A multi-scale link prediction method and system based on hierarchical link patterns

Abstract

The present application discloses a multi-scale link prediction method and system based on a hierarchical link pattern. The method includes: constructing K k-order link graphs based on the visible graph of the actual target network; obtaining vector representations of nodes at different scales according to the k-order link graphs, and obtaining the final representation of each node by splicing these vectors; constructing a binary classification training set; and establishing a binary classification model for multi-scale link prediction. The system includes: a link graph module for constructing K k-order link graphs based on the visible graph of the actual target network; a node representation module for obtaining vector representations and final representations of nodes on link graphs at different scales; a classification module for constructing a binary classification training set; and a prediction module for establishing a binary classification model for multi-scale link prediction. The present application can effectively capture high-order links of the network, better solve the problem of the network being too sparse; overcome the bias of artificially defined edge embedding binary operators; and improve prediction performance.

Description

Technical Field

[0001] The present application belongs to the field of network topology technology, and specifically relates to a multi-scale link prediction method and system based on a hierarchical link pattern. Background Art

[0002] The purpose of link prediction is to predict the probability that two nodes in a network are connected, which is crucial for many applications. For example, in e-commerce networks, personalized product recommendations are made to improve user experience and merchant sales; in online social networks, friend recommendations are made based on user relationship topology; in biological protein interaction networks, it can assist in predicting the interaction relationship between proteins; in transportation networks, new transportation routes are added based on the connectivity of existing transportation modes between cities.

[0003] The development of link prediction can be roughly divided into two phases. The first phase saw the emergence of a large number of heuristic methods, which essentially rely on manually defining features on the network. These methods, however, suffer from the designer's biases. Their applicability to one type of network is not guaranteed to be equally applicable to other types, making them unsuitable for the rich and diverse network data found in real-world scenarios. The second phase saw the emergence of learning approaches, with typical work including the matrix factorization-based method GraphFactorization, the random walk-based method DeepWalk, and graph neural network-based methods SEAL and HalpNet. Through learning mechanisms, these methods possess strong adaptability to network data, achieving advanced results across a wide range of networks. However, methods such as matrix factorization often incur excessive memory overhead and computational complexity due to matrix storage and computation. Graph neural network-based methods, such as SEAL, require constructing a subgraph for each pair of nodes for binary classification, which presents the following drawbacks: 1) subgraph construction is often time-consuming; 2) each predicted link requires the construction of a corresponding subgraph. Therefore, when predicting the probability of all links in a network, the number of constructed subgraphs reaches the square of the node size. 3) When constructing reachable subgraphs for adjacent node pairs, there is a large amount of overlap and redundancy in the traversed paths and nodes, resulting in a waste of computing resources. Random walk-based methods such as DeepWalk and Node2Vec, on the other hand, construct node sequences that grow linearly with the node size, enabling rapid sampling of large-scale networks.

[0004] However, the random walk-based method also has obvious flaws: first, it cannot capture the hierarchical structure in the network; second, the graph embedding method represented by Node2Vec constructs manual features of the edges in an artificially defined manner for binary classification, which lacks sufficient adaptability to the data. Summary of the Invention

[0005] This application proposes a multi-scale link prediction method and system based on a hierarchical link pattern, which uses the hierarchical link pattern to capture the reachable information of real-life network graph nodes at different scales for link prediction.

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] A multi-scale link prediction method based on hierarchical link patterns includes the following steps:

[0008] Based on the visible graph of the real target network, construct K k-order link graphs;

[0009] According to the k-order link graph, vector representations of nodes at different scales are obtained, and the vector representations are concatenated to obtain a final representation of each node;

[0010] Constructing a binary classification training set based on the final representation of each node;

[0011] Based on the binary classification training set, a binary classification model is established, and the binary classification model is used for multi-scale link prediction.

[0012] Preferably, the method for constructing K k-order link graphs includes:

[0013] Based on the visible graph of the actual target network, a breadth-first search with a depth of K is performed on each node in the network to obtain k-order links between nodes, which are used to construct K k-order link graphs, where 1≤k≤K.

[0014] Preferably, the method for obtaining k-order links between nodes includes:

[0015] Based on the visible graph, starting from the starting point of the network, all its neighboring nodes are added to a queue, and then the distances of these nodes from the starting node are marked. Similarly, compared with the newly traversed nodes in the previous round, the distances of the newly traversed nodes from the root node in each round are increased by 1. This is repeated K times in total, and the nodes connected to the root node through the k-longest shortest paths are obtained in turn; all nodes are traversed to obtain all k-order links on the entire graph.

[0016] Preferably, the method for calculating the final representation of each node in each k-order link graph includes:

[0017] Based on each of the k-order link graphs, a random walk is performed with each node in the network as the origin to obtain the context sequence of the node;

[0018] Based on the context sequence, a context embedding vector of any node on the k-order link graph is obtained through a word vector embedding model Word2Vec;

[0019] Based on the context embedding vector, the embedding vectors of the nodes on the 1st to Kth order link graphs are sequentially concatenated to obtain the final representation of the node.

[0020] Preferably, the final representation of each node is:

[0021] embed(v i )=CONCAT(embed(v i ,1),embed(v i ,2),…,embed(v i , K))

[0022] Among them, embed(v i , k) represents the context embedding vector of any node on the k-order link graph, and CONCAT(*) represents the vector concatenation operation.

[0023] Preferably, the method for constructing the binary classification training set includes:

[0024] Based on the final representation of each node, all connected node pairs on the visible graph are sampled as positive examples, and the same number of disconnected node pairs as positive examples are negatively sampled as negative examples;

[0025] The binary classification training set is constructed based on the positive examples and the negative examples.

[0026] Preferably, the method for establishing the binary classification model includes:

[0027] The binary classification training set is input into a multi-layer neural network to learn the implicit features of the edges, and supervised training is performed based on the true labels to obtain the binary classification model.

[0028] Preferably, the method for supervised training based on real labels is:

[0029]

[0030] Among them, y i represents the true category label, Represents the predicted value of the model, and N is the total number of training samples.

[0031] On the other hand, to achieve the above-mentioned purpose, the present application also provides a multi-scale link prediction system based on a hierarchical link pattern, comprising a link graph module, a node representation module, a classification module and a prediction module;

[0032] The link graph module is used to construct K k-order link graphs based on the visible graph of the actual target network;

[0033] The node representation module is used to collect node sequences through random walks based on each k-order link graph, and use the word vector embedding model Word2Vec based on negative sampling to process the context information of the nodes in the walk sequence, obtain vector representations of the nodes on link graphs of different scales, and splice the vector representations of the nodes on each order graph to obtain the final representation of the nodes;

[0034] The classification module is configured to sample all connected node pairs on the visible graph as positive examples based on the final representation of each node, negatively sample the same number of disconnected node pairs as positive examples as negative examples, and construct a binary classification training set based on the positive examples and the negative examples;

[0035] The prediction module is used to input the binary classification training set into a multi-layer neural network, learn the implicit features of the links, and perform supervised training based on the true labels to obtain the binary classification model, which is used for multi-scale link prediction.

[0036] Preferably, the method for constructing K k-order link graphs by the link graph module includes:

[0037] Based on the visible graph, starting from the starting point of the network, all its neighboring nodes are added to a queue, and then the distances of these nodes from the starting node are marked. Similarly, compared with the newly traversed nodes in the previous round, the distances of the newly traversed nodes from the root node in each round are increased by 1. This is repeated K times in total, and the nodes connected to the root node through the k-longest shortest paths are obtained in turn; all nodes are traversed to obtain all k-order links on the entire graph, and then all k-order link graphs are constructed.

[0038] The beneficial effects of this application are:

[0039] The present application discloses a multi-scale link prediction method and system based on a hierarchical link pattern. By utilizing the hierarchical link pattern, high-order links of the network are effectively captured through random walks on a K-order link graph, thereby improving the link prediction performance and better solving the problem of overly sparse networks. The method improves the learning method from the edge representation layer to the task layer, overcoming the bias of the artificially defined edge embedding binary operator. The method utilizes a multi-layer neural network to complete the automatic embedding learning of the links, thereby improving the prediction performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solution of the present application, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0041] Figure 1This is a flowchart of a multi-scale link prediction method based on a hierarchical link pattern according to the first embodiment of the present application;

[0042] Figure 2 Schematic diagram of the multi-layer neural network implementing automatic learning and classification of link features in Example 1 of the present application;

[0043] Figure 3 This is a schematic diagram of the degree distribution of eight classical networks and three sparse networks in Example 2 of this application;

[0044] Figure 4 Schematic diagram of AUC values ​​under different test link ratios (10% / 20% / 50%) in Example 2 of this application;

[0045] Figure 5 This is a schematic diagram of the structure of a multi-scale link prediction system based on a hierarchical link pattern according to the fourth embodiment of the present application. DETAILED DESCRIPTION

[0046] For a real-life visible network G′=(V,E′), the goal of link prediction is to predict the missing links in the network so as to reconstruct the complete network G=(V,E) to the greatest extent possible. Where V is the node set of the network G, E is the edge set. And E′ is the edge set of the visible network G′, and has Visible networks include but are not limited to transportation networks, social networks, biological research, etc.

[0047] Current network prediction methods mainly include: 1. Heuristic-based methods, based on certain heuristic ideas and using artificially defined similarity metrics, predict missing links in the network and possible future links. However, these methods are subject to designer bias and cannot adapt to the rich and diverse network data in real-world scenarios. 2. Learning-based methods, from a machine learning perspective, treat link prediction as a binary classification problem to determine whether an edge exists, or a regression problem to calculate the probability of an edge existing. However, these methods suffer from extremely large computational requirements and waste computing resources.

[0048] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0049] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0050] Example 1

[0051] The embodiment of the present application draws on the ideas of hierarchical structure modeling and graph sampling to construct a set of reachable graphs consisting of links of different orders between nodes, and samples node sequences on link graphs of different levels through random walks for context embedding, thereby learning the hierarchical pattern of links and improving the performance of link prediction.

[0052] like Figure 1 , which is a flow chart of a multi-scale link prediction method based on a hierarchical link pattern according to the first embodiment of the present application.

[0053] First, we extract a k-order link graph between nodes using a hierarchical approach. Next, we collect node sequences through random walks and use the negative sampling-based word embedding model Word2Vec to process the contextual information of the nodes in the walk sequence, thereby obtaining vector representations of the nodes on link graphs of different scales. Next, by concatenating the node representations on each order of the graph, we obtain the final representation of the node. We further concatenate the feature vectors of the two target nodes to obtain the initial feature representation of the link. Next, we sample all connected node pairs on the visible graph as positive examples and negatively sample an equal number of disconnected node pairs as negative examples to construct a binary classification training set. This input is fed into a multi-layer neural network to automatically learn the implicit features of the edges. Supervised training is then performed based on the true labels to obtain a binary classification model for link prediction.

[0054] The following describes the main steps of this embodiment:

[0055] 1. k-order link reachable graph

[0056] In this embodiment, a k-order link is defined as follows: if two nodes in a network are connected by a shortest path of length k, then there is said to be a k-order link between the node pair. That is: 1) The edges between the original graphs can be regarded as first-order links. 2) For any two nodes, if they are reachable from each other, there are one or more shortest paths whose length k is determined and unique. Therefore, there is information complementarity between links of different orders. For example, two nodes are connected by a k-order link. Since the length of the shortest path between the nodes is uniquely determined, the node pair only has a link under the k-th order link. At the same time, nodes that were originally unconnected under low-order links become connected at high orders, thus forming a supplement to the low-order link information. Therefore, extracting link relationships of different orders can better capture the reachability information of nodes through paths of different scales, thereby better representing the hierarchical information on link relationships.

[0057] Definition of a k-order link graph: A graph consisting of k-order links between all nodes in a network is called a k-order link graph. In this embodiment, a breadth-first search (BFS) with a depth of K is performed on each node in the network to obtain k-order links between nodes, which are used to construct K k-order link graphs, where 1≤k≤K. Specifically, starting from the starting point, all adjacent nodes are added to a queue, and their distances from the starting node are marked. Similarly, the distance from the root node to each newly traversed node is increased by 1 compared to the newly traversed node in the previous round. This is repeated K times, and the nodes connected to the root node by the k-longest shortest paths are sequentially obtained. BFS can find the shortest path because each increase in depth brings all nodes in the queue one step forward, ensuring that the number of steps taken when the final destination is reached is minimized. Finally, by applying this process to all nodes, all k-order links in the entire graph are obtained, and the complete k-order link graph is constructed.

[0058] 2. Multi-scale node context embedding based on random walks in k-order link graphs

[0059] For each k-order link graph constructed above, we take each node in the network as the origin, perform random walks, sample node context sequences, and input the word embedding model Word2Vec to obtain the v of any node. i ∈V context embedding vector embed(v i ,k), where k∈{1,2,...,K}, which is any integer from 1 to the maximum order K. Thus, the final representation of the node is:

[0060] embed(v i )=CONCAT(embed(v i ,1),embed(v i ,2),…,embed(v i ,K)) (1)

[0061] Among them, CONCAT(*) represents the vector concatenation operation.

[0062] 3. Automatic classification of k-order link features based on neural networks

[0063] Existing link prediction methods based on node embedding often use artificially defined binary operators, which are difficult to adapt to diverse network data. To solve this problem, this application uses a multi-layer neural network to realize automatic learning and classification of link features, such as Figure 2Specifically, the embodiment of the present application generates an initial representation of a node pair by vector concatenation of the node representations obtained in the above part, and uses the softmax output layer of a single node to transform the link prediction task into a binary classification problem (0 to 1 probability prediction) of predicting whether there is an edge between node pairs.

[0064] It is worth noting that the concatenated node pair vector is only the initial representation of the link. For example, when considering the case of 1 to 2 order links, let the initial vector of the node pair (a, b) be (a 11 ,a 12 ,a 21 ,a 22 ,b 11 ,b 12 ,b 21 ,b 22 ), the initial vector of the node pair (b,a) is expressed as (b 11 ,b 12 ,b 21 ,b 22 ,a 11 ,a 12 ,a 21 ,a 22 ), obviously, these two vector representations are not equal, but as an undirected link, the characteristics of the link should be independent of the order of node vector splicing. The embodiment of the present application eliminates the influence of this order through the neural network. For a fully trained neural network model, given the input node pair initial vector (a 11 ,a 12 ,a 21 ,a 22 ,b 11 ,b 12 ,b 21 ,b 22 ) or (b 11 ,b 12 ,b 21 ,b 22 ,a 11 ,a 12 ,a 21 ,a 22 ), after forward propagation, the last hidden layer can learn the vector representation (c1, c2, c3, c4) as the feature of the link, which is equivalent to the neural network from the input layer to the last hidden layer acting as a binary operator. The difference is that compared with the manually defined method, the generating function of the link feature is automatically learned, achieving better adaptability to the data.

[0065] 4. Training

[0066] The loss function is a log-likelihood loss:

[0067]

[0068] Among them, y i represents the true category label (0 means there is no edge between nodes, 1 means there is), represents the model's predicted value, and N is the total number of training samples. The parameters are updated using the Adam optimizer to minimize the logarithmic loss. Due to the sparsity of existing real-world networks, the total number of edges is far smaller than the number of possible node pair combinations, resulting in an imbalance between positive and negative samples in the training set, which can mislead predictions. To balance this ratio, the present embodiment randomly selects an equal number of positive and negative samples for training.

[0069] Analysis of the examples of this application:

[0070] In this embodiment of the application, all k-length shortest paths associated with the root node are obtained through a BFS tree with a maximum depth of K. When the value of K is small, the BFS tree with a maximum depth of K is a local subgraph. The average degree of nodes in the network is 2|E| / |V|. Since each node in the subgraph needs to be searched once, the complexity of constructing a local subgraph is, on average, As we all know, most real-world complex networks are sparse, meaning the average degree is much smaller than the number of nodes. Therefore, when K is small, this value is usually quite small. Therefore, the runtime of constructing a k-order link graph is primarily proportional to the node size.

[0071] The Katz method, which also uses path information at different levels, has an algorithm complexity of O(|V| 3 The probability-based hierarchical structure method HSM proposed by Newman et al. also requires a large amount of statistical averaging and brings about excessive computational complexity.

[0072] Graph-collapse methods such as HARP and EdgePool reduce computational requirements by reducing the number of nodes. However, these methods can produce counterintuitive aggregation. This is because during edge contraction, the edges to be contracted are randomly selected. When multiple edges associated with a node have equal chances of being aggregated, different random selections lead to different collapse outcomes. WALKLETS generates multi-scale relationships on a network by sampling short random walk sequences at nodes. It then uses inter-node hopping to approximate the sampling process on the higher-order structure represented by the higher powers of the network's adjacency matrix. The adjacency matrix is ​​raised to a higher power, k, whose elements represent the number of different paths of length k between node i and node j—in other words, the number of different random walk solutions with k steps. A problem with this method for extracting network hierarchies is that walk paths can lead to repeated round trips on simple paths. For example, if node i is reachable from node j via a one-step walk from i→j, it can also be reached via a four-step walk from i→j→i→j, or via a seven-step walk from i→j→i→j→i→j, and so on. Therefore, for such node pairs, this method captures the same graph structure at different scales (k=1, 4, 7, ...), and cannot reflect the differences in graph structure at different scales. WALKLETS, which adopts this approximate goal, also has this problem. In contrast, the method of this application describes the hierarchical structure of the network through the shortest path. Since the shortest path is also a simple path, there is no problem of repeated round trips, and it can more reasonably capture the reachable information of the network at different scales. It is a relatively effective way to extract the hierarchical structure of the network.

[0073] In addition, compared with graph neural network-based methods such as SEAL and HalpNet, since they need to construct a subgraph for each pair of nodes for binary classification, they also have the following disadvantages: 1) The subgraph construction process is often too time-consuming; 2) For each link prediction, the corresponding subgraph needs to be constructed. Therefore, when it is necessary to predict the possibility of the existence of all links in the network, the number of constructed subgraphs reaches the square of the node size, that is, O(|V| 2 ); 3) When constructing a reachable subgraph of adjacent node pairs, there is a lot of overlap and redundancy in the traversed paths and nodes, resulting in a waste of computing resources.

[0074] Finally, the method of this application also automatically encodes edge embeddings through a multi-layer neural network, overcoming the bias of manually defined edge embedding operators, thereby achieving better generalization capabilities on different data sets.

[0075] Example 2

[0076] Based on the prediction model constructed in this application, this embodiment 2 conducted experiments on eight classical networks and three sparse networks.

[0077] Eight classic network datasets: USAir is a US airline network with 332 nodes and 2,126 edges. NS is a research collaboration network for researchers in the field of network science, with 1,589 nodes and 2,742 edges. PB is a US political blog network with 1,222 nodes and 16,714 edges. Yeast is a protein interaction network of yeast with 2,375 nodes and 11,693 edges. C.ele is a neural connection network of Caenorhabditis elegans with 297 nodes and 2,148 edges. Power is a power transmission network in the western United States with 4,941 nodes and 6,594 edges. Router is a router network with 5,022 nodes and 6,258 edges. E.coli is a metabolite interaction network of Escherichia coli with 1,805 nodes and 14,660 edges.

[0078] Three sparse network datasets: Figeys is a human (Homo sapiens) protein interaction network derived from the first large-scale mass spectrometry-based study of protein reactions in human cells, with 2,239 nodes and 6,452 edges. Vidal is a protein-scale graph of the human protein interaction network, with 3,133 nodes and 6,726 edges. Eurorods is a road network primarily located in Europe, with nodes representing cities, with 1,174 nodes and 1,417 edges.

[0079] For each dataset, we extracted its largest connected subgraph for experiments, and its statistical information is shown in Table 1.

[0080] Table 1

[0081]

[0082] Among them, |V| and |E| are the number of nodes and edges respectively. is the average degree of nodes in the network, that is, the average number of directly adjacent nodes of all nodes. assort and C cluster They are the associativity coefficient and clustering coefficient of the network. The larger the associativity coefficient, the more nodes with similar degrees tend to connect to each other, and the larger the clustering coefficient, the more nodes in the network tend to cluster. It is the average shortest path length between nodes in the network.

[0083] Figure 3The degree distribution of each network is shown, with the horizontal axis representing degree and the vertical axis representing node frequency. It can be seen that these networks generally follow a power-law distribution: as the degree (the horizontal axis) increases, the node frequency (the vertical axis) decreases polynomially, with a large number of nodes concentrated on the left side of the horizontal axis, where the degree is relatively low. Looking at the three sparse networks (Figeys, Vidal, and Eurorods), nodes with degrees of 2 and 3 on the horizontal axis account for approximately half of all nodes. The same pattern is observed in the single-layer networks Power and Router. Furthermore, Table 1 shows that these networks all have long average shortest path lengths, indicating that a large number of nodes in the network require long paths to reach each other, i.e., sparse links within the network. These sparse links also exist to varying degrees in other real-world networks and can affect the accuracy of link prediction algorithms.

[0084] For comparison, this example uses six classic similarity-based link prediction methods: CN, AA, RA, JC, PA, and Katz. It also compares the random walk-based method Node2Vec with the graph neural network-based methods SEAL and HalpNet.

[0085] Since link prediction is a binary classification problem with highly unbalanced classes, this example uses the classic AUC (Area Under ROC Curve) metric, which is one of the most commonly used metrics in imbalanced data classification. It indicates the probability that the predicted positive examples are ranked before the negative examples.

[0086] It's worth noting that when training a model using a classification method, all visible edges must be sampled as positive examples, and an equal number of non-existent edges as negative examples to construct a training set. However, methods based on structural similarity, such as CN, AA, RA, JC, and Katz, use direct calculations based on topological features, eliminating the need for model training and retaining all non-existent edges for testing. To ensure a fair comparison, this example removes an equal number of non-existent edges as negative examples in the classification method's training when evaluating the performance of the similarity method, ensuring that the test sets for both methods have an equal proportion of positive and negative samples.

[0087] For each dataset, we extracted its largest connected subgraph and randomly removed existing edges while maintaining connectivity as positive test cases. To evaluate the overall performance of the algorithm, negative test cases consisted of all node pairs in the training sample that did not have any edges.

[0088] The settings of the baseline method are as follows: 1) For the Katz method, the attenuation factor β is set to 0.01; 2) For the Node2Vec method, the implementation and default parameter settings of the original paper are adopted, the classifier uses logistic regression, and the default parameter settings of the Python toolkit Scikit-learn are adopted; 3) For the SEAL and HalpNet methods, the implementation and settings of the original paper are adopted. Among them, for fair comparison, the batch size is set to 256, which is consistent with the method of this embodiment.

[0089] For the model HieLink proposed in the embodiment of the present application, a basic random walk strategy is used to obtain the node context sequence, and the node embedding is obtained by the word embedding method Word2Vec based on negative sampling, which is equivalent to Node2Vec (p=1, q=1) or DeepWalk. For a fair comparison, the parameters are consistent with those of the Node2Vec (p=1, q=1) model, that is, the default settings in the Node2Vec paper implementation are adopted. In the construction of the multi-layer neural network model for downstream classification tasks, in order to obtain sufficient learning ability, this embodiment constructs a 5-layer neural network with 4 hidden layers, and the hidden units of each hidden layer are set to 256. In order to prevent overfitting, we set the dropout rate of each hidden layer to 0.4 and the output layer to 0.1. The early stopping method is used to automatically determine the number of epochs. Training is carried out in a mini-batch manner, and the batch size is set to 256.

[0090] All experimental results are the mean and standard deviation of 10 independent experiments.

[0091] Experimental results and analysis

[0092] 1. AUC Accuracy Comparison on Classic Network Datasets

[0093] For 8 classic network datasets, 10% of the visible edges were randomly removed as test links, and the prediction performance of the comparison method and the proposed method was tested when applying 1st-order, 2nd-order and 3rd-order links respectively.

[0094] Table 2

[0095]

[0096] As shown in Table 2, the highest prediction value among the comparison methods is underlined, and the cases where the proposed algorithm outperformed all the comparison methods are highlighted in bold. It can be seen that compared to the comparison algorithms, HieLink, which uses high-order links, generally achieves higher prediction accuracy. Among them, HieLink (K=3), which uses links of order 1 to 3, achieves the best values ​​on six single-layer networks: USAir, PB, Yeast, C.ele, Power, and E.coli. HieLink (K=2), which uses links of order 1 to 2, achieves the best values ​​on four single-layer networks: PB, Yeast, C.ele, and E.coli. HieLink (K=1), which does not use high-order links, only achieves the best values ​​on PB and E.coli. For HieLink (K=3), AUC results close to the best values ​​were also achieved on the NS and Router networks, which did not achieve the best prediction accuracy. It is worth noting that the Katz method that achieved the best value on these two networks is also a link prediction algorithm that utilizes path information at different levels, demonstrating the effectiveness of constructing hierarchical link features in improving link prediction accuracy.

[0097] Taking Power as an example, which has a more obvious effect, when high-order links are applied (i.e., K=2, K=3), the performance is improved by 3.45% and 4.26% respectively compared with the case where high-order links are not applied (i.e., K=1). Figure 3 As shown in the figure, the degree of most nodes in the Power dataset is relatively small, and based on the observation that the average shortest path between nodes is long in Table 3, it is shown that there are a large number of sparse links in the network. This poses a great difficulty for similarity methods that rely on neighborhood, such as CN, AA, RA, JC, and PA, which only consider first-order neighbor information and have a very small model perception range, resulting in low accuracy. HieLink, on the other hand, effectively expands the model's perception range by modeling high-order link information and improves its ability to cope with sparsity in low-order links. In addition to the Power dataset, the application of high-order links has also improved networks with many sparse links, such as C.ele, PB, USAir, and Yeast, to varying degrees.

[0098] In addition, this second embodiment also verifies the impact of different test edge ratios on the accuracy of the algorithm. Figure 4 We show the AUC values ​​when randomly removing 10%, 20%, and 50% of the test links. Our algorithms all achieve optimal or near-optimal performance. As the proportion of test links increases, the performance of all algorithms decreases to varying degrees. HieLink's performance decreases within a relatively small range. By leveraging high-level link information, the proposed algorithm can more easily handle missing low-level link information, resulting in stronger noise immunity.

[0099] 2. AUC Accuracy Comparison on Sparse Network Datasets

[0100] In order to verify whether the improvement effect of the model on processing sparse links is consistent, this embodiment further conducts experiments in a real network with a large number of sparse links.

[0101] As shown in Table 3, when 10% of the edges were randomly removed as test links, HieLink (K=3) using links of order 1 to 3 and HieLink (K=2) using links of order 1 to 2 achieved the best results on all networks, while HieLink (K=1) without higher-order links achieved the best results only on the Vidal network. As the proportion of edges removed from the network as test links increased to 20%, HieLink (K=3) using links of order 1 to 3 still achieved the best results on all networks, while HieLink (K=2) using links of order 1 to 2 achieved the best results on the Vidal and Euroroads networks, while HieLink (K=1) without higher-order links failed to achieve the best results.

[0102] Further observation of the impact of high-order link features on the proposed method shows that in the Vidal protein network, the extracted high-order link features HieLink (K=2, K=3) have a maximum improvement of 3.07% and 4.09% respectively compared with HieLink (K=1); in the Figeys protein network, the maximum improvement is 2.93% and 3.63% respectively; in the Eurorods road traffic network, the maximum improvement is 7.27% and 9.69% respectively.

[0103] Table 3

[0104]

[0105] It can be seen that as the number of network links decreases, HieLink can more effectively deal with the prediction difficulties caused by the network being too sparse by extracting high-order link features.

[0106] Example 3

[0107] In the third embodiment of the present invention, the technical solution of the present application is applied to aviation route planning.

[0108] In this embodiment, the route network composed of existing air routes between several cities in the region is taken as an example. The cities are used as nodes, and the shortest paths between cities are obtained through breadth-first search. Based on this, route link reachability graphs of different distance scales are generated to depict the hierarchical link pattern in the inter-city route network. Then, the node sequence (city sequence) is sampled by random walk, and the context embedding learning of the city nodes is performed according to the word embedding method in the language model to generate a vector representation of each city under the link pattern of different distance scales. Then, the vector representations of these inter-city routes are merged to obtain the route feature representation of each city. Using the cities with existing route connections in the existing route network as positive examples and the cities without route connections as negative examples, a binary classification training set is constructed. Combined with a multi-layer neural network, a prediction model is learned to predict new air routes.

[0109] Example 4

[0110] like Figure 5 As shown, this is a schematic diagram of the structure of a multi-scale link prediction system based on a hierarchical link pattern according to the fourth embodiment of the present application, which mainly includes four parts: a link graph module, a node representation module, a classification module and a prediction module.

[0111] Specifically, in this embodiment, the link graph module is used to construct K k-order link graphs based on the visible graph of the real target network. Specifically, based on the visible graph of the real target network, starting from the starting point of the network, all its neighboring nodes are added to a queue, and then the distance of these nodes from the starting node is marked. Similarly, compared with the newly traversed nodes in the previous round, the distance from the root node of each newly traversed node is increased by 1. This is repeated K times in total, and the nodes connected to the root node through the k-longest shortest paths are obtained in sequence. All nodes are traversed to obtain all k-order links in the entire graph, and then all k-order link graphs are constructed.

[0112] The node representation module is used to collect node sequences through random walks on each k-order link graph. The node context information in the walk sequence is processed using the negative sampling-based word vector embedding model Word2Vec to obtain vector representations of nodes on link graphs of different scales. The vector representations of nodes on each order graph are then concatenated to obtain the final representation of the node.

[0113] The classification module is used to sample all connected node pairs on the visible graph as positive examples based on the final representation of each node, and negatively sample the same number of disconnected node pairs as positive examples as negative examples. Based on the positive and negative examples, a binary classification training set is constructed.

[0114] The prediction module is used to input the binary classification training set into the multi-layer neural network, learn the implicit features of the links, and perform supervised training based on the true labels to obtain a binary classification model. The binary classification model is used for multi-scale link prediction.

[0115] The embodiments described above are merely descriptions of the preferred embodiments of the present application and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements made to the technical solutions of the present application by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present application.

Claims

1. A multi-scale link prediction system based on hierarchical link patterns, characterized in that: The prediction system is used for air route planning; The prediction system includes a link graph module, a node representation module, a classification module and a prediction module; The link graph module is used to construct K k-order link graphs based on the visible graph of the real target network; the real target network is a route network consisting of existing air routes between several cities in the region. The shortest paths between cities are obtained through breadth-first search using cities as nodes, and based on this, route link reachability graphs at different distance scales are generated, namely the k-order link graphs; The node representation module is used to collect node sequences, i.e., city sequences, based on each k-order link graph through random walks, and use the word vector embedding model Word2Vec based on negative sampling to process the context information of the nodes in the walk sequence, thereby obtaining vector representations of the nodes on link graphs of different scales, i.e., vector representations of each city under link modes at different distance scales, and concatenating the vector representations of the city nodes on each order graph to obtain the final representation of the city nodes; The classification module is configured to sample, based on the final representation of each city node, all city nodes connected by routes in the existing route network on the visible graph as positive examples, and negatively sample an equal number of unconnected node pairs as positive examples, i.e., city nodes without route connections as negative examples, and construct a binary classification training set based on the positive examples and the negative examples; The prediction module is used to input the binary classification training set into a multi-layer neural network, learn the implicit features of the edges, and perform supervised training based on the true labels to obtain the binary classification model, which is used for air route planning.

2. The multi-scale link prediction system based on hierarchical link patterns according to claim 1, characterized in that: The method for constructing K k-order link graphs by the link graph module includes: Based on the visible graph, starting from the starting point of the network, all its neighboring nodes are added to a queue, and then the distances of these nodes from the starting node are marked. Similarly, compared with the newly traversed nodes in the previous round, the distances of the newly traversed nodes from the root node in each round are increased by 1. This is repeated K times in total, and the nodes connected to the root node through the k-longest shortest paths are obtained in turn; all nodes are traversed to obtain all k-order links on the entire graph, and then all k-order link graphs are constructed.

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