Multilayer network representation learning-based reverse random walk central expression method and system, and storage medium

Abstract

The invention provides a reverse random walk central expression method and system based on multilayer network representation learning and a storage medium, and relates to the technical field of representation learning and online social network analysis. Through learning abundant node representation, the method can measure the similarity between the nodes more effectively, capture influence nodes in a multilayer network through reverse random walk, indirectly describe the similarity degree and potential influence between the nodes in combination with city-level energy consumption and traffic jam data, and improve the reliability of the network. And the seed node with the most influence is effectively identified, so that the limitation of a traditional method in a multi-layer network is overcome.

Description

Technical Field

[0001] The present invention relates to the technical field of representation learning and online social network analysis, and specifically to a reverse random walk centrality expression method, system and storage medium based on multi-layer network representation learning. Background Art

[0002] A city-level multi-layered logistics and social network for emergency material distribution and information dissemination; the network includes not only the conventional social layer, such as user social relationships, but also the actual logistics and transportation layer, such as the relationship between different sites, warehouses and vehicles, as well as the public opinion and offline activity information layer, such as the relationship between large conferences and public event locations;

[0003] Discovering the most influential seed nodes in a multi-layer network requires both rapid information dissemination and efficient resource organization. This is of great significance for emergency response, policy dissemination, and resource allocation. However, due to the complex structure of multi-layer networks and the existence of multiple relationships between nodes, the traditional random walk centrality method is difficult to fully utilize cross-domain information, and the impact assessment is not accurate enough. In this background technology, "nodes" can represent individuals, important organizations, transportation stations, etc. in the city; "edges" represent multiple connections, including the social layer, physical logistics layer, information dissemination layer, etc.

[0004] In the prior art, the publication number is CN109447261A, and the name is a method for learning network representation based on multi-order neighbor similarity. Compared with the traditional network representation based on structural analysis, which only considers the relationship between the first-order neighbor similarity and the second-order neighbor similarity, the focus is on modeling the high-order neighbor similarity between nodes, and different types of calculation methods for indirect neighbor similarity are designed respectively, especially considering that information will decay with the increase of distance during network propagation. Therefore, this method can predict different neighbor nodes of the current node and more accurately find the neighbor nodes with the greatest correlation with the target node, so as to obtain a representation vector with richer semantics, higher reliability and authenticity.

[0005] At present, the research on the influence maximization problem is mainly concentrated in single-layer social networks. The complexity and diversity of multi-layer social networks make it difficult for traditional methods to effectively identify seed nodes, especially in the case of multiple influence interactions. How to use the cross-domain fusion of urban energy consumption and traffic congestion sensor data, and then combine the city-level "energy consumption and traffic congestion" data to indirectly characterize the similarity and potential influence between nodes, and effectively identify the most influential seed nodes is a technical problem that needs to be solved at present. Among them, the most influential seed node is the problem of maximizing the influence of multi-layer networks.

[0006] The above information disclosed in the above Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not form the prior art that is already known to one of ordinary skill in the art. Summary of the invention

[0007] The purpose of the present invention is to provide a reverse random walk centrality expression method, system and storage medium based on multi-layer network representation learning to solve the problems raised in the above background technology.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] The reverse random walk centrality expression method based on multi-layer network representation learning includes the following specific steps:

[0010] S1. Obtain urban energy consumption and traffic congestion data of urban areas corresponding to multi-layer social network nodes, extract embedded features of multi-layer social network nodes, and calculate the initialization association weights between nodes, and use the urban energy consumption and traffic congestion data to adjust the initialization association weights between nodes;

[0011] S2, perform reverse random walk according to the adjusted inter-node weights, and record all visited nodes to form a candidate node set;

[0012] S3. Count the number of visits to each node in the candidate node set, and select the top-k nodes with the most visits as the most influential seed node set in the multi-layer network, thereby solving the problem of maximizing the influence of the multi-layer network.

[0013] A reverse random walk centrality expression system based on multi-layer network representation learning, the system is used to execute the reverse random walk centrality expression method based on multi-layer network representation learning, comprising:

[0014] Initialization association weight determination module: used to obtain urban energy consumption and traffic congestion data of urban areas corresponding to multi-layer social network nodes, extract embedded features of multi-layer social network nodes, and calculate the initialization association weights between nodes, and use urban energy consumption and traffic congestion data to adjust the initialization association weights between nodes;

[0015] Reverse random walk module: used to perform reverse random walk according to the adjusted inter-node weights and record all visited nodes to form a candidate node set;

[0016] Seed node set determination module: used to count the number of visits to each node in the candidate node set, and select the top-k nodes with the most visits as the most influential seed node set in the multi-layer network, thereby solving the problem of maximizing the influence of the multi-layer network.

[0017] A readable storage medium stores a computer program, and when the computer program is executed by a processor, the reverse random walk centrality expression method based on multi-layer network representation learning is implemented.

[0018] Compared with the prior art, the beneficial effects of the present invention are: by evaluating the coupled propagation of single influence and multiple influences to enhance the effect of information dissemination, by learning rich node representations, this method can more effectively measure the similarity between nodes, and capture the influential nodes in the multi-layer network through reverse random walks, and combine the city-level "energy consumption and traffic congestion" data to indirectly characterize the similarity and potential influence between nodes, effectively identify the most influential seed nodes, thereby overcoming the limitations of traditional methods in multi-layer networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is the algorithm framework diagram of the present invention:

[0020] Figure 2 It is a single influence propagation graph in a multi-layer social network;

[0021] Figure 3 Schematic diagram of multi-influence coupling propagation parameters in multi-layer social networks;

[0022] Figure 4-Figure 6 The results of the single influence propagation experiment based on different data sets are shown in the figure;

[0023] Figure 7-Figure 9 The results of multi-impact coupled propagation experiments based on different data sets are shown in Figure 2.

[0024] Fig.10 A comparison chart of running time on different data sets;

[0025] Fig.11 It is a schematic diagram of the overall method flow of the present invention;

[0026] Fig.12 It is a system module block diagram of the present invention. DETAILED DESCRIPTION

[0027] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0028] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0029] Embodiment 1:

[0030] See also Figures 1 to 11 , the present invention provides a technical solution:

[0031] The reverse random walk centrality expression method based on multi-layer network representation learning is applied to multi-layer social network nodes composed of social-logistics networks. The specific steps include:

[0032] S1. Obtain urban energy consumption and traffic congestion data of urban areas corresponding to multi-layer social network nodes, extract embedded features of multi-layer social network nodes, and calculate the initialization association weights between nodes, and use the urban energy consumption and traffic congestion data to adjust the initialization association weights between nodes;

[0033] S2, perform reverse random walk according to the adjusted inter-node weights, and record all visited nodes to form a candidate node set;

[0034] S3. Count the number of visits to each node in the candidate node set, and select the top-k nodes with the most visits as the most influential seed node set in the multi-layer network, thereby solving the problem of maximizing the influence of the multi-layer network.

[0035] Further, in step S1, extracting embedded features of multi-layer social network nodes includes the following steps:

[0036] S11. Construct a multi-layer social network structure. In order to solve the problem of maximizing the influence of a multi-layer network, it is necessary to first construct a multi-layer social network.

[0037] S12, extracting embedded features from a multi-layer social network structure; this embodiment uses the RMNE method to learn node features in a multi-layer network structure;

[0038] S13, calculating the similarity between different nodes based on the embedded features. In this embodiment, the cosine similarity between different nodes is used to initialize the weight value of each edge in each network layer.

[0039] Further, in step S11, when constructing a multi-layer social network structure, the following single influence propagation model and multi-influence coupling propagation model are considered respectively;

[0040] In order to comprehensively evaluate the effectiveness of the reverse random walk centrality expression method based on multi-layer network representation learning proposed in this embodiment in solving the problem of maximizing the influence of multi-layer networks, this stage considers different situations of single influence and multi-influence coupling propagation when constructing the multi-layer social network structure;

[0041] First, for the single influence propagation model in a multi-layer network, this method defines it as:

[0042] Description of the single influence propagation model: Given a If a node u corresponding to a node feature of any layer in a multi-layer social network structure is activated, then the node u in other layers The corresponding nodes in the layer will also be transformed into the activated state; then, the influence caused by node u will continue to propagate according to the different diffusion models of the network structure of each layer until no new nodes are activated, and the influence propagation process stops;

[0043] The single influence propagation model is as follows Figure 2 As shown, Figure 2 The activated seed node in (a) is {3}; Figure 2 In (b), nodes propagate according to the propagation model of each layer; Figure 2 In (c), the nodes in other layers corresponding to the activated nodes in any layer are also activated, and the propagation process continues.

[0044] The process of node activation and influence propagation can be divided into the following two cases:

[0045] Multiplex independent cascade model (MIC) and multiplex linear threshold model (MLT);

[0046] In the multi-layer independent cascade model, if the selected node is activated, it will have one chance to activate its adjacent inactive nodes;

[0047] In the multi-layer linear threshold model, each node has a threshold, and the node will be activated only when the sum of the influence of other nodes on the selected inactivated node exceeds the threshold;

[0048] Explanation of the multi-influence coupled propagation model in a multi-layer network: Consider the competition and cooperation information between different network layers; competition information inhibits the propagation of target information between nodes, while cooperation information promotes the propagation of target information, as follows:

[0049] Multi-influence coupled propagation model such as Figure 3 As shown in the figure, a social network with three layers is set, L0 is the target layer, L1 and L2 are the competition layer and the cooperation layer respectively; the mutual influence relationship between different layers will adjust the activation probability of node u to node v; the specific influence relationship between different layers is quantified by the following formula:

[0050]

[0051] Among them, setting represents the activation probability of node u in the lth layer to node v, l∈{0,1,2}, Represents the activation state of node v in the lth layer, 0 is inactive and 1 is activated; λ1 represents the influence coefficient of L1 on L0, λ2 represents the influence coefficient of L1 on L2, α1 represents the influence coefficient of L0 on L1, and α2 represents the influence coefficient of L0 on L2. The influence relationship coefficient is estimated by analyzing actual data, using social networks, communication behaviors or experimental results; it can be used to analyze the influence of different nodes on different layers; γ1 represents the influence coefficient of L2 on L0, and γ2 represents the influence coefficient of L2 on L1; taking node v in the L0 layer as an example, if it is not affected by other layers, the activation probability of node u in the L0 layer to node v is When When , that is, node v is affected by the competition layer L1, then the activation probability of node u in the L0 layer to node v becomes when and When node v is affected by both the competition layer L1 and the cooperation layer L2, the activation probability of node u in the L0 layer to node v becomes w1 and w2 are the influence weights of L1 and L2 layers on L0; similarly, w0 and w′2 are the influence weights of L0 and L2 on L1 layer, and w′0 and w′1 are the influence weights of L0 and L1 on L2 layer; in addition, considering the influence of competition and cooperation information, this embodiment extends the MIC model to the CCMIC model, and the MLT model evolves into the CCMLT model;

[0052] Finally, the multi-layer network influence maximization problem is defined as follows:

[0053] Given a containing Multi-layer social network and an influence propagation model σ and a node set of size k; where, represents the set of all nodes in a multi-layer social network, ε represents the set of edges between different nodes, Indicates the number of network layers;

[0054] The goal of the multi-layer network influence maximization problem is to select an optimal node set with a maximum value of k nodes. To maximize the multi-layer social network The influence propagation process in , namely:

[0055]

[0056] Among them, (S) represents the selected node set, which is a subset of k nodes. The goal is to maximize the effect of influence propagation by selecting these nodes;

[0057] (S * ) represents a potential optimal node set, which is also a subset containing k nodes. The solution goal in the formula is to find this optimal node set from all possible node sets so that its influence propagation effect is maximized.

[0058] σ is a function of the influence propagation model defined in a multi-layer social network, which includes different cases of a single influence propagation model and a multi-influence coupling propagation model; this function is used to calculate the influence of a given node set, conveying the degree of influence of the nodes activated from the node set (S) on other nodes in the entire network;

[0059] argmax means to find the independent variable that maximizes the function affecting the propagation model. Here, it is used to express the search for the function that makes σ(S * ) The node set (S) with the maximum value.

[0060] Further, in step S12, the embedded features are extracted from the multi-layer social network structure, specifically including:

[0061] This embodiment uses the RMNE method to learn node feature representations in a multi-layer social network structure to obtain embedded features;

[0062] Node feature representation includes: node proximity and structural role information. The specific process is as follows:

[0063]

[0064] Among them, RMNE(·) is the mapping function of RMNE; Represents the feature representation of node u in the l-th layer of the social network structure.

[0065] Further, in step S13, the similarity between different nodes is calculated based on the embedded features, specifically including:

[0066] Calculate the cosine similarity between different nodes to obtain the initial association weight value of each edge in each network layer; the specific process is as follows:

[0067]

[0068] Among them, cossim(·) is the mapping function of cosine similarity; w l (u,v) represents the similarity between nodes u and v in the l-th layer network structure, that is, the initialization association weight of the edge between the two nodes. The overall meaning of the function indicates that there is also a weight on the set of edges.

[0069] Further explanation: Using urban energy consumption and traffic congestion data, the initial association weights between nodes are adjusted, including:

[0070] Based on the existing social-logistics network, urban energy consumption and traffic congestion data are introduced for simulation experiments and converted into new indicators that can be combined with the original network edge weights; the original network edge weights are the initialization association weights wl(u,v) of the edge between nodes u and v;

[0071] For the areas where nodes u and v are located, if their energy consumption and traffic data show similar or synchronous fluctuation characteristics, their edge weights need to be increased to more accurately reflect the potential connection between the two nodes;

[0072] Energy consumption and traffic data can reflect the current level of activity and bottleneck areas of urban operations in a more timely manner, thereby obtaining a more accurate assessment of node influence during emergency deployment;

[0073] For energy consumption data acquisition:

[0074] Obtain energy consumption statistics for each city area within a set time window from the monitoring system of the city power grid company or the main transmission and substation;

[0075] The temporal resolution is 15 minutes or hours to balance data availability and accuracy;

[0076] The data format is: {(t,η1 j )∣t∈{1,2,…,T1},j∈{1,2,…,M}}; (t,η1 j) represents the energy consumption data of the jth urban area in time period t; T1 represents the total number of time periods; j represents the index of urban area j, and M is the total number of urban areas; the energy consumption data includes but is not limited to the electricity consumption;

[0077] Traffic congestion data acquisition:

[0078] Based on the urban traffic management platform or roadside sensors and vehicle network data, real-time road network congestion level data of each urban area is obtained; in this embodiment, the real-time road network congestion level data is represented by a traffic congestion index, which is determined by calculating the proportion of congestion in all road sections of the current j-th urban area, and the congestion of the road section is divided according to the road section congestion of the existing real-time navigation system;

[0079] The temporal resolution and energy consumption are kept consistent, facilitating subsequent alignment;

[0080] The data format is: {(t,η2 j )∣t∈{1,2,…,T1},j∈{1,2,…,M}}; (t,η2 j ) represents the traffic congestion data of the j-th urban area in time period t;

[0081] Social-logistics network data acquisition:

[0082] Get the similarity between nodes u and v in the lth layer network structure, that is, the initialization association weight w of the edge between the two nodes l (u,v);

[0083] Delete missing data or interpolate noisy data, specifically perform linear interpolation on the missing time periods in energy consumption data;

[0084] Perform outlier detection on the traffic congestion index and remove extreme outliers;

[0085] Unify the time scale to ensure accurate matching between energy consumption, traffic, and network relationships in each period;

[0086] Matching geographic or administrative regions:

[0087] Coordinate mapping or area mapping of network nodes to urban areas corresponding to energy consumption and traffic data;

[0088] If the node crosses regions, the region where the main part is located is used as the main part; the main part means the part that exceeds 50% of the current node;

[0089] The energy consumption indexes of nodes u and v in urban area j are defined as η1(u) j ,η1(v) j ;

[0090] Define the traffic congestion index of nodes u and v in urban area j as η2(u) j ,η2(v) j ;

[0091] The calculation formulas for the energy consumption index and traffic congestion index of node u are given below. The calculation methods for the energy consumption index and traffic congestion index of node v are the same as those of node u and will not be described in detail.

[0092] Calculate the energy consumption index η1(u) of node u:

[0093] For node u in the time window {1, 2, ..., T1}, the time window in this embodiment is the peak interval of the past 24 hours or the past week, and the average energy consumption of the corresponding urban area is counted;

[0094] The average energy consumption level value of the past T1 period is used as the energy consumption index η1(u) of urban area j j :

[0095]

[0096] where η1 u,j (t) represents the energy consumption level of urban area j where node u is located in time period t; SNH u,j (t) represents the actual electricity consumption of the city area j where the node u is located in time period t; ENH u,j (t) represents the maximum rated electricity consumption of the city area j where the node u is located in time period t;

[0097] The average traffic congestion index of the past T1 periods is used as the traffic congestion index η2(u) of urban area j j , the calculation formula is as follows:

[0098]

[0099] where η2 u,j (t) represents the traffic congestion index of urban area j where node u is located in time period t;

[0100] DSLD u,j (t) represents the number of blocked road sections in the city area j where the node u is located in time period t;

[0101] ZL u,j( t) represents the total number of all road sections in the city area j where the node u is located in time period t;

[0102] Get the energy consumption index of nodes u and v in urban area j as η1(u) j ,η1(v) j ; and the traffic congestion index of nodes u and v in urban area j are η2(u)j ,η2(v) j , and perform the following calculation analysis:

[0103]

[0104] Among them, Sim(η1(u) j ,η1(v) j ) and Sim(η2(u) j ,η2(v) j ) both represent similarity calculations, and Sim(η1(u) j ,η1(v) j ) is used to measure the similarity between two nodes regarding the energy consumption index; Sim(η2(u) j ,η2(v) j ) is used to measure the similarity between two nodes regarding the traffic congestion index; the similarity is calculated using cosine similarity; the form is as follows:

[0105]

[0106] corr(η1(u) j ,η1(v) j ) and corr(η2(u) j ,η2(v) j ) all represent the correlation coefficient calculation, and corr(η1(u) j ,η1(v) j ) is used to measure the linear relationship between two nodes regarding the energy consumption index, and the value range is [-1, 1]; a correlation coefficient of 1 indicates a completely positive correlation, 0 indicates no correlation, and -1 indicates a completely negative correlation; corr(η2(u) j ,η2(v) j ) is used to measure the linear relationship between two nodes regarding the traffic congestion index, and the value range is also [-1,1]; in this embodiment, the correlation coefficient adopts the Pearson correlation coefficient;

[0107] When calculating the energy consumption index or traffic congestion index of a node, the Pearson correlation coefficient needs to be in vector form. At this time, the energy consumption sequence of node u in each time period is correlated with the energy consumption sequence of node v in a finer time period, and a value is obtained as the similarity.

[0108] The following similarity is selected for example calculation:

[0109] In the original network edge weight w lOn the basis of (u,v), an adjustment factor δ is added, 0.1≤δ≤0.5; the specific value of δ is determined by the expert group based on experimental data;

[0110] w″ l (u,v)=w l (u,v)·[1+δ·Sim(η1(u) j ,η1(v) j )·Sim(η2(u) j ,η2(v) j )]

[0111] where w″ l (u,v) is the output value of the initial association weight between nodes u and v after adjustment. When the energy consumption index and traffic congestion index of the two nodes are highly similar, w″ l (u,v) will be numerically amplified to highlight such potentially highly correlated nodes;

[0112] The corrected edge weight w″ l (u,v) are written into a new network representation or database to prepare for the subsequent random walk analysis algorithm.

[0113] For node pairs without direct social or logistics edges, keep the original weight as 0. If you want to add potential links introduced across layers, you can perform strategy screening in the business;

[0114] This embodiment has the following beneficial effects:

[0115] Emergency supplies deployment:

[0116] The selected seed nodes are regarded as the highest priority material distribution points or coordination nodes to ensure that materials can reach the target location faster and more efficiently during peak traffic or high energy consumption periods in the city;

[0117] Combined with geographic and traffic monitoring systems, real-time monitoring of the traffic conditions of material vehicles in traffic congestion areas can be used to make timely route adjustments;

[0118] Information release and public opinion response:

[0119] If the selected nodes include key media, self-media or organizers of public events, information dissemination through these nodes can quickly form public opinion dissemination among similar highly active areas;

[0120] Before and after large-scale conferences or public events, these nodes can more effectively drive the spread of information in surrounding areas;

[0121] Improvements compared to traditional solutions:

[0122] Traditionally, only social intensity and logistics distance are used to measure the importance of nodes, ignoring the macro-operation status of the city. For example, a specific area may be very busy at one time, but it is not necessarily a social or logistics center;

[0123] The new solution uses energy consumption and traffic congestion data to track 5% to 10% efficiency gains during key periods, especially during holiday peaks and major events.

[0124] The cross-layer fusion dimensions are richer: Based on the existing social-logistics network, the urban energy consumption index and traffic flow intensity index are added to make the network representation more in line with the real situation of the city.

[0125] Further, in step S2, a reverse random walk is performed according to the adjusted inter-node weights, including the following steps:

[0126] S21. Reverse all directed edges in the entire multi-layer network structure:

[0127] Directed edges represent unidirectional relationships or connections between nodes; in social networks or graph structures, "directed" means that the connection has a direction, that is, it points from one node to another, rather than a bidirectional connection. In the case of a reverse random walk, it is usually started from a node and randomly follows the directed edges in the graph to traverse in reverse. This means starting from a node and randomly walking along the incoming edges pointing to the node, so that other nodes that affect the node can be traced back. The purpose of this is to explore and analyze the source of influence or traceability of the node.

[0128] In order to perform a reverse random walk in a multi-layer network structure, it is necessary to reverse all the initial directed edges in the entire multi-layer network structure. The specific process is as follows:

[0129]

[0130] Among them, ReversedAllEdges{·} is the operation function of reversing directed edges, ε′ represents the reversed directed edges, Represents the inverted multi-layer social network;

[0131] S22, perform a reverse random walk, specifically:

[0132] Given a node u, a reverse random walk is performed K times starting from node u, with each walk length being Le; the reverse random walk method is referred to as RRW; the calculation steps of the reverse random walk method (RRW) are as follows:

[0133] 22.1) Input: Initial node u,walk length Le;

[0134] 22.2)Output:A node sequence walk with a maximum length ofLe;

[0135] 22.3)Initialize walk with node u;

[0136] 22.4)While(len(walk) <Le)do;

[0137] 22.5)cur = walk[-1];

[0138] 22.6)

[0139] 22.7)

[0140] 22.8)Append w to walk;

[0141] 22.9)end While;

[0142] 22.10)return walk;

[0143] Among them, Initial node u means that the initial node is u, which specifically means that the node at which the random walk starts is u;

[0144] walk length Le means the walk length is Le, which indicates the maximum step length or number of steps of the random walk, and determines the duration of the walk or the number of nodes visited;

[0145] Output: A node sequence walk with a maximum length of Le is the output parameter description: that is, a node sequence (walk) is returned, and the maximum length of the sequence is the walk length previously input; this sequence represents the nodes visited by the reverse random walk in the network;

[0146] Initialize walk with node u is to initialize the walk: it means to use the input initial node to initialize the walk sequence, which means that when the walk starts, the first node u is the set initial node;

[0147] While(len(walk)<Le)do is the loop condition: It indicates a loop, meaning that while the condition len(walk)<Le is satisfied, the random walk will continue; this loop is the core part for performing the reverse random walk.

[0148] cur = walk[-1]: Extract the last node of the current random walk sequence walk as the starting node for the next step.

[0149] Among them represents extracting the set of neighbor nodes at the current node cur, represents extracting the set of nodes corresponding to the current node cur in the other layer networks of the multi-layer network, and finally merging them into which represents the set of optional nodes for the next step of the random walk of the current node.

[0150] According to the extracted in the previous step and the sampling weight ε′, perform biased sampling to obtain the next node w of the random walk.

[0151] Append w to walk is to add the visited node w to the random walk sequence walk.

[0152] end While is the end of the loop, specifically indicating that the above while loop has ended and the random walk process is completed.

[0153] return walk is to return the result: It means that after the algorithm is completed, return the previously constructed node sequence (walk), which is the final output result.

[0154] 22.6) Retrieved the set of adjacent nodes of the current node in the same layer and the corresponding node sets in other layers of the multi-layer network; in addition, RRW uses the cosine similarity between nodes to measure the weights between the same nodes in different layers, and the specific formula is as follows:

[0155]

[0156] where f(u) and f(v) are the feature representations of nodes u and v respectively; RRW uses biased sampling based on the edge weights between nodes to determine the node that the current node will visit in the next step; d is the dimension of the node feature representation, that is, the representation of each node in the feature space is a d-dimensional vector, and i represents the i-th element in the feature vector, which is used to represent the specific dimension index in the node features. This means that nodes with higher edge weights connected to the current node are more likely to be selected as the next node in the random walk sequence; finally, 22.10) returns the set of nodes selected after the reverse random walk.

[0157] Further explanation: in step S3, the number of visits to each node in the candidate node set is counted, and the top-k nodes with the most visits are selected as the most influential seed node set in the multi-layer network, specifically including:

[0158] The number of visits to all nodes returned by the reverse random walk method is counted, and each node is sorted in descending order according to its number of visits. The specific process is as follows:

[0159] counts=CountingAndSorted(walks)

[0160] Among them, CountingAndSorted(·) is the counting and descending sorting operation function, walks is the set of all nodes returned by the reverse random walk method, and counts represents the number of visits to each node;

[0161] According to the number of visits to each node in the reverse random walk sequence, the first k nodes are selected as the seed nodes with the greatest influence. The specific process is as follows:

[0162] S = top-k (counts)

[0163] Where top-k(·) represents the first k nodes in the candidate node set, and S is the seed node set with the greatest influence.

[0164] Embodiment 2:

[0165] See also Fig.12 , a reverse random walk centrality expression system based on multi-layer network representation learning, the system is used to execute the reverse random walk centrality expression method based on multi-layer network representation learning, comprising:

[0166] Initialization association weight determination module: used to obtain urban energy consumption and traffic congestion data of urban areas corresponding to multi-layer social network nodes, extract embedded features of multi-layer social network nodes, and calculate the initialization association weights between nodes, and use urban energy consumption and traffic congestion data to adjust the initialization association weights between nodes;

[0167] Reverse random walk module: used to perform reverse random walk according to the adjusted inter-node weights and record all visited nodes to form a candidate node set;

[0168] Seed node set determination module: used to count the number of visits to each node in the candidate node set, and select the top-k nodes with the most visits as the most influential seed node set in the multi-layer network, thereby solving the problem of maximizing the influence of the multi-layer network.

[0169] A readable storage medium stores a computer program, and when the computer program is executed by a processor, the reverse random walk centrality expression method based on multi-layer network representation learning is implemented.

[0170] Based on the problems existing in the prior art, the present invention proposes a reverse random walk centrality expression method based on multi-layer network representation learning;

[0171] On the one hand, most existing studies still focus on the problem of maximizing influence in single-layer social networks, and there are relatively few studies on multi-layer networks combined with representation learning methods. In order to make up for this gap, this embodiment proposes a reverse random walk centrality expression method based on multi-layer network representation learning to solve the multi-layer influence maximization problem, and simultaneously evaluates the different situations of single influence propagation and multi-influence coupling propagation. On the other hand, in order to learn the information-rich node feature representation in a multi-layer network, the reverse random walk centrality method proposed in the present invention can effectively measure the similarity between nodes and ensure that the reverse random walk captures the influential nodes in the entire multi-way network.

[0172] Finally, in order to verify the prediction effect of the proposed method, the present invention conducted extensive experiments on multiple datasets (Friendfeed, Sanremo2016 and Higgs datasets).

[0173] The experimental process includes the following steps:

[0174] S101, data preparation and data preprocessing;

[0175] S102, design comparison model;

[0176] S103. Conduct experiments to find seed nodes.

[0177] The specific implementation steps are as follows:

[0178] S101. Data preparation and data preprocessing:

[0179] In order to verify the effectiveness of the reverse random walk centrality expression method based on multi-layer network representation learning proposed in the present invention in solving the multi-layer influence maximization problem, the present invention has been experimentally verified on three datasets: Friendfeed, Sanremo2016 and Higgs; these datasets are composed of three-layer networks, and each layer represents a different type of interactive relationship; for example: the Friendfeed dataset consists of the interactive relationships of nodes on the Friendfeed platform, specifically including relationships such as "like", "comment" and "follow". The statistical information of the three datasets is shown in Table 1:

[0180] Table 1 Statistics of the dataset:

[0181]

[0182] S102, design comparison model:

[0183] In order to evaluate the effectiveness of the present invention, a comparison is made with the classic seed node selection algorithm, including the centrality-based method and the embedding-based method; the specific benchmark models determined are as follows: Degree centrality (DC), DC measures the number of directly adjacent nodes of a node, and intuitively reflects the importance of the node according to the direct connectivity of the node in the network; Betweenness centrality (BC), BC measures the number of times a node serves as a bridge for the shortest path between two other nodes; k-shell coefficient (KS), KS is a coarse-grained node importance classification method; Eigenvector centrality (EC), EC believes that the importance of a node depends on both the number of its neighboring nodes and the importance of its neighboring nodes; PageRank Centrality (PG), PG is the key technology behind Google's web page ranking, and its basic concept is that the importance of a web page depends on the number of other web pages linked to it, as well as the quality or importance of those linked web pages; Sequential seeding (SS, sequential seeding), SS is a node sequence selection strategy in multi-layer networks; Randomwalkcentrality (RW, random walk centrality), RW is a traditional random walk method; DeepIM, DeepIM method uses graph embedding technology to solve the problem of maximizing influence; RMNE_R, RMNE_R combines the RMNE method with the DeepIM method; RMNE_C, RMNE_C is a method that combines the RMNE method with K-means clustering. The RMNE method includes three variants, namely RMNE_motif, RMNE_wl, RMNE_degree methods; therefore, the corresponding two methods have a total of 6 variants: RMNE_motif_R, RMNE_motif_C, RMNE_wl_R, RMNE_R_C, RMNE_degree_R, RMNE_degree_C.

[0184] S103. Conduct experiments to find seed nodes:

[0185] This experiment evaluates the effectiveness of the RRW method proposed in this invention on multiple data sets, and considers both single influence propagation and multi-influence coupled propagation. For the RRW method, the number of walks is set to K=5, and the walk length is set to Le=5.

[0186] First, for the single influence propagation results, the experimental results are as follows Figure 4 , Figure 5 and Figure 6 shown. Figure 4 The influence propagation results of the MIC model and the MLT model on the Friendfeed dataset are shown; Figure 5 The influence propagation results of the MIC model and the MLT model on the Sanremo2016 dataset are shown; Figure 6 The results of the influence propagation of the MIC model and the MLT model on the Higgs dataset are shown. In the three result figures, the left column ((a), (c)) compares the RRW method with the centrality-based comparison method, while the right column ((b), (d)) compares the RRW method with the embedding-based method and the traditional random walk method (RW). Due to the limited propagation range of the DeepIM method, its results are not included in the figure for the convenience of presentation. Figure 4 In order to ensure that the experimental results of other methods are more clearly presented. The experimental results show that the RRW method proposed in this paper outperforms other comparison methods on the three data sets and shows the best overall performance.

[0187] Secondly, for the multi-influence coupling propagation results, the experimental results are as follows Figure 7 , Figure 8 and Fig. 9 shown. Figure 7 , Figure 8 and Fig. 9 The influence propagation results of CCMIC model and CCMLT model on Friendfeed dataset, Sanremo2016 dataset and Higgs dataset are shown respectively. Taking into account the competition and complementary relationship between different layers, the influence coefficients between different layers in CCMIC model and CCMLT model are set as: λ1=λ2=γ2=α1=0.5,γ1=α2=1.5,w0=w1=w2=w′0=w′1=w′2=0.5. For the propagation of competitive information and cooperative information, 10 nodes are randomly selected to be activated in the initial stage. Experimental results show that the RRW method proposed in this invention always performs best on all datasets under the condition of multi-influence coupling propagation. The running time results are shown in the figure. Fig.10 As shown, Fig.10 The X in the figure indicates that the running time exceeds 24 hours. It can be seen that the running efficiency of the RRW method proposed in the present invention is the best compared with most methods.

[0188] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0189] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination thereof. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product. Those skilled in the art may appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in this embodiment may be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0190] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0191] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application.

Claims

1. A reverse random walk centrality expression method based on multi-layer network representation learning, characterized in that: The specific steps include: S1. Obtain urban energy consumption and traffic congestion data of urban areas corresponding to multi-layer social network nodes, extract embedded features of multi-layer social network nodes, and calculate the initialization association weights between nodes, and use the urban energy consumption and traffic congestion data to adjust the initialization association weights between nodes; S2, perform reverse random walk according to the adjusted inter-node weights, and record all visited nodes to form a candidate node set; S3. Count the number of visits to each node in the candidate node set, and select the top-k nodes with the most visits as the most influential seed node set in the multi-layer network, thereby solving the problem of maximizing the influence of the multi-layer network.

2. The reverse random walk centrality expression method based on multi-layer network representation learning according to claim 1 is characterized by: Extracting embedded features of multi-layer social network nodes includes the following steps: S11. Construct a multi-layer social network structure; S12. Extracting embedded features from multi-layer social network structures.

3. The reverse random walk centrality expression method based on multi-layer network representation learning according to claim 2 is characterized by: When constructing a multi-layer social network structure in S11, the following single influence propagation model and multi-influence coupling propagation model are considered respectively; Description of the single influence propagation model: Given a Multi-layer social network, is a positive integer greater than 1; if the node u corresponding to the node feature of any layer in the multi-layer social network structure is activated, then the node u in other The corresponding nodes in the layer will also be transformed into the active state; Subsequently, the influence caused by node u will continue to spread according to the different diffusion models of each layer of the network structure until no new nodes are activated, and the influence propagation process stops; The process of node activation and influence propagation can be divided into the following two cases: Multi-layer independent cascade model and multi-layer linear threshold model; Explanation of the multi-influence coupled propagation model in a multi-layer network: Consider the competition and cooperation information between different network layers; competition information inhibits the propagation of target information between nodes, while cooperation information promotes the propagation of target information, as follows: A three-layer social network is set up, where L0 is the target layer, L1 and L2 are the competition layer and the cooperation layer respectively; the mutual influence relationship between different layers is calculated to adjust the activation probability of node u to node v, where node v is a node different from node u.

4. The reverse random walk centrality expression method based on multi-layer network representation learning according to claim 3 is characterized by: The multi-layer network influence maximization problem is defined as follows: Given a containing Multi-layer social network and an influence propagation model σ and a node set of size k; where, represents the set of all nodes in a multi-layer social network, ε represents the set of edges between different nodes, Indicates the number of network layers; The goal of the multi-layer network influence maximization problem is to select an optimal node set with a maximum value of k nodes. To maximize the multi-layer social network The influence propagation process in , namely: Among them, (S) represents the selected node set, which is a subset of k nodes. The goal is to maximize the effect of influence propagation by selecting these nodes; (S * ) represents a potential optimal node set, which is also a subset containing k nodes; σ is a function of the influence propagation model defined in a multi-layer social network, which includes different cases of a single influence propagation model and a multi-influence coupling propagation model; argmax means obtaining the independent variable that maximizes the function that affects the propagation model.

5. The reverse random walk centrality expression method based on multi-layer network representation learning according to claim 4 is characterized in that: S12 extracts embedded features from multi-layer social network structures, including: The RMNE method is used to learn the node feature representation in the multi-layer social network structure to obtain embedded features; Node feature representation includes: node proximity and structural role information. The specific process is as follows: Among them, RMNE(·) is the mapping function of RMNE; Represents the feature representation of node u in the l-th layer of the social network structure, and l is the index of the network layer number.

6. The reverse random walk centrality expression method based on multi-layer network representation learning according to claim 5 is characterized by: Calculate the similarity between different nodes based on embedded features, including: Calculate the cosine similarity between different nodes to obtain the initial association weight value of each edge in each network layer; the specific process is as follows: Among them, cossim(·) is the mapping function of cosine similarity; w l (u,v) represents the similarity between nodes u and v in the l-th layer network structure, that is, the initialization association weight of the edge between the two nodes.

7. The reverse random walk centrality expression method based on multi-layer network representation learning according to claim 6 is characterized in that: Using urban energy consumption and traffic congestion data, the initial association weights between nodes are adjusted, including: Based on the existing social-logistics network, urban energy consumption and traffic congestion data are introduced for simulation experiments, and these data are converted into new indicators that can be combined with the original network edge weights; the original network edge weights are the initialization association weights wl(u,v) of the edge between nodes u and v; Obtain energy consumption statistics for each city area within a set time window from the monitoring system of the city power grid company or transmission and substation; The energy consumption data format is: {(t,η1j)|t∈{1,2,…,T1},j∈{1,2,…,M}}; (t,η1j) represents the energy consumption data of urban area j in time period t; T1 represents the total number of time periods; j represents the index of urban area j, and M represents the total number of urban areas; energy consumption data includes but is not limited to electricity consumption; Based on the urban traffic management platform or roadside sensors and vehicle network data, obtain real-time road network congestion level data for each urban area; The format of real-time road network congestion level data is: {(t,η2j)|t∈{1,2,…,T1},j∈{1,2,…,M}}; (t,η2j) represents the traffic congestion data of urban area j in time period t; Get the similarity between nodes u and v in the l-th layer network structure, that is, the initialization association weight wl(u,v) of the edge between the two nodes; Coordinate mapping or area mapping of network nodes to urban areas corresponding to energy consumption and traffic data; If the network nodes span multiple regions, the region where the main part of the network nodes is located will be used as the basis; Define the energy consumption indexes of nodes u and v in urban area j as η1(u)j and η1(v)j respectively; use the cosine similarity calculation method to calculate the similarity between nodes u and v regarding the energy consumption index, and obtain Sim(η1(u)j,η1(v)j); Define the traffic congestion indexes of nodes u and v in urban area j as η2(u)j and η2(v)j respectively; use the cosine similarity calculation method to calculate the similarity of traffic congestion index between nodes u and v, and obtain Sim(η2(u)j,η2(v)j); On the basis of the original network edge weight wl(u,v), add an adjustment factor δ, 0.1≤δ≤0.5; w′ l ′(u,v)=w l (u,v)·[1+δ·Sim(η1(u) j ,η1(v) j )·Sim(η2(u) j ,η2(v) j )] Where w′l′(u,v) is the output value of the adjusted initial association weight of the edge between nodes u and v. When the energy consumption index and traffic congestion index of two nodes are highly similar, w′l′(u,v) will be numerically amplified to highlight such potential highly associated nodes. Write the corrected edge weights w′l′(u,v) into a new network representation or database to prepare for the subsequent random walk analysis algorithm.

8. The reverse random walk centrality expression method based on multi-layer network representation learning according to claim 7 is characterized in that: Performing a reverse random walk based on the adjusted inter-node weights and selecting the top-k nodes with the most visits as the most influential seed node set in the multi-layer network includes the following steps: S21. Reverse all directed edges in the entire multi-layer network structure: In order to perform a reverse random walk in a multi-layer network structure, it is necessary to reverse all the initial directed edges in the entire multi-layer network structure. The specific process is as follows: Among them, ReversedAllEdges{·} is the operation function of reversing directed edges, ε′ represents the reversed directed edges, Represents the inverted multi-layer social network; S22, perform a reverse random walk, specifically: Given a node u, a reverse random walk is performed K times starting from node u, with each walk length being Le; the reverse random walk method is referred to as RRW below; RRW uses the cosine similarity between nodes to measure the weights between the same nodes in different layers. The specific formula is as follows: Where f(u) and f(v) are the feature representations of nodes u and v respectively; RRW uses biased sampling based on the edge weights between nodes to determine the node that the current node will visit in the next step; d is the dimension of the node feature representation, that is, the representation of each node in the feature space is a d-dimensional vector, i represents the i-th element in the feature vector, which is used to represent the specific dimension index in the node feature; The number of visits to all nodes returned by the reverse random walk method is counted, and each node is sorted in descending order according to its number of visits. The specific process is as follows: counts=CountingAndSorted(walks) Among them, CountingAndSorted(·) is the counting and descending sorting operation function, walks is the set of all nodes returned by the reverse random walk method, and counts represents the number of visits to each node; According to the number of visits to each node in the reverse random walk sequence, the first k nodes are selected as the seed nodes with the greatest influence. The specific process is as follows: S = top-k (counts) Where top-k(·) represents the first k nodes in the candidate node set, and S is the seed node set with the greatest influence.

9. A reverse random walk centrality expression system based on multi-layer network representation learning, characterized by: The system is used to execute the reverse random walk centrality expression method based on multi-layer network representation learning according to any one of claims 1 to 8, comprising: Initialization association weight determination module: used to obtain urban energy consumption and traffic congestion data of urban areas corresponding to multi-layer social network nodes, extract embedded features of multi-layer social network nodes, and calculate the initialization association weights between nodes, and use urban energy consumption and traffic congestion data to adjust the initialization association weights between nodes; Reverse random walk module: used to perform reverse random walk according to the adjusted inter-node weights and record all visited nodes to form a candidate node set; Seed node set determination module: used to count the number of visits to each node in the candidate node set, and select the top-k nodes with the most visits as the most influential seed node set in the multi-layer network, thereby solving the problem of maximizing the influence of the multi-layer network.

10. A readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it implements the reverse random walk centrality expression method based on multi-layer network representation learning as described in any one of claims 1 to 8.

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