A multi-layer network link prediction method, system and device

Abstract

The present application belongs to the field of computer science and specifically discloses a link prediction method, system and device for a multi-layer network. The method includes: representing each node in the target layer and each auxiliary layer as a low-dimensional continuous vector; calculating the first inter-layer Wasserstein distance based on the low-dimensional continuous vector of each node in the target layer; calculating the second inter-layer Wasserstein distance based on the low-dimensional continuous vector of each node in the auxiliary layer; symmetrically averaging the first and second inter-layer Wasserstein distances of each node to determine the inter-layer similarity between the auxiliary layer and the target layer; determining the Wasserstein distance between any two nodes in the target layer and the auxiliary layer based on the probability distribution of the first and fourth context neighbor vectors of each node in the target layer, and determining the intra-layer similarity of any two nodes; and performing link prediction on the multi-layer network based on the intra-layer similarity of any two nodes in each layer and the inter-layer similarity between each auxiliary layer and the target layer. Through the present application, more universal multi-layer network link prediction can be achieved.

Description

Technical Field

[0001] The present application relates to the field of computers, and more specifically, to a link prediction method, system, and device for a multi-layer network. Background Art

[0002] Research on link prediction in multi-layer networks has important theoretical and practical implications. In most complex systems, the same node often possesses multiple functions and attributes, participating in a variety of interactions, connections, and effects, forming a multi-layer network. Compared to single-layer networks, multi-layer networks can more comprehensively depict real-world complex systems. Research has shown that the formation and evolution of the network topology of a single layer in a multi-layer network is influenced by the topology of other layers. Therefore, how to leverage the topological characteristics of multi-layer networks, while focusing on intra-layer features while also considering the influence of inter-layer features, to improve the performance of link prediction in multi-layer networks is a currently worthy research topic.

[0003] Link prediction technology for single-layer networks is relatively mature and has been widely applied in various fields. However, there is still considerable room for research on link prediction in multi-layer networks. Current methods for link prediction in multi-layer networks are mostly extensions of single-layer methods. In addition, there are also model-based methods and machine learning-based methods. Extensions based on single-layer methods primarily determine the importance of the auxiliary layer to the target layer by analyzing the association between the auxiliary layer and the target layer. Link prediction for the target layer is then performed by combining the intra-layer features of the auxiliary layer, the inter-layer associations between the auxiliary layer and the target layer, and the intra-layer features of the target layer. Model-based methods utilize random block models, GCN-GAN models, and other models to model the affiliation of nodes in different layers, thereby predicting intra-layer and inter-layer links. Machine learning-based methods focus on feature extraction. Based on the extraction of inter-layer and intra-layer features of the auxiliary layer and the intra-layer features of the target layer, machine learning algorithms such as naive Bayes, logistic regression, and decision trees are used to perform a binary classification of link presence or absence, thereby completing link prediction.

[0004] However, there is still a lack of algorithm designs specifically for multi-layer network link prediction. Even the application of methods based on model building and machine learning in the field of link prediction has just begun. The established models and extracted features are subject to strong human intervention and still deserve in-depth research to improve their applicability in practical applications. At the same time, most predictions and analyses are still biased towards social networks, with fewer data sets and relatively simple samples. They are highly specific and less scalable, and the proposed methods are difficult to extend to other networks. Patent document CN116743620A, targeting the cold start problem of social software, proposes a link prediction method for social multiplexing networks. It outputs the link labels of the auxiliary layer network topology by fusing the fused link information of the multi-layer network topology. However, this method mainly focuses on the characteristics of social temporal networks and lacks universal value. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the purpose of this application is to provide a link prediction method, system and equipment for multi-layer networks, aiming to solve the problem of deviation in measuring the similarity between multi-layer networks and the similarity within the node layer by relying on single network indicators such as global network characteristics or local network characteristics.

[0006] To achieve the above objectives, in a first aspect, the present application provides a link prediction method for a multi-layer network, wherein the multi-layer network includes a target layer and at least one auxiliary layer, wherein the target layer and the auxiliary layer have the same node set, and the method includes:

[0007] Represent each node in the target layer and each auxiliary layer as a low-dimensional continuous vector;

[0008] Based on the low-dimensional continuous vector of each node in the target layer, the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer are determined to calculate the first-layer Wasserstein distance of each node; based on the low-dimensional continuous vector of each node in the auxiliary layer, the probability distribution of the third context neighbor vector and the fourth context neighbor vector of each node in the target layer and the auxiliary layer are determined respectively to calculate the second-layer Wasserstein distance of each node; the first-layer Wasserstein distance and the second-layer Wasserstein distance of each node are symmetrically averaged to determine the inter-layer similarity between the corresponding auxiliary layer and the target layer;

[0009] Determine the Wasserstein distance between any two nodes in the target layer based on the probability distribution of the first context neighbor vector of each node in the target layer, determine the Wasserstein distance between any two nodes in the auxiliary layer based on the probability distribution of the fourth context neighbor vector of each node in the auxiliary layer, and determine the intra-layer similarity between any two nodes in the corresponding layer based on the Wasserstein distance between any two nodes in the target layer or the auxiliary layer;

[0010] Link prediction is performed on the multi-layer network according to the intra-layer similarity of any two nodes in each layer and the inter-layer similarity between each auxiliary layer and the target layer.

[0011] It should be noted that for the similarity between layers of a multi-layer network, existing studies have adopted local network features, such as degree correlation coefficient, average neighbor overlap and other indicators to measure the measurement, or adopted global network features, such as average node importance correlation (betweenness centrality) and other indicators to measure. However, on the one hand, degree correlation coefficient, average neighbor overlap and the like cannot fully reflect the local network characteristics of the node, and average node betweenness centrality and the like cannot fully reflect the global network characteristics of the node, which will cause measurement deviation; on the other hand, only using local network features or global network features will also cause feature deviation. The present application can achieve a balance between global and local features by representing each node as a low-dimensional continuous vector, and then calculate the Wasserstein distance between nodes through the probability distribution of the node's neighbor vector, which can unbiasedly calculate the similarity of the nodes and realize unbiased prediction of multi-layer network links.

[0012] Specifically, the above-mentioned multi-layer network link prediction method can be applied to multi-layer social network link prediction, multi-layer protein interaction network link prediction, multi-layer transportation network link prediction, etc.

[0013] In an optional example, each node in the target layer and each auxiliary layer is represented as a low-dimensional continuous vector based on the Node2Vec biased random walk sampling algorithm.

[0014] It can be understood that the Node2Vec biased random walk algorithm uses a low-dimensional vector representation for each node based on each network layer of the multi-layer network, and uses biased random walks to obtain the node's contextual neighbor distribution at each network layer, thereby achieving a low-dimensional continuous vector representation of the node's contextual neighbor distribution at each network layer. By representing nodes with low-dimensional continuous vectors, on the one hand, the network characteristics of the nodes can be preserved, and on the other hand, the distribution of node neighbors can be represented as a probability distribution in a low-dimensional continuous space, thereby achieving an unbiased measure of node context similarity.

[0015] In an optional example, determining a first context neighbor vector probability distribution and a second context neighbor vector probability distribution of each node in the target layer and the auxiliary layer based on a low-dimensional continuous vector of each node in the target layer includes:

[0016] Based on the Node2Vec biased random walk sampling algorithm, a biased random walk is performed on each node on the target layer or auxiliary layer to obtain the contextual neighbor distribution of each node on the target layer or auxiliary layer.

[0017] Determine the probability distribution of the first context neighbor vector of each node in the target layer by combining the low-dimensional continuous vector of each node in the target layer and the proportion of the number of occurrences of each node in the context neighbor distribution of each node in the target layer;

[0018] Determine the probability distribution of the second context neighbor vector of each node in the auxiliary layer by combining the low-dimensional continuous vector of each node in the target layer and the proportion of the number of occurrences of each node in the context neighbor distribution of each node in the auxiliary layer; and / or

[0019] Based on the low-dimensional continuous vector of each node in the auxiliary layer, the probability distribution of the third context neighbor vector and the probability distribution of the fourth context neighbor vector of each node in the target layer and the auxiliary layer are determined respectively, including:

[0020] Based on the Node2Vec biased random walk sampling algorithm, a biased random walk is performed on each node on the target layer or auxiliary layer to obtain the contextual neighbor distribution of each node on the target layer or auxiliary layer.

[0021] Determine the probability distribution of the third context neighbor vector of each node in the target layer by combining the low-dimensional continuous vector of each node in the auxiliary layer and the proportion of the occurrence of each node in the context neighbor distribution of each node in the target layer;

[0022] The probability distribution of the fourth context neighbor vector of each node in the auxiliary layer is determined by combining the low-dimensional continuous vector of each node in the auxiliary layer and the proportion of the occurrence of each node in the context neighbor distribution of each node in the auxiliary layer.

[0023] In an optional example, the first inter-layer Wasserstein distance is determined by the following steps:

[0024] Determine an embedding vector at a corresponding layer for each node that appears in the first context neighbor vector probability distribution and the second context neighbor vector probability distribution;

[0025] Determining the first inter-layer Wasserstein distance by combining the difference in the proportion of occurrences of each node between the first context neighbor vector probability distribution and the second context neighbor vector probability distribution, and the distance between the embedding vectors of nodes with different proportions of occurrences; and / or

[0026] The second inter-layer Wasserstein distance is determined by the following steps:

[0027] Determine an embedding vector at a corresponding layer for each node appearing in the third context neighbor vector probability distribution and the fourth context neighbor vector probability distribution;

[0028] Determine the second inter-layer Wasserstein distance by combining the difference in the proportion of occurrences of each node between the third context neighbor vector probability distribution and the fourth context neighbor vector probability distribution, and the distance between the embedding vectors of nodes with different proportions of occurrences; and / or

[0029] The Wasserstein distance between any two nodes in the target layer or auxiliary layer is determined by the following steps:

[0030] Determine the embedding vector of each node in the target layer that appears in the probability distribution of the first context neighbor vector of each node in the target layer;

[0031] Determine the Wasserstein distance between any two nodes in the target layer by combining the difference in the proportion of occurrences of each node between the probability distributions of the first context neighbor vectors of any two nodes in the target layer and the distance between the embedding vectors of nodes with different proportions of occurrences;

[0032] Determine an embedding vector in the auxiliary layer for each node that appears in the probability distribution of the fourth context neighbor vector of each node in the auxiliary layer;

[0033] The Wasserstein distance between any two nodes in the auxiliary layer is determined by combining the difference in the proportion of the number of occurrences of each node between the probability distributions of the fourth context neighbor vectors of any two nodes in the auxiliary layer and the distance between the embedding vectors of nodes with different proportions of the number of occurrences.

[0034] In an optional example, the intra-layer similarity of any two nodes is determined by the following steps:

[0035] Determine the maximum and minimum Wasserstein distances between any two nodes in the target layer or auxiliary layer;

[0036] Combined with the maximum and minimum values ​​of the Wasserstein distance in the target layer or the auxiliary layer, the Wasserstein distance between any two nodes in the corresponding layer is normalized to obtain the intra-layer similarity of any two nodes in the target layer or the auxiliary layer.

[0037] In an optional example, the inter-layer similarity is determined by the following steps:

[0038] Determine the maximum and minimum values ​​of the Wasserstein distance between the first layer or the Wasserstein distance between the second layer of all nodes;

[0039] Combining the maximum and minimum values ​​of the first-layer Wasserstein distances, the first-layer Wasserstein distances of each node are normalized to obtain the first-layer similarity of each node;

[0040] Combining the maximum and minimum values ​​of the second-layer Wasserstein distance, the second-layer Wasserstein distance of each node is normalized to obtain the second-layer similarity of each node;

[0041] The first-layer similarity and the second-layer similarity of each node between the target layer and the auxiliary layer are summed and averaged to obtain the inter-layer similarity between the corresponding auxiliary layer and the target layer.

[0042] In an optional example, the normalization is specifically: the ratio of the difference between the corresponding maximum value and the corresponding minimum value after subtracting the corresponding minimum value from the Wasserstein distance;

[0043] Subtract the normalized value from 1 to obtain the corresponding similarity.

[0044] In an optional example, performing link prediction on the multi-layer network includes:

[0045] The probability of any two nodes forming an edge in the target layer is predicted based on the intra-layer similarity of any two nodes in the target layer, the intra-layer similarity of any two nodes in the auxiliary layer, the product of the inter-layer similarity between the auxiliary layer and the target layer, and the preset intra-layer and inter-layer similarity adjustment parameters;

[0046] Determine the ranking of the probability of forming an edge between any two nodes in the target layer; and use the node pairs with the highest ranking as the link prediction result.

[0047] In a second aspect, the present application provides a link prediction system for a multi-layer network, wherein the multi-layer network includes a target layer and at least one auxiliary layer, wherein the target layer and the auxiliary layer have the same node set, and the system includes:

[0048] A low-dimensional vector representation module is used to represent each node in the target layer and each auxiliary layer as a low-dimensional continuous vector;

[0049] An inter-layer similarity determination module is configured to determine the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the target layer, so as to calculate the first inter-layer Wasserstein distance of each node; determine the probability distribution of the third context neighbor vector and the fourth context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the auxiliary layer, so as to calculate the second inter-layer Wasserstein distance of each node; and perform symmetrical averaging of the first inter-layer Wasserstein distance and the second inter-layer Wasserstein distance of each node to determine the inter-layer similarity between the corresponding auxiliary layer and the target layer;

[0050] The intra-layer similarity determination module is used to determine the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the target layer, so as to calculate the first inter-layer Wasserstein distance of each node; based on the low-dimensional continuous vector of each node in the auxiliary layer, determine the probability distribution of the third context neighbor vector and the fourth context neighbor vector of each node in the target layer and the auxiliary layer respectively, so as to calculate the second inter-layer Wasserstein distance of each node; symmetrically average the first inter-layer Wasserstein distance and the second inter-layer Wasserstein distance of each node to determine the inter-layer similarity between the corresponding auxiliary layer and the target layer;

[0051] The link prediction module is used to perform link prediction on the multi-layer network based on the intra-layer similarity of any two nodes in each layer and the inter-layer similarity between each auxiliary layer and the target layer.

[0052] In a third aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any optional example of the first aspect.

[0053] In a fourth aspect, the present application provides a computer-readable storage medium storing a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any optional example of the first aspect.

[0054] In a fifth aspect, the present application provides a computer program product. When the computer program product runs on a processor, it enables the processor to execute the method described in the first aspect or any optional example of the first aspect.

[0055] It can be understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0056] In general, the above technical solutions conceived by this application have at least the following beneficial effects compared with the prior art:

[0057] The present application provides a link prediction method, system and device for a multi-layer network. Through the Node2Vec biased random walk sampling algorithm, a low-dimensional vector representation is performed for each node based on each network layer of the multi-layer network, and the context neighbor distribution of the node in each network layer is obtained by biased random walk, thereby realizing a low-dimensional continuous vectorized representation of the context neighbor distribution of the node in each network layer. Based on the low-dimensional continuous vectorized representation of the context neighbor distribution of the node in each layer of the network, the present application uses the Wasserstein distance to unbiasedly calculate the distance between the context neighbor vector distributions of the node pair, the intra-layer distance of each network layer, and further calculates the intra-layer similarity of the node pair in each network layer. For the inter-layer similarity between the target layer and a certain auxiliary layer, combined with the context neighbors of the node in the target layer and the auxiliary layer, the Node2Vec biased random walk sampling algorithm is used based on the low-dimensional continuous vectorized representation of the target layer network and the low-dimensional continuous vectorized representation based on the auxiliary layer network, and the Wasserstein distance is further used to calculate the distance based on the context neighbor distribution of the target layer and the distance based on the context neighbor distribution of the auxiliary layer vector, forming a symmetrical inter-layer distance and calculating the inter-layer similarity.

[0058] This application is based on each layer of the network, uses Node2Vec to represent the nodes with low-dimensional continuous vectors, and then samples the node context through the Node2Vec biased random walk sampling algorithm to represent the node context probability distribution, and calculates the node inter-layer similarity and intra-layer similarity based on the Wasserstein distance. The Node2Vec biased random walk can achieve a balance between global network characteristics and local network characteristics, and realize unbiased measurement of the global network characteristics and local network characteristics of the nodes. Through symmetric processing, it can achieve accurate characterization of the similarity between layers of multi-layer complex networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a flow chart of a link prediction method for a multi-layer network provided by an embodiment of the present application;

[0060] Figure 2 This is a flow chart of inter-layer similarity calculation provided by an embodiment of the present application;

[0061] Figure 3 This is a comparison chart of the accuracy of the method of the present application and the existing method provided in the embodiments of the present application;

[0062] Figure 4 This is a comparison chart of the F1 index of the method of the present application and the existing method provided in the examples of the present application;

[0063] Figure 5 This is a diagram of the link prediction system architecture of a multi-layer network provided by an embodiment of the present application;

[0064] Figure 6 This is an electronic device architecture diagram provided in an embodiment of the present application. DETAILED DESCRIPTION

[0065] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0066] The term "and / or" as used herein describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. The symbol " / " as used herein indicates that the related objects are in an "or" relationship, for example, A / B means either A or B.

[0067] In the specification and claims herein, the terms "first" and "second" are used to distinguish different objects rather than to describe a specific order of objects. For example, the first inter-layer Wasserstein distance and the second inter-layer Wasserstein distance are used to distinguish different inter-layer Wasserstein distances rather than to describe a specific order of inter-layer Wasserstein distances.

[0068] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0069] First, the technical terms involved in the embodiments of this application are introduced.

[0070] (1) Wasserstein distance

[0071] Wasserstein distance refers to the minimum cost required to transition from one probability distribution to another in terms of the probability movement distance.

[0072] (2) Multi-layer network

[0073] In a multi-layer network, the target layer typically refers to the network layer whose links we want to predict, while the auxiliary layers refer to other network layers that may provide useful information for predicting the links in the target layer. In the study of link prediction in multi-layer networks, researchers often consider how to use the information in the auxiliary layers to improve the accuracy of link prediction in the target layer. This is because in a multi-layer network, nodes and edges between different layers may have certain correlations. The information in the auxiliary layers can serve as additional features or data sources to help us better understand and predict link formation in the target layer.

[0074] (3) Link Prediction

[0075] Link prediction refers to predicting new edges that may appear in the network in the future or identifying edges that are currently missing in the network but potentially exist.

[0076] Next, the technical solutions provided in the embodiments of this application are introduced.

[0077] This application proposes a link prediction method, system and device for a multi-layer network. For a multi-layer network, link prediction is performed on the network target layer by combining inter-layer features of the network auxiliary layer with intra-layer features of the network auxiliary layer and the network target layer. First, the Node2Vec biased random walk sampling algorithm (hereinafter referred to as the Node2Vec algorithm) is used to represent each node with a low-dimensional continuous vector based on the network topology of each layer. Second, a biased random walk is performed on each node in each layer to obtain the contextual neighbor distribution of each node in each layer. The low-dimensional continuous vector representation of the node in each layer and the context node distribution of the node in each layer are combined to obtain the low-dimensional continuous vector distribution of the context node distribution of each node pair in the layer. The distance between the context vector distributions of the node pair is calculated using the Wasserstein distance, and the intra-layer similarity of the node pair is calculated. Then, the distance between the context vector distributions of the node in the target layer and the auxiliary layer is calculated using the Wasserstein distance. The average distance between the context node distributions of all nodes in the target layer and the auxiliary layer is further calculated to calculate the inter-layer similarity between the target layer and each auxiliary layer. Finally, based on the intra-layer similarity of the target layer, the intra-auxiliary layer similarity, and the inter-layer similarity between the target layer and the auxiliary layer, multi-layer network link prediction is performed.

[0078] Figure 1 is a flow chart of a link prediction method for a multi-layer network provided by an embodiment of the present application; the multi-layer network includes a target layer and at least one auxiliary layer, and the target layer and the auxiliary layer have the same node set, such as Figure 1 As shown, the following steps are included:

[0079] Step S101, representing each node in the target layer and each auxiliary layer as a low-dimensional continuous vector;

[0080] Step S102: Based on the low-dimensional continuous vector of each node in the target layer, determine the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer to calculate the first inter-layer Wasserstein distance of each node; based on the low-dimensional continuous vector of each node in the auxiliary layer, determine the probability distribution of the third context neighbor vector and the fourth context neighbor vector of each node in the target layer and the auxiliary layer respectively to calculate the second inter-layer Wasserstein distance of each node; symmetrically average the first inter-layer Wasserstein distance and the second inter-layer Wasserstein distance of each node to determine the inter-layer similarity between the corresponding auxiliary layer and the target layer;

[0081] Step S103: Determine the Wasserstein distance between any two nodes in the target layer based on the probability distribution of the first context neighbor vector of each node in the target layer, determine the Wasserstein distance between any two nodes in the auxiliary layer based on the probability distribution of the fourth context neighbor vector of each node in the auxiliary layer, and determine the intra-layer similarity between any two nodes in the corresponding layer based on the Wasserstein distance between any two nodes in the target layer or the auxiliary layer;

[0082] Step S104 , performing link prediction on the multi-layer network according to the intra-layer similarity between any two nodes in each layer and the inter-layer similarity between each auxiliary layer and the target layer.

[0083] In a specific embodiment, this application first proposes a mathematical symbolic representation of a multi-layer network with the same nodes. Secondly, the technology proposed in this application is described from three parts: inter-layer similarity measurement, intra-layer node similarity measurement, and link prediction. Finally, the data source selected to verify this technology is described in detail.

[0084] 1. Multi-layer network representation

[0085] The technical solution proposed in this application is applied to a multi-layer network with the same nodes. The edges between nodes in each layer represent different association relationships. The multi-layer network is defined as There are N layers in total, where G T =(V T ,E T ) is the target layer; the remaining layers are auxiliary layers and can be used with G A =(V A ,E A ) means A=1,2,…N-1. At the same time, V=(v1,v2…v n) represents the set of nodes on the network (the same in each layer), that is, |V T |=|V A |; and E T and E A Represent the target layer G T and auxiliary layer G A The set of middle edges.

[0086] 2. Low-dimensional continuous vector representation of nodes based on Node2Vec

[0087] To achieve a comprehensive and fine-grained representation of node context distribution, this application uses the Node2Vec algorithm to embed each node into a low-dimensional continuous vector space based on the network topology characteristics of each layer. The Node2Vec algorithm considers the following two phenomena in network structure: homogeneity and structural similarity. Through semi-supervised network learning, the Node2Vec algorithm can obtain the optimal parameters p and q, achieving an optimal balance in the sampling strategy, thereby comprehensively considering the structural information present in the network.

[0088] 3. Intra-layer node similarity measurement based on Wasserstein distance

[0089] Wasserstein distance, as a method to measure the distance between two probability distributions, can provide a means for quantifying the similarity of node neighbor distributions for this application. This application measures the distance between nodes i and j by measuring the Wasserstein distance between the vector distributions of the contextual neighbor distributions of node pair (i, j) at a specific network layer. The contextual neighbor distribution of node i at a specific network layer can be obtained by a biased random walk of Node2Vec, which constitutes a second-order Markov chain, where the transition probability p i→j (t) depends only on the node i visited at the current time t and the nodes visited at the previous time step t-1. By adjusting the parameter value, it is possible to balance local and global search in the network, thereby balancing the consideration of low-order and high-order neighbors.

[0090] For example, in this application, the target layer G T Perform five steps of biased random walk on node pairs i and j to obtain their contextual neighbor distribution: Each node i is based on the target layer G T The Node2Vec algorithm can be used to represent it as a low-dimensional continuous vector And based on any auxiliary layer G A , using the Node2Vec algorithm to represent it as a low-dimensional continuous vector At the same time, nodes i and j are in the target layer G T The contextual neighbor distribution in the target layer G TThe vector probability distribution representations are and Assume that based on the target layer G T The embedding vectors of nodes a, b and c Then G T superior and The Wasserstein distance between

[0091] Based on the target layer GT, the minimum and maximum Wasserstein distances of any node pair in the vector space are MinD VecGT and MaxD VecGT , this application normalizes the Wasserstein distance of the node pair (i, j) based on the minimum and maximum Wasserstein distances mentioned above, and defines the target layer G T The intra-layer similarity of the previous node pair (i, j) as follows:

[0092]

[0093] 4. Inter-layer similarity based on symmetric average Wasserstein distance

[0094] like Figure 2 As shown, for any node i, let The target layer G T The context neighbors of the node, Represents an auxiliary layer G A As mentioned above, using the Node2Vec algorithm, based on the target layer G T , The node α in can be represented as a low-dimensional continuous vector Similarly, based on the auxiliary layer G A , The node α in can be represented as a low-dimensional continuous vector Therefore, based on G T Perform vector representation by G T Execute Node2Vec biased random walk sampling on it, and you can get The vector probability distribution representation is denoted as Similarly, based on G T Perform vector representation by G A Executing Node2Vec biased random walk sampling on the The vector probability distribution representation is denoted as Based on G A Perform vector representation by G TExecute Node2Vec biased random walk sampling on it, and you can get The vector probability distribution representation is denoted as Similarly, based on G A Perform vector representation by G A Executing Node2Vec biased random walk sampling on the The vector probability distribution representation is denoted as Finally, this application calculates and as well as and The normalized Wasserstein distance between the two is used as the first-layer similarity between the corresponding and the second-level similarity

[0095]

[0096] Therefore, G T and G A The similarity between layers for:

[0097]

[0098] 5. Link Prediction Framework

[0099] Based on the obtained G T and G A Inter-layer similarity and G T and G A The intra-layer node similarity between nodes i and j and Then the probability of these two nodes forming an edge is:

[0100]

[0101] Among them, α is the adjustment parameter of the similarity between layers within the layer. A Similarity between nodes i and j The higher the G A With G T The greater the similarity, the higher the target layer G T China and Vietnam are likely to form this connection.

[0102] Furthermore, after determining the probability of any two nodes forming a connection in the target layer, all probabilities are sorted; the node pairs with the highest ranking are used as link prediction results.

[0103] Specifically, multi-layer network link prediction can be used to predict multi-layer social networks (the same group of nodes in the QQ network, WeChat network, Weibo network, etc.), inter-city transportation networks (aviation, high-speed rail, ordinary trains, etc.), or social support networks (social support network, information support network, emotional support network), etc. For example, in a multi-layer social network, the WeChat network can be used as the target layer, and the QQ network and Weibo network as auxiliary layers. The intra-layer similarity and inter-layer similarity between node pairs can be calculated, and the QQ network and Weibo network features can be used to assist in WeChat network link prediction.

[0104] Figure 3 and Figure 4 This is a comparison chart of the accuracy and F1 index of the method of the present application (abbreviated as PLRWD) provided in the embodiment of the present application and the existing benchmark models CMIS, LPGRI, LPIDE, LPIS, and MLRW methods; Figure 3 and Figure 4 The horizontal axis in the figure represents the number of node pairs recommended by link prediction. It can be seen that the accuracy and F1 index of the method provided by this application are the highest when recommending links in multi-layer networks, and the recommendation effect is the best. The method provided by this application can achieve unbiased measurement of the global network characteristics and local network characteristics of nodes, and through symmetric processing, it can achieve accurate characterization of the similarity between layers of multi-layer complex networks.

[0105] Figure 5 : is a diagram of the link prediction system architecture of a multi-layer network provided by an embodiment of the present application; Figure 5 Shown, including:

[0106] A low-dimensional vector representation module 510 is used to represent each node in the target layer and each auxiliary layer as a low-dimensional continuous vector;

[0107] The inter-layer similarity determination module 520 is configured to determine the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the target layer, so as to calculate the first inter-layer Wasserstein distance of each node; determine the probability distribution of the third context neighbor vector and the fourth context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the auxiliary layer, so as to calculate the second inter-layer Wasserstein distance of each node; and symmetrically average the first inter-layer Wasserstein distance and the second inter-layer Wasserstein distance of each node to determine the inter-layer similarity between the corresponding auxiliary layer and the target layer;

[0108] The intra-layer similarity determination module 550 is configured to determine the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the target layer, so as to calculate the first inter-layer Wasserstein distance of each node; determine the probability distribution of the third context neighbor vector and the fourth context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the auxiliary layer, so as to calculate the second inter-layer Wasserstein distance of each node; and symmetrically average the first inter-layer Wasserstein distance and the second inter-layer Wasserstein distance of each node to determine the inter-layer similarity between the corresponding auxiliary layer and the target layer;

[0109] The link prediction module 540 is configured to perform link prediction on the multi-layer network based on the intra-layer similarity between any two nodes in each layer and the inter-layer similarity between each auxiliary layer and the target layer.

[0110] It should be understood that the above-mentioned system is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the system are similar to those described in the above-mentioned method. The working process of the system can refer to the corresponding process in the above-mentioned method and will not be repeated here.

[0111] Based on the method in the above embodiment, the embodiment of the present application provides an electronic device, such as Figure 6 As shown, the electronic device may include: a processor 610, a communication interface 620, a memory 630, and a communication bus 660, wherein the processor 610, the communication interface 620, and the memory 630 communicate with each other via the communication bus 660. The processor 610 may call the logic instructions in the memory 630 to execute the method in the above embodiment.

[0112] In addition, the logic instructions in the above-mentioned memory 630 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application.

[0113] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0114] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0115] It is understood that the processor in the embodiments of the present application may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0116] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0117] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server or data center to another website, computer, server or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) method. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid state drive (SSD)).

[0118] It will be understood that the various numerical numbers involved in the embodiments of the present application are merely distinctions for the convenience of description and are not intended to limit the scope of the embodiments of the present application.

[0119] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A link prediction method for a multi-layer network, wherein the multi-layer network includes a target layer and at least one auxiliary layer, wherein the target layer and the auxiliary layer have the same node set, characterized in that: Methods include: Represent each node in the target layer and each auxiliary layer as a low-dimensional continuous vector; Based on the low-dimensional continuous vector of each node in the target layer, the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer are determined to calculate the first-layer Wasserstein distance of each node; based on the low-dimensional continuous vector of each node in the auxiliary layer, the probability distribution of the third context neighbor vector and the fourth context neighbor vector of each node in the target layer and the auxiliary layer are determined respectively to calculate the second-layer Wasserstein distance of each node; the first-layer Wasserstein distance and the second-layer Wasserstein distance of each node are symmetrically averaged to determine the inter-layer similarity between the corresponding auxiliary layer and the target layer; Determine the Wasserstein distance between any two nodes in the target layer based on the probability distribution of the first context neighbor vector of each node in the target layer, determine the Wasserstein distance between any two nodes in the auxiliary layer based on the probability distribution of the fourth context neighbor vector of each node in the auxiliary layer, and determine the intra-layer similarity between any two nodes in the corresponding layer based on the Wasserstein distance between any two nodes in the target layer or the auxiliary layer; Link prediction is performed on the multi-layer network according to the intra-layer similarity of any two nodes in each layer and the inter-layer similarity between each auxiliary layer and the target layer.

2. The method according to claim 1, characterized in that Based on the Node2Vec biased random walk sampling algorithm, each node in the target layer and each auxiliary layer is represented as a low-dimensional continuous vector.

3. The method according to claim 1, characterized in that Based on the low-dimensional continuous vector of each node in the target layer, determining the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer, including: Based on the Node2Vec biased random walk sampling algorithm, a biased random walk is performed on each node on the target layer or auxiliary layer to obtain the contextual neighbor distribution of each node on the target layer or auxiliary layer. Determine the probability distribution of the first context neighbor vector of each node in the target layer by combining the low-dimensional continuous vector of each node in the target layer and the proportion of the number of occurrences of each node in the context neighbor distribution of each node in the target layer; Determine the probability distribution of the second context neighbor vector of each node in the auxiliary layer by combining the low-dimensional continuous vector of each node in the target layer and the proportion of the number of occurrences of each node in the context neighbor distribution of each node in the auxiliary layer; and / or Based on the low-dimensional continuous vector of each node in the auxiliary layer, the probability distribution of the third context neighbor vector and the probability distribution of the fourth context neighbor vector of each node in the target layer and the auxiliary layer are determined respectively, including: Based on the Node2Vec biased random walk sampling algorithm, a biased random walk is performed on each node on the target layer or auxiliary layer to obtain the contextual neighbor distribution of each node on the target layer or auxiliary layer. Determine the probability distribution of the third context neighbor vector of each node in the target layer by combining the low-dimensional continuous vector of each node in the auxiliary layer and the proportion of the occurrence of each node in the context neighbor distribution of each node in the target layer; The probability distribution of the fourth context neighbor vector of each node in the auxiliary layer is determined by combining the low-dimensional continuous vector of each node in the auxiliary layer and the proportion of the occurrence of each node in the context neighbor distribution of each node in the auxiliary layer.

4. The method according to claim 1, wherein The first inter-layer Wasserstein distance is determined by the following steps: Determine an embedding vector at a corresponding layer for each node that appears in the first context neighbor vector probability distribution and the second context neighbor vector probability distribution; Determining the first inter-layer Wasserstein distance by combining the difference in the proportion of occurrences of each node between the first context neighbor vector probability distribution and the second context neighbor vector probability distribution, and the distance between the embedding vectors of nodes with different proportions of occurrences; and / or The second inter-layer Wasserstein distance is determined by the following steps: Determine an embedding vector at a corresponding layer for each node appearing in the third context neighbor vector probability distribution and the fourth context neighbor vector probability distribution; Determine the second inter-layer Wasserstein distance by combining the difference in the proportion of occurrences of each node between the third context neighbor vector probability distribution and the fourth context neighbor vector probability distribution, and the distance between the embedding vectors of nodes with different proportions of occurrences; and / or The Wasserstein distance between any two nodes in the target layer or auxiliary layer is determined by the following steps: Determine the embedding vector of each node in the target layer that appears in the probability distribution of the first context neighbor vector of each node in the target layer; Determine the Wasserstein distance between any two nodes in the target layer by combining the difference in the proportion of occurrences of each node between the probability distributions of the first context neighbor vectors of any two nodes in the target layer and the distance between the embedding vectors of nodes with different proportions of occurrences; Determine an embedding vector in the auxiliary layer for each node that appears in the probability distribution of the fourth context neighbor vector of each node in the auxiliary layer; The Wasserstein distance between any two nodes in the auxiliary layer is determined by combining the difference in the proportion of the number of occurrences of each node between the probability distributions of the fourth context neighbor vectors of any two nodes in the auxiliary layer and the distance between the embedding vectors of nodes with different proportions of the number of occurrences.

5. The method according to claim 1, wherein The intra-layer similarity of any two nodes is determined by the following steps: Determine the maximum and minimum Wasserstein distances between any two nodes in the target layer or auxiliary layer; Combined with the maximum and minimum values ​​of the Wasserstein distance in the target layer or the auxiliary layer, the Wasserstein distance between any two nodes in the corresponding layer is normalized to obtain the intra-layer similarity of any two nodes in the target layer or the auxiliary layer.

6. The method according to claim 1, characterized in that The inter-layer similarity is determined by the following steps: Determine the maximum and minimum values ​​of the Wasserstein distance between the first layer or the Wasserstein distance between the second layer of all nodes; Combining the maximum and minimum values ​​of the first-layer Wasserstein distances, the first-layer Wasserstein distances of each node are normalized to obtain the first-layer similarity of each node; Combining the maximum and minimum values ​​of the second-layer Wasserstein distance, the second-layer Wasserstein distance of each node is normalized to obtain the second-layer similarity of each node; The first-layer similarity and the second-layer similarity of each node between the target layer and the auxiliary layer are summed and averaged to obtain the inter-layer similarity between the corresponding auxiliary layer and the target layer.

7. The method according to claim 5 or 6, characterized in that The standardization is specifically: the ratio of the difference between the corresponding maximum and minimum values ​​after subtracting the corresponding minimum value from the Wasserstein distance; Subtract the normalized value from 1 to obtain the corresponding similarity.

8. The method according to claim 1, characterized in that Performing link prediction on the multi-layer network includes: The probability of any two nodes forming an edge in the target layer is predicted based on the intra-layer similarity of any two nodes in the target layer, the intra-layer similarity of any two nodes in the auxiliary layer, the product of the inter-layer similarity between the auxiliary layer and the target layer, and the preset intra-layer and inter-layer similarity adjustment parameters; Determine the ranking of the probability of forming an edge between any two nodes in the target layer; and use the node pairs with the highest ranking as the link prediction result.

9. A link prediction system for a multi-layer network, the multi-layer network comprising a target layer and at least one auxiliary layer, the target layer and the auxiliary layer having the same node set, characterized in that the system include: A low-dimensional vector representation module is used to represent each node in the target layer and each auxiliary layer as a low-dimensional continuous vector; An inter-layer similarity determination module is configured to determine the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the target layer, so as to calculate the first inter-layer Wasserstein distance of each node; determine the probability distribution of the third context neighbor vector and the fourth context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the auxiliary layer, so as to calculate the second inter-layer Wasserstein distance of each node; and perform symmetrical averaging of the first inter-layer Wasserstein distance and the second inter-layer Wasserstein distance of each node to determine the inter-layer similarity between the corresponding auxiliary layer and the target layer; The intra-layer similarity determination module is used to determine the probability distribution of the first context neighbor vector and the second context neighbor vector of each node in the target layer and the auxiliary layer based on the low-dimensional continuous vector of each node in the target layer, so as to calculate the first inter-layer Wasserstein distance of each node; based on the low-dimensional continuous vector of each node in the auxiliary layer, determine the probability distribution of the third context neighbor vector and the fourth context neighbor vector of each node in the target layer and the auxiliary layer respectively, so as to calculate the second inter-layer Wasserstein distance of each node; symmetrically average the first inter-layer Wasserstein distance and the second inter-layer Wasserstein distance of each node to determine the inter-layer similarity between the corresponding auxiliary layer and the target layer; The link prediction module is used to perform link prediction on the multi-layer network based on the intra-layer similarity of any two nodes in each layer and the inter-layer similarity between each auxiliary layer and the target layer.

10. An electronic device, characterized in that: include: at least one memory for storing a computer program; At least one processor is used to execute the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method according to any one of claims 1 to 8.

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