aggregation value; and comprises: For a labeled user v∈V L , the initial locality value and the initial clustering value are determined by their true location L v Decision; and for unlabeled user v∈V U , at each candidate position L x ∈L, L is the candidate position set, based on the user's historical blog text T v And the user mention relationship subgraph of that location Calculate the user's initial locality value and initial aggregation value; The loop iteration module is used to update the user attribute value based on the social graph loop iteration; including: At each candidate position L x ∈L, use the initial attribute value of the user at that position respectively, and iterate in the social relationship graph G until the network converges; in each round of iteration, cross-update the two attribute values ​​of the unmarked users in the graph according to the attribute information of the user's neighbors, and perform normalization; The user location inference module is used to infer the user location; it includes: When the network iterations in all candidate regions have reached convergence, for each unlabeled user v∈V U , and place it at each candidate position L x ∈L, and the candidate location with the highest user locality value is taken as the user's inferred location 7. The user position inference system based on loop coupling according to claim 6, characterized in that: In the initial attribute value calculation module, the initial locality value and aggregation value of the marked user are calculated as follows: First, the set of labeled users V L Divide the user into multiple subsets according to their actual location, as shown in formula (1): Among them, L x ∈L represents the candidate position, Indicates that the real position is at L x The set of tagged users; Then, at each candidate position L x ∈L, respectively for all labeled users v∈V L Assign initial locality and clustering values, if the marked user v is located at the candidate location L x , then the user is placed at the candidate location L x The initial attribute values ​​of are all set to 1; otherwise, they are all set to 0, as shown in formula (2) and formula (3): in, Indicates that user v is at candidate location L x The initial locality value of Indicates that user v is at candidate location L x The initial aggregation value of .

8. The user position inference system based on loop coupling according to claim 6, characterized in that: In the initial attribute value calculation module, the initial locality value of the unlabeled user is calculated as follows: At each candidate position L x ∈L, according to the unlabeled user v∈V U Historical blog text of T v , calculate the probability that the user is located at the candidate location according to the following formula as its initial locality value; in, Indicates that user v is at candidate location L x The initial locality value of card() is the number of elements in the collection, T v is all the historical tweets of user v, card(T v ) is the number of tweets posted by the user, T′ v ={t i |t i ∈T v andt i is in L x } is the user in L x A collection of tweets that were published.

9. The user position inference system based on loop coupling according to claim 6, characterized in that: In the initial attribute value calculation module, the initial aggregation value of the unlabeled user is calculated as follows: Based on the user social relationship graph G, for each candidate location L, x ∈L generates a social relationship subgraph, denoted as The real position is not in L x The marked users are removed from the graph G, and only the real location is kept in L x Tagged users and all unlabeled users V U , the obtained subgraph is the position L x User social relationship subgraph Then in the subgraph Based on graph theory, the local clustering coefficient CC of all nodes is calculated, that is, the closeness of the neighbor relationship around the user. The clustering coefficient of the unlabeled user is the initial clustering value of the user. The user v is at the candidate position L x The initial aggregation value of is shown in formula (5): in, Indicates that user v is at candidate location L x The initial aggregation value of Indicates that user v is at candidate location L x The local clustering coefficient, N v is the first-order neighbor set of user v, represents the set of edges between the first-order neighbors of user v.

10. The user position inference system based on loop coupling according to claim 6, characterized in that: The loop iteration module is specifically used for: During the iteration process, the two attribute values ​​of the marked users remain unchanged. For the unmarked users, the attribute information of their neighbors is cross-aggregated in each iteration; In the nth iteration, the unlabeled user v∈V U The locality value of is updated to the sum of the aggregation values ​​of all the first-order neighbors of the user, as shown in formula (6); the aggregation value of the user is updated to the sum of the locality values ​​of all the first-order neighbors of the user, as shown in formula (7): Among them, N v represents the first-order user neighbor set of user v; and Respectively represent the candidate positions L x In the network cycle iteration, the locality value and aggregation value of user v in the nth iteration; The normalization formula is as follows: At each candidate position L x , and iterate according to the above formulas until the sum of the changes in the attribute values ​​of all nodes is less than the set threshold, or the number of iterations reaches the maximum number of rounds, as shown in formula (11). At this time, it is determined that the network iteration converges and the loop ends: Loop termination condition: Δ n <f Δ or n>f max (11) Among them, f Δ is the set change value threshold, f max is the maximum number of iterations set, Δ n is the sum of the attribute value changes of all nodes in round n, as shown in formula (12):