A multi-layer network link prediction method based on naive Bayes model

Abstract

The present invention provides a multi-layer network link prediction method based on a naive Bayes model, including: dividing the links in the target layer into a training set and a test set; based on the topological structure information of the training set and the information of the auxiliary layer, obtaining the first probability score of the existence of links in all the node pairs remaining in the target layer after removing the training set, wherein the information of the auxiliary layer is the correlation information between the layers in the auxiliary layer; arranging all the node pairs remaining in the target layer after removing the training set in descending order according to the probability score to complete the multi-layer network link prediction; based on the probability scores of the node pairs in the test set, using the evaluation index to evaluate the multi-layer network link prediction results. The prediction method proposed by the present invention can achieve good prediction performance. For example, when applied to aviation route planning, it can realize the overall management and optimization of the complete network of the entire region, rationally utilize aviation resources, and achieve the best overall efficiency of the planning results.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent prediction, and in particular relates to a multi-layer network link prediction method based on a naive Bayes model. Background Art

[0002] A large number of complex systems in the real world, such as social systems, computer network communication systems, and neural network systems, have an impact on humans in various aspects. One of the main tasks of studying such systems is to model them reasonably to help people identify their principles and basic structures, and to manage and use them conveniently, which helps to understand various phenomena in the real world. At the end of the 20th century, based on a large number of research works, a research direction called "complex networks" gradually emerged. Many complex systems can be modeled using complex networks, in which nodes represent different basic units of the system, and the links between nodes represent the interactions and relationships between units. The method of abstracting complex systems into complex networks is generally to aggregate all observed units and the links between them into a graph. However, this aggregation method may lose some important information. Because the basic units of complex systems may be connected by various relationships with different meanings. Such complex systems can be better modeled using multi-layer networks.

[0003] The purpose of link prediction is to evaluate the possibility of a link between two nodes. Link prediction includes lost link prediction and future link prediction. Lost link prediction is to find out the links that may exist in the network but have not been observed. Future link prediction is to predict the links that may appear in the future based on the existing historical information and node information. Under the condition of the continuous growth of the network, in order to meet the needs of complex network mechanism analysis, link prediction has become a necessary condition for solving the problem of lost links. Link prediction not only occupies a place in complex network research, but is also widely used in real life. Link prediction is present in various recommendation systems such as online marketing, e-commerce and friend recommendation in social networks.

[0004] Single-layer network models can only simulate the same type of interaction between nodes in a complex system. However, there are usually different types of links between units in the system. For example, biologists have found that information exchange between cells can be divided into electrical signals and chemical signals, the relationship between paper authors can be divided into co-authors, co-publications (published papers in the same journal) and co-citations (co-cited the same paper), etc., and the social relationships between people can be divided into family, colleagues and friends, etc. This will lead to incorrect or incomplete collection of information about complex systems during the abstraction process. In order to address this substantial limitation, multi-layer networks are used to expand the traditional single-layer network theory, abstracting various types of interaction relationships between entities into different types of links between the same nodes, and each type of link describes a specific interaction relationship.

[0005] Although the link prediction problem of complex networks has been studied in depth, existing research mainly focuses on single-layer networks, and there is relatively little research on the link prediction problem of multi-layer networks. Summary of the invention

[0006] To solve the above technical problems, the present invention proposes a multi-layer network link prediction method based on a naive Bayes model, which counts the probability distribution of whether there is a link between the node pairs in the target layer and the auxiliary layer, and then fuses and calculates the probability of whether there is a missing link or a potential link between the node pairs in the target layer, and can achieve good prediction performance in both positively correlated and negatively correlated multi-layer networks.

[0007] To achieve the above object, the present invention provides a multi-layer network link prediction method based on a naive Bayes model, comprising:

[0008] Divide the links in the target layer into training set and test set;

[0009] Based on the topological structure information of the training set and the information of the auxiliary layer, obtaining a first probability score that links exist for all the node pairs remaining in the target layer after removing the training set, wherein the information of the auxiliary layer is the correlation information between layers in the auxiliary layer;

[0010] Arrange all the node pairs remaining in the target layer after removing the training set in descending order according to the first probability scores to complete multi-layer network link prediction;

[0011] Based on the probability scores of the node pairs in the test set, the multi-layer network link prediction results are evaluated using an evaluation index.

[0012] Optionally, the topological structure information includes: the names corresponding to the network layers, the total number of nodes in the multi-layer network, the nodes activated in the target layer, the number of links in the target layer, the average degree of the network, the average clustering coefficient of the network, the network density, the heterogeneity of the network degree and the degree homogeneity coefficient;

[0013] The network average clustering coefficient is used to characterize the average degree of clustering between nodes in the network;

[0014] The network degree heterogeneity is used to describe the balance of degree distribution of nodes in the network;

[0015] The degree associativity coefficient is used to measure whether a node tends to connect to other nodes with the same properties as itself.

[0016] Optionally, the step of obtaining the first probability score includes:

[0017] Based on the topological structure information of the training set, obtaining a second probability score of the existence of a link between the node pairs in the target layer according to a naive Bayes model;

[0018] Based on the information of the auxiliary layer, obtaining a third probability score of the node pair having a link in the auxiliary layer according to a naive Bayes model;

[0019] The second probability score and the third probability score are fused using the maximum and minimum normalization method, and the first probability score is obtained by adjusting the ratio parameter between the topological structure information of the training set and the information of the auxiliary layer.

[0020] Optionally, the expression of the second probability score is:

[0021]

[0022] in, is the third probability score, Indicates that the node pair (x, y) has an edge in the target layer, Indicates that the node pair (x, y) has no edges in the target layer. xy is the feature set, When nodes x and y have an edge in the auxiliary layer, Otherwise, 0;

[0023] in, Indicates that nodes x and y are in the auxiliary layer G A There is an edge, and in G T The probability that a layer also has an edge is calculated as follows:

[0024]

[0025]

[0026] Among them, n 11 is the number of node pairs that are linked in both layers of the network, n 01 is the number of node pairs that do not have links in the target layer but have links in the auxiliary layer, n 00 is the number of node pairs that do not have links in both layers, n 10 is the number of node pairs that are linked in the target layer but not in the auxiliary layer, is the probability that x and y have an edge in the target layer when there is an edge in the auxiliary layer, is the probability that x and y have edges in the target layer when there are no edges in the auxiliary layer. p1, p2 and q are approximately calculated by the following formula:

[0027]

[0028]

[0029]

[0030] Optionally, the expression of the maximum and minimum normalization method is:

[0031]

[0032] Among them, r max With r min are the maximum and minimum values ​​respectively, r′ is the normalized value, and r is the original value.

[0033] Optionally, the first probability score is expressed as:

[0034]

[0035]

[0036]

[0037] Among them, α is the ratio parameter between the topological structure information and the auxiliary layer information, α∈[0,1], are three different first probability scores obtained according to three different second probability score expressions, is the third probability score.

[0038] Optionally, based on adjusting the change of the ratio parameter between the topological structure information of the training set and the information of the auxiliary layer, the multi-layer network link prediction result is evaluated by an evaluation index;

[0039] The evaluation indicators include: AUC, Ranking score, Precision;

[0040] The AUC is used to evaluate the overall correctness of the algorithm, the Ranking score is used to measure the scores of the links in the test set in descending order in the predicted links, and the Precision is used to sort the node pairs in descending order according to the probability scores to obtain the ratio of the number of potential links to the number of selected node pairs.

[0041] Compared with the prior art, the present invention has the following advantages and technical effects:

[0042] The present invention uses a naive Bayes model, takes whether a node pair has an edge in the auxiliary layer as a feature, counts the probability distribution of whether a node pair has a link between the target layer and the auxiliary layer, and then fuses and calculates the probability of whether a node pair in the target layer has a lost link or a potential link. The prediction method of the present invention is applied to air route planning to predict new air routes, which can achieve the overall management and optimization of the complete network of the entire region, rationally utilize aviation resources, and achieve the best overall efficiency of the planning results. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0044] Figure 1 This is a flow chart of a multi-layer network link prediction method based on a naive Bayes model according to Embodiment 1 of the present invention;

[0045] Figure 2 The MLP of Example 1 of the present invention NB Schematic diagram of the prediction performance of the method on the C. Elegans network;

[0046] Figure 3 The MLP of Example 1 of the present invention NB Schematic diagram of the prediction performance of the method on TF networks;

[0047] Figure 4 The MLP of Example 1 of the present invention NB Schematic diagram of the prediction performance of the method on the Vickers network;

[0048] Figure 5 The MLP of Example 1 of the present invention NB Schematic diagram of the AUC results based on different α values ​​on a multi-layer network;

[0049] Figure 6 The MLP of Example 1 of the present invention NB Schematic diagram of the ranking score results based on different α values ​​on a multi-layer network;

[0050] Figure 7 The MLP of Example 1 of the present invention NB Schematic diagram of the Precision results of the method based on different α values ​​on a multi-layer network. DETAILED DESCRIPTION

[0051] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0052] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0053] Example 1

[0054] like Figure 1 As shown, this embodiment provides a multi-layer network link prediction method based on a naive Bayes model, including:

[0055] Divide the links in the target layer into training set and test set;

[0056] Based on the topological structure information of the training set and the information of the auxiliary layer, obtaining a first probability score that links exist for all the node pairs remaining in the target layer after removing the training set, wherein the information of the auxiliary layer is the correlation information between layers in the auxiliary layer;

[0057] Furthermore, the topological structure information includes: the names corresponding to the network layers, the total number of nodes in the multi-layer network, the nodes activated in the target layer, the number of links in the target layer, the average degree of the network, the average clustering coefficient of the network, the network density, the network degree heterogeneity and degree homogeneity coefficient;

[0058] The average network clustering coefficient is used to characterize the average degree of clustering between nodes in the network;

[0059] Network degree heterogeneity is used to describe the balance of degree distribution of nodes in the network;

[0060] The degree associativity coefficient is used to measure whether a node prefers to connect to other nodes with the same properties as itself.

[0061] Furthermore, the correlation between layers in the auxiliary layer can be reflected by the following three commonly used inter-layer correlation indicators, which characterize the similarity between layers from different perspectives.

[0062] Edge Overlap Rate (EOR): This metric describes the ratio of repeated edges between two layers of networks to the total number of edges (Edge Overlap Rate). It is believed that the more repeated edges there are, the more similar the two layers of networks are. Calculate the target layer G T With auxiliary layer G A The edge overlap ratio between them is shown in the following formula:

[0063]

[0064] Among them, e TA Represents the target layer G T and auxiliary layer GA Edges that appear at the same time are links that appear at the same time. EOR ∈[0,1] when When there are no simultaneous links in the two layers of the network, the edges of the two layers of the network are exactly the same. Dataset In the CS-Aarhus network, the edge repetition rate between layers is high in most networks, such as Physicians, Lazega, and Vickers. However, since the third layer of the CS-Aarhus network has fewer edges, the edge repetition rate with other layers is low. The first layer of C.Elegans describes the connection relationship between synaptic electrical signals, and the second and third layers are chemical signals, so the edge repetition rate between the first layer and other layers is low.

[0065] Pearson Correlation Coefficient (PCC): Pearson Correlation Coeffffi-cient can measure the similarity between two vectors. The value range is [-1,1], where negative values ​​indicate negative correlation between the two vectors, 0 indicates no correlation, and positive values ​​indicate positive correlation. T Layer and G A Adjacency matrix of the layer Concatenate rows into two long vectors as well as Then calculate the correlation between the two layers using the method of calculating the Pearson correlation coefficient The formula is as follows:

[0066]

[0067] in, represents the mean of the vector, σ(g T ) is the standard deviation of the vector. In a multi-layer network When G T Layer and G A The layer has a strong positive (negative) correlation, that is, in G T The edges that appear in the layer will (will not) be in G A The results of the inter-layer Pearson correlation coefficient are roughly the same as those of the inter-layer edge repetition rate. If the edge repetition rate of the two-layer network is high, then their Pearson correlation coefficients are also relatively high. However, there are some differences. For example, the edge repetition rates of the first layer and other layers of the Vickers network are 0.689 and 0.724, respectively, and the Pearson correlation coefficients are 0.567 and 0.552, respectively. This is because the Pearson correlation coefficient not only considers the repeated edges between layers but also the non-repeated edges between layers. The reason for the above result is that the number of links in the first layer of the Vickers network is much larger than the number of links in the other two layers of the network.

[0068] Asymmetric Neighbors Similarity (AASN) compares the number of links that exist in both layers of the network with the number of links in the current layer to obtain the Asymmetric Average Similarity of the Neighbors. The intuition behind this correlation is that if there is enough similarity between the two layers of the network, the greater the density of one network, the more information it provides for link prediction in the other layer. The indicator is defined as follows:

[0069]

[0070] in, is the number of links that node u has in both layers of the network; is the node u in G T The number of links in the layer network, i.e., the degree value Measured G A Layer pair G T The similarity of the layer describes the T When layer G performs link prediction A Compared with the above two correlation indicators, AASN is more in line with common sense. T Layer pair G A The influence of the layer is not necessarily equal to G A Layer pair G T The influence of the layer. For example, the influence of the first layer of Vickers on the second layer is 0.525, and the influence of the second layer on the first layer is 1. According to the calculation formula and topological information, it can be concluded that the links of the second layer of Vickers all appear in the first layer, so all the information of the second layer can be used when predicting the links of the first layer.

[0071] Furthermore, unlike the existing methods, the present invention no longer focuses on the node neighborhood information of the auxiliary layer. This is because in a multi-layer network, although there is correlation between layers, local changes may be large. For the sake of convenience and clarity, the prediction method proposed in the present invention is referred to as MLP. NB Method, in order to utilize the influence of other layers on the target layer, MLP NB The method takes whether there is a link between node pairs in the auxiliary layer as a feature, and uses the naive Bayes model to calculate the probability that the target layer node pairs have an edge under these features. The probability that there is a link between the target layer node pairs is obtained by combining the probability obtained based on the influence of other layers and the probability calculated based on the target layer's own structural information.

[0072] The specific steps of obtaining the first probability score include:

[0073] The first step is to obtain a second probability score of the existence of a link between the node pairs in the target layer according to a naive Bayes model based on the topological structure information of the training set;

[0074] The Naive Bayes model is a theorem in probability theory that describes the probability of an event occurring under certain known conditions. For example, if it is known that a certain cancer is related to age, the Naive Bayes model can be used to calculate the probability score of a person suffering from this cancer by knowing his age. If it is known that the structural information of other layers of a multi-layer network is related to the structure of the target layer, then the structural information of other layers can be used to predict the structure of the target layer.

[0075] In this embodiment, the target layer G is calculated T The probability score of the existence of a link between the nodes in the target layer. This step only uses the intra-layer topology information of the target layer, and the probability score is determined by LNB (Local The second probability score is calculated using the Naive Bayes model. This model assumes that each common neighbor contributes differently to the formation of a link between nodes, and evaluates the contribution of neighbors based on the Naive Bayes model. The calculation method of the second probability score is shown in the following formula:

[0076]

[0077]

[0078]

[0079] Among them, O xy is the set of common neighbor nodes of nodes x and y, and Three different calculation methods are obtained to consider different contributions of common neighbors, k w is the degree of node w, s is a constant calculated based on the number of nodes and edges in the network, R w is the role function of node w.

[0080] The second step is to obtain, based on the information of the auxiliary layer, a third probability score of the node pair having a link in the auxiliary layer according to a naive Bayes model;

[0081] In this embodiment, according to the correlation between the layers of the multi-layer network, the influence of whether the node pair has an edge in other layers on the target layer is considered, and whether the node pair has an edge in other layers is used as a feature. The following two posterior probabilities are obtained according to the naive Bayes model:

[0082]

[0083]

[0084] in, Represents the node pair (x, y) in G T There are edges within the layer. Represents the node pair (x, y) in G T No edge within the layer. xy is the feature set, When nodes x and y are in G A When the layer has edges, Otherwise 0. Indicates that nodes x and y are in G T The posterior probability of having an edge within a layer, Indicates that nodes x and y are in G T The posterior probability of no edge within the layer. In order to compare the probability of a link between node pairs, we define for Divide by get:

[0085]

[0086] Take the logarithm of both sides of the above formula and ignore the constant s -1 ,get:

[0087]

[0088] in, is the third probability score, Represents a node pair There are edges in the target layer, Indicates that the node pair (x, y) has no edges in the target layer. xy is the feature set, When nodes x and y have an edge in the auxiliary layer, Otherwise, 0;

[0089] in Indicates that nodes x and y are in the auxiliary layer G A There is an edge, and in G T Layers also have edge probabilities. To calculate definition:

[0090]

[0091]

[0092]

[0093] in is the adjacency matrix, Represents node i and T There is an edge within the layer, otherwise it is 0. Represents nodes x and y in GT The probability that a layer has an edge, Represents the node pair (x, y) in G T Layer and G A The joint probability of the layers having edges at the same time, and the joint probability distribution of the rest of the cases are as follows:

[0094]

[0095]

[0096]

[0097] Calculate the conditional probability:

[0098]

[0099]

[0100]

[0101]

[0102] p1, p2 and q can be approximately calculated by the following formula:

[0103]

[0104]

[0105]

[0106] where n 11 It indicates the number of node pairs that are linked in both layers of the network. The calculation formula is as follows:

[0107]

[0108]

[0109]

[0110]

[0111] So:

[0112]

[0113]

[0114] Among them, n 11 is the number of node pairs that are linked in both layers of the network, n 01is the number of node pairs that do not have links in the target layer but have links in the auxiliary layer, n 00 is the number of node pairs that do not have links in both layers, n 10 is the number of node pairs that are linked in the target layer but not in the auxiliary layer, is the probability that x and y have an edge in the target layer when there is an edge in the auxiliary layer, is the probability that x and y have edges in the target layer when there are no edges in the auxiliary layer.

[0115] In the third step, the second probability score and the third probability score are merged using the maximum and minimum normalization method; and the first probability score is obtained by controlling the ratio parameter between the topological structure information of the training set and the information of the auxiliary layer.

[0116] The expression of the maximum and minimum normalization method is:

[0117]

[0118] Among them, r max With r min are the maximum and minimum values ​​respectively, r′ is the normalized value, and r is the original value.

[0119] The expression of the first probability score is:

[0120]

[0121]

[0122]

[0123] Among them, α is the ratio parameter between the topological structure information and the auxiliary layer information, α∈[0,1], are three different first probability scores obtained according to three different second probability score expressions, is the third probability score.

[0124] All node pairs remaining in the target layer after removing the training set are arranged in descending order according to the first probability scores to complete multi-layer network link prediction.

[0125] Based on the probability scores of node pairs in the test set, the evaluation indicators are used to evaluate the link prediction results of the multi-layer network.

[0126] Based on the parameters controlling the ratio between the topological structure information of the training set and the information of the auxiliary layer, the multi-layer network link prediction results are evaluated through evaluation indicators;

[0127] Evaluation indicators include: AUC, Ranking score, Precision;

[0128] AUC is used to evaluate the overall correctness of the algorithm, the Ranking score is used to measure the scores of the links in the test set in descending order in the predicted links, and the Precision is used to sort the node pairs in descending order according to the probability scores to obtain the ratio of the number of potential links to the number of selected node pairs.

[0129] AUC, Ranking score, and Precision are three classic evaluation indicators of link prediction algorithms.

[0130] AUC: Using AUC as the evaluation index of link prediction can evaluate the overall correctness of the algorithm. AUC represents the accuracy of the link prediction algorithm from the test set E. T test The probability that the score of a randomly selected node pair from is higher than the score of a randomly selected node pair from the set U-ET where no links exist is as follows:

[0131]

[0132] Where n is the number of comparisons (in this example, n=10000). The fraction of randomly selected potential links times higher than the fraction of randomly selected links that do not actually exist, When the node pair ranking is the perfect ranking, AUC = 1. When all node pair scores are independent and identically distributed, AUC = 0.5. The higher the algorithm performance, the closer the AUC value is to 1.

[0133] Ranking score: This indicator measures the performance of all test sets E T test The score of the link in the predicted link UE T train The descending ranking in . If the ranking of the links in all test sets is higher, the value of Ranking score will be smaller, which means the prediction performance is higher. The calculation method is as follows:

[0134]

[0135] Among them, r e is the score of link e and its ranking in the predicted links.

[0136] Precision: UE T trainThe node pairs in are arranged in descending order according to the probability scores, and the ratio of the number of potential links to the number of selected node pairs is the Precision. If there are actually L links among the first K links, then the calculation method of Precision is as shown in the following formula.

[0137]

[0138] In this embodiment, That is, the test set size. If there are more actual links among the first K predicted links, the Precision value will be higher, that is, the accuracy of the prediction algorithm will be higher.

[0139] In this embodiment, after completing the multi-layer network link prediction, the proposed prediction method is also verified. Since the inter-layer Pearson correlation coefficient of the multi-layer network used in this embodiment is positive, and most comparative methods pay less attention to multi-layer networks with negative inter-layer Pearson correlation coefficients, this embodiment is also experimented on a synthetic network. In order to verify the performance of the method of this embodiment on a negatively correlated network, two negatively correlated multi-layer network data Syn1 and Syn2, an unrelated network data Syn3, and two positively correlated network data Syn4 and Syn5 are generated according to the ER model (random graph model, adding new edges with a certain probability). Their topological information and correlation are respectively displayed by the topological characteristics of the synthetic multi-layer network in Table 2 and the correlation of the synthetic multi-layer network in Table 3. The topological information and inter-layer correlation calculation methods have been described in the previous content. Wherein layer1→layer2 is the AASN correlation of layer1 to layer2.

[0140] Table 2

[0141]

[0142] Table 3

[0143]

[0144] In the method proposed in the present invention, there is a parameter α that controls the ratio of target layer information to auxiliary layer information. When α=0, it means that only the structural information of the target layer is used, and when α=1, it means that only the information provided by the auxiliary layer is used. Figure 2 , Figure 3 and Figure 4 MLP NB -CN、 MLP NB -AA and MLPNB-RA methods obtained link prediction results on C.Elegans, TF and Vickers networks. The error bars are the standard deviations of 20 independent experimental results. As can be seen from the figure, the curve trends of the three methods are roughly the same, but MLPNB -RA method performs slightly better than the other two methods. Figure 5 , Figure 6 as well as Figure 7 Only MLP is shown in NB -The AUC, Ranking score, and Precision results obtained by the RA method on the remaining multi-layer networks according to different α values, where each broken line represents the prediction result obtained when the corresponding layer is used as the target layer.

[0145] According to the results in the above figure, it can be seen that MLP NB The performance of the method quickly reaches a peak as the α value increases and then tends to stabilize. When α = 1, the performance drops rapidly. This shows that the link prediction performance of the target layer can be improved by adding information from other layers, but if the structural information of the target layer is not used, the prediction performance will be greatly reduced. The prediction results of the Padgett network show continuous improvement. This is because its target layer network structure is simple and cannot provide effective information for link prediction. Figure 5 As shown in Figure 2, when only the target layer information is used, the AUC index of its prediction result is about 0.5, which is close to the prediction performance of the random model. NB This method can improve the accuracy of prediction when there is less information in the target layer. Figure 4 In the figure, it can be found that the prediction performance when α=1 is better than that when α=0. Combined with the high correlation between the layers of the Vickers network, the links that appear in other layers will most likely appear in the target layer. Similar properties are also shown on the second layer of the Physicians network and the C.Elegans network. Although the prediction accuracy when α=1 is lower than that when α=0 on the other networks, better prediction performance is also achieved. This shows that when it is difficult to obtain the specific topological information of the target layer, the purpose of link prediction can be achieved using only the information provided by the auxiliary layer.

[0146] In addition, Figure 7 In MLP NB The precision results of the method on most networks are similar to Figure 5 and 6 The Precision evaluation index measures the proportion of actual links in the top K predicted node pairs. When α changes, the probability scores of the node pairs that actually have links change greatly. Therefore, the number of actual links in the top K node pairs in descending order of probability scores also changes greatly. However, AUC and Ranking score evaluate the overall prediction performance. Therefore, their trends with the change of α are relatively stable, and MLP NBThe reason why the Precision value of the third layer of the Krackhardt network is always 0 as α increases is that this layer lacks local information and has low correlation with other layers.

[0147] In summary, using the information of the target layer and the auxiliary layer at the same time can greatly improve the performance of the target layer link prediction compared to using only the information of the target layer, which verifies the correctness of the method of the present invention. In addition, from the above experimental results, it can be seen that when α = 0.5, MLP NB The method achieved the best prediction results on almost all networks.

[0148] Example 2

[0149] The prediction method of the present invention is applied to aviation route planning.

[0150] At present, when planning air routes, business personnel are mainly responsible for planning and adjusting the aviation network structure based on historical experience. The decision on which routes to open is highly dependent on the business personnel's knowledge and experience of traffic data such as passenger flow between cities, cargo and mail flow, and airport throughput capacity. In addition, since business personnel are usually only familiar with the traffic data of the part of the area where they are located, there is no unified standard for aviation networks planned in different regions, and there is a lack of coordinated management and optimization of the complete network in the entire region. There is an unreasonable utilization of aviation resources, such as the planning results do not achieve the optimal overall efficiency, and the service scope of the aviation network is small.

[0151] A multi-layer network link prediction method based on a naive Bayesian model of the present invention is used. For example, a three-layer transportation network including aviation, railways and roads is constructed with existing air routes, railway transportation routes and highway routes between several cities in a certain area, wherein cities are used as nodes, and different cities can be reached by three ways: aviation, railways and roads. Since air route planning is to be carried out, the aviation network is used as the target layer, and the railway and highway networks are used as auxiliary layers. First, in the target layer, the common neighbors between the nodes are used as features, and the local naive Bayesian model is used to calculate the connection probability between different cities. Then, the railway and highway traffic conditions between these cities are considered, and whether there are railway routes and highway routes between two cities is used as a feature, and then the naive Bayesian model is used to calculate the connection probability between different cities again. Finally, these probabilities are combined to predict new air routes. It is possible to achieve the overall management and optimization of the complete network of the entire region, rationally utilize aviation resources, and achieve the best overall efficiency in the planning results.

[0152] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A multi-layer network link prediction method based on a naive Bayes model, characterized in that: include: Divide the links in the target layer into a training set and a test set; wherein the target layer is an aviation network with cities as nodes; Based on the topological structure information of the training set and the information of the auxiliary layer, a first probability score of the existence of links for all the node pairs remaining in the target layer after removing the training set is obtained, wherein the information of the auxiliary layer is the correlation information between the layers in the auxiliary layer; the auxiliary layer includes: a railway network and a highway network; Arrange all the node pairs remaining in the target layer after removing the training set in descending order according to the first probability scores to complete multi-layer network link prediction; wherein the multi-layer network link prediction is to predict new air routes; The step of obtaining the first probability score comprises: Based on the topological structure information of the training set, obtaining a second probability score of the existence of a link between the node pairs in the target layer according to a naive Bayes model; Based on the information of the auxiliary layer, obtaining a third probability score of the node pair having a link in the auxiliary layer according to a naive Bayes model; The second probability score and the third probability score are merged by using a maximum-minimum normalization method, and the first probability score is obtained by adjusting a ratio parameter between the topological structure information of the training set and the information of the auxiliary layer; Based on the probability scores of the node pairs in the test set, the multi-layer network link prediction results are evaluated using an evaluation index.

2. The multi-layer network link prediction method based on the naive Bayes model according to claim 1 is characterized in that: The topological structure information includes: the name corresponding to the network layer, the total number of nodes in the multi-layer network, the nodes activated in the target layer, the number of links in the target layer, the average degree of the network, the average clustering coefficient of the network, the network density, the heterogeneity of the network degree and the degree homogeneity coefficient; The network average clustering coefficient is used to characterize the average degree of clustering between nodes in the network; The network degree heterogeneity is used to describe the balance of degree distribution of nodes in the network; The degree associativity coefficient is used to measure whether a node tends to connect to other nodes with the same properties as itself.

3. The multi-layer network link prediction method based on the naive Bayes model according to claim 1 is characterized in that: The expression of the second probability score is: Among them, O xy is the set of common neighbor nodes of nodes x and y, and Three different calculation methods are obtained to consider different contributions of common neighbors, k w is the degree of node w, s is a constant calculated based on the number of nodes and edges in the network, R w is the role function of node w.

4. The multi-layer network link prediction method based on the naive Bayesian model according to claim 1, characterized in that: The expression of the third probability score is: in, is the third probability score, Indicates that the node pair (x, y) has an edge in the target layer, Indicates that the node pair (x, y) has no edge in the target layer, U xy is the feature set, When nodes x and y have an edge in the auxiliary layer, Otherwise, 0; in, Indicates that nodes x and y are in the auxiliary layer G A There is an edge, and in G T The probability that a layer also has an edge is calculated as follows: Among them, n 11 is the number of node pairs that are linked in both layers of the network, n 01 is the number of node pairs that do not have links in the target layer but have links in the auxiliary layer, n 00 is the number of node pairs that do not have links in both layers, n 10 is the number of node pairs that are linked in the target layer but not in the auxiliary layer, is the probability that x and y have an edge in the target layer when they have an edge in the auxiliary layer, is the probability that x and y have edges in the target layer when there are no edges in the auxiliary layer. p1, p2 and q are approximately calculated by the following formula:

5. The multi-layer network link prediction method based on the naive Bayes model according to claim 1 is characterized in that: The expression of the maximum and minimum normalization method is: Among them, r max With r min are the maximum and minimum values ​​respectively, r is the normalized value, and r is the original value.

6. The multi-layer network link prediction method based on the naive Bayes model according to claim 1, characterized in that: The expression of the first probability score is: Among them, α is the ratio parameter between the topological structure information and the auxiliary layer information, α∈[0,1], are three different first probability scores obtained according to three different second probability score expressions, is the third probability score.

7. The multi-layer network link prediction method based on the naive Bayes model according to claim 1 is characterized in that: Based on the change of the ratio parameter between the topological structure information of the training set and the information of the auxiliary layer, the multi-layer network link prediction result is evaluated by an evaluation index; The evaluation indicators include: AUC, Ranking score, Precision; The AUC is used to evaluate the overall correctness of the algorithm, the Ranking score is used to measure the scores of the links in the test set in descending order in the predicted links, and the Precision is used to sort the node pairs in descending order according to the probability scores to obtain the ratio of the number of potential links to the number of selected node pairs.

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