Integrated link prediction method based on multiple similarity indexes and storage medium

Abstract

The invention discloses an integrated link prediction method based on multiple similarity indexes and a storage medium. The integrated link prediction method comprises the following steps: step 1, sampling a complex network to obtain node pairs; 2, similarity indexes between the node pairs are calculated based on multiple similarity algorithms, and normalization processing is carried out on the similarity indexes between the multiple node pairs to obtain multiple similarity index scores; 3, integrating multiple similarity index scores based on an OWA operator to construct a mapping relation; 4, converting the mapping relation in the step 3 into an optimization problem based on a maximum entropy method, and solving the score weight of each similarity index; step 5, solving a comprehensive similarity score of the node pair based on the plurality of similarity index scores in the step 2 and each similarity index score weight in the step 4; and performing link prediction based on the comprehensive similarity score of the node pair. According to the method, the link prediction precision can be improved to a certain extent, and the stability is relatively good.

Description

Technical Field

[0001] The present invention relates to the technical field of link prediction, and in particular to an integrated link prediction method and storage medium based on multiple similarity indicators. Background Art

[0002] Complex networks are the core tools for studying complex systems. Complex networks abstract individuals and relationships in real systems into nodes and links, helping people understand the overall structure and function of complex systems. Link prediction is a basic and important topic in complex network science research. Its purpose is to predict ungenerated or unobserved links in the network through observable network structures. Link prediction can not only deepen our understanding of network evolution, but also be widely used in various fields of natural and artificial complex systems. For example, link prediction can help discover potential protein interactions and reduce experimental costs; when shopping on e-commerce platforms, based on the previous purchase information and related attribute information of individuals and their friends, the next purchase behavior of online users can be predicted and corresponding recommendations can be made; in addition, in online social networks such as Facebook and Twitter, link prediction plays a vital role in recommending new friends.

[0003] The core issue of link prediction research is how to design algorithms to extract effective features from the existing structural information of the network to predict potential links. There are many existing link prediction methods, among which similarity-based algorithms play a very important role in link prediction. Its basic assumption is that the more similar the nodes are, the more likely they are to have links. The current similarity-based algorithms can be roughly divided into three categories: local algorithms, semi-local algorithms, and global algorithms. Each algorithm has its own advantages and disadvantages. Local algorithms such as CN, AA, RA, etc. have low computational complexity, but do not consider more network topology information and have average prediction accuracy; global algorithms such as KATZ, LHN-II, MFI, etc., although they fully consider the global topology information and have high prediction accuracy, their computational complexity is too high and are not suitable for large-scale networks; semi-local algorithms such as LRW, SRW, LP, etc., although they take into account both prediction accuracy and computational complexity, they are more dependent on special network structures.

[0004] In recent years, the research on ensemble learning has achieved many satisfactory theoretical and practical results, but there are few studies on the integration of link prediction algorithms. At present, most of the ensemble methods for link prediction focus on the integration of algorithms of the same type, and lack effective integration between algorithms of different types. Therefore, the integration of different types of algorithms has important theoretical and practical significance. Summary of the invention

[0005] In view of the technical problems existing in the prior art, the present invention integrates different types of algorithms so that the proposed integrated algorithm can have better performance in different scenarios. Different algorithms may have different performances under different graph structures. By combining these algorithms, the integrated algorithm can perform more balanced in different scenarios, thereby improving the accuracy and stability of the algorithm.

[0006] In a first aspect, the present invention provides an integrated link prediction method based on multiple similarity indicators, comprising the following steps:

[0007] Step 1: Sample the complex network to obtain node pairs;

[0008] Step 2: Based on multiple similarity algorithms, similarity indices between the node pairs are calculated respectively, and similarity indices between any node pairs are normalized to obtain multiple similarity index scores;

[0009] Step 3: Based on the OWA operator, multiple similarity index scores are integrated to construct a mapping relationship;

[0010] Step 4: Based on the maximum entropy method, the mapping relationship in step 3 is converted into an optimization problem, and the score weight of each similarity index is solved;

[0011] Step 5: Based on the multiple similarity index scores in step 2 and the weight of each similarity index score in step 4, the comprehensive similarity score of the node pair is solved; and link prediction is performed based on the comprehensive similarity score of the node pair.

[0012] Furthermore, the method further includes step 6: verifying the link prediction performance based on the AUC value.

[0013] Furthermore, the multiple similarity algorithms in step 1 include: CN algorithm, LRW algorithm and KATZ algorithm.

[0014] Furthermore, the similarity index s between node pairs calculated based on the CN algorithm is ij CN for:

[0015]

[0016] Among them, Γ(i) is the set of neighbors of node i, Γ(j) is the set of neighbors of node j, and N is the total number of nodes in the complex network.

[0017] Furthermore, the similarity index between node pairs calculated based on the LRW algorithm is for:

[0018]

[0019] Among them, ki is the degree of node i, k j is the degree of node j, E = E train ∪E test is the set of links in the complex network G, E train is the training set, E test is the test set, π ij (t) represents the probability that a random walker at node i will be at node j after t steps, π ji (t) represents the probability that a random walker at node j will be at node i after t steps.

[0020] Furthermore, the similarity index between node pairs calculated based on the KATZ algorithm is for:

[0021]

[0022] in, is the set of all paths of length l connecting node i and node j; β is a free parameter that controls the path weight, A ij is an element of the adjacency matrix A of the complex network G. If node i and node j have a link, A ij is 1 if the value is true, otherwise it is 0.

[0023] Furthermore, the mapping relationship constructed in step 3 is:

[0024]

[0025] in, and They are the similarity index scores based on CN algorithm, LRW algorithm and KATZ algorithm respectively. For about and The mapping function, c k for and The kth value in the sequence according to some criteria; w k is the kth weight.

[0026] Furthermore, the optimization problem in step 4 is:

[0027]

[0028] w k ∈[0,1],k=1,2,...,m

[0029] Among them, θ is the optimistic factor, θ∈[0,1], m represents the number of similarity index scores, max is the maximum value, st is the constraint condition, ln is the natural logarithm, and ∑ represents the sum.

[0030] Furthermore, the comprehensive similarity score of the node pair in step 5 is:

[0031]

[0032] in, is the comprehensive similarity score between node i and node j.

[0033] In another aspect, the present invention provides a computer readable medium, wherein the computer readable medium is a server workstation;

[0034] The server workstation stores a computer program executed by the electronic device. When the computer program is executed on the electronic device, the electronic device executes the steps in the integrated link prediction method based on multiple similarity indicators.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention integrates a variety of different types of classic link prediction algorithms based on similarity. The OCLK integrated algorithm is theoretically valid, and its feasibility and effectiveness have been proven in multiple real networks. Compared with the three independent algorithms, the OCLK algorithm can improve the accuracy of link prediction in a certain integrated weight distribution range; moreover, in the face of different test set ratios, the OCLK integrated algorithm always performs best and has better stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art description. Obviously, the drawings described below are some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0038] Figure 1 : A schematic diagram of the method flow provided by an embodiment of the present invention;

[0039] Figure 2 : AUC trend diagram of the integrated algorithm OCLK under different optimistic factors according to the embodiment of the present invention;

[0040] Figure 3 : A trend diagram showing the change of AUC values ​​of the four link prediction algorithms in the PB network with the proportion of the test set according to the embodiment of the present invention;

[0041] Figure 4 : Trend diagram of the AUC values ​​of the four link prediction algorithms according to the embodiments of the present invention changing with the optimistic factor θ. DETAILED DESCRIPTION

[0042] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present application. Therefore, the present application is not limited by the specific embodiments disclosed below.

[0043] The terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments described here can be implemented in an order other than the content illustrated or described here. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or modules is not necessarily limited to those steps or modules clearly listed, but may include other steps or modules that are not clearly listed or inherent to these processes, methods, products or devices. The naming or numbering of steps in this application does not mean that the steps in the method flow must be executed in the time / logical sequence indicated by the naming or numbering. The process steps that have been named or numbered can change the execution order according to the technical purpose to be achieved, as long as the same or similar technical effects can be achieved. The division of units that appear in this application is a logical division. There may be other division methods when implementing in actual applications. For example, multiple units can be combined or integrated in another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between each other shown or discussed may be through some interfaces, and the indirect coupling or communication connection between units may be electrical or other similar forms, which are not limited in this application. Moreover, the units or subunits described as separate components may or may not be physically separated, may or may not be physical units, or may be distributed in multiple circuit units, and some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this application.

[0044] In the description of the present invention, it should be noted that the professional terms used in the present invention are first explained and annotated as follows:

[0045] CN algorithm (Common Neighbor Algorithm): CN algorithm refers to the common neighbor algorithm, which is a commonly used similarity measurement method in graph theory and is widely used in social network analysis, recommendation systems, link prediction and other fields. The algorithm measures the similarity of nodes based on the number of common neighbors between nodes in the graph.

[0046] LRW algorithm (Local Random Walk Algorithm): LRW algorithm refers to the local random walk algorithm. The local random walk algorithm is an efficient and flexible graph (network) exploration method, which is widely used in network analysis, machine learning, and recommendation systems. Its core idea is to explore the local structure of the graph (network) by simulating random jumps between nodes, and it can quickly process large-scale graph (network) data.

[0047] KATZ algorithm (Katz Indices): The KATZ algorithm was first proposed by Leo Katz. It can effectively measure the similarity between nodes by comprehensively considering the influence of all paths in the graph and adjusting the contribution of path length to similarity using a decay factor. It is suitable for scenarios that need to consider indirect relationships, such as social network analysis, link prediction, and recommendation systems.

[0048] OWA operator (Ordered Weighted Averaging Operator): OWA operator refers to the ordered weighted average operator. By introducing the concepts of weight and ranking, the OWA operator provides a more flexible decision-making method than the traditional weighted average in multi-criteria decision-making. It can not only consider the relative importance of different criteria, but also show different decision-making tendencies (such as optimism, pessimism or averaging) according to the selection of weight vectors.

[0049] MEM (Maximum Entropy Method): MEM is an entropy-based statistical inference method that is widely used in many fields such as physics, informatics, and economics. The maximum entropy principle comes from information theory, which is to infer the most "uniform" or "unbiased" distribution given known constraints. Simply put, the maximum entropy method selects the probability distribution that best fits the known information without making any additional assumptions by maximizing entropy.

[0050] Example 1

[0051] This embodiment provides an integrated link prediction method based on multiple similarity indicators, including the following steps:

[0052] Step 1: Sample the complex network to obtain node pairs;

[0053] Step 2: Calculate the similarity indexes between the node pairs based on multiple similarity algorithms respectively, and normalize the similarity indexes between multiple node pairs to obtain multiple similarity index scores;

[0054] Similarity index between node pairs calculated based on CN algorithm for:

[0055]

[0056] Among them, Γ(i) is the set of neighbors of node i, Γ(j) is the set of neighbors of node j, and N is the total number of nodes in the complex network. The CN algorithm points out that if two unconnected nodes have more common neighbor nodes, the two nodes are more likely to be linked.

[0057] Similarity index between node pairs calculated based on LRW algorithm for:

[0058]

[0059] Among them, k i is the degree of node i, k j is the degree of node j, E = E train ∪E test is the set of links in the complex network G, E train is the training set, E test is the test set, π ij (t) represents the probability that a random walker at node i will be at node j after t steps, π ji (t) represents the probability that a random walker at node j will be at node i after t steps.

[0060] LRW only focuses on the local information of nodes within a limited step size, so it can effectively measure the local structural similarity.

[0061] Similarity index between node pairs calculated based on KATZ algorithm for:

[0062]

[0063] in, is the set of all paths of length l connecting node i and node j; β is a free parameter that controls the path weight, A ij is an element of the adjacency matrix A of the complex network G. If node i and node j have a link, A ij is 1 if the value is true, otherwise it is 0.

[0064] The KATZ algorithm takes into account the path information of the global network and can adaptively handle different network structures. It has high prediction accuracy, but the computational complexity is also high and it is not suitable for large-scale networks. The KATZ algorithm is based on all path information of the network and directly sums the path set, decaying exponentially by length to give more weight to shorter paths. Obviously, very small β produces measurements close to the CN indicator because long paths contribute little. The similarity matrix can be written as:

[0065]

[0066] Where I is the identity matrix. Note that β must be less than the inverse of the largest eigenvalue of the adjacency matrix A to ensure convergence.

[0067] In this embodiment, in order to make the integration more effective, the similarity scores obtained above are and Normalization is performed so that the link likelihood score can fall within the interval [0,1]. Assume and Respectively indicate the score and The results are obtained using the normalization formula below.

[0068]

[0069] In the formula, x new Represents the result after normalization; x i represents the i-th score; x min and x max Represent the minimum and maximum scores respectively.

[0070] Step 3: Based on the OWA operator, multiple similarity index scores are integrated to construct a mapping relationship;

[0071] The MEM (maximum entropy) method is used to solve the OWA operator, that is, to solve the weight vector of the OCLK integration algorithm. The OWA operator is a commonly used information integration technology, which is a mapping F:R m →R, which can be expressed as

[0072]

[0073] Among them, s k (k=1,2,...,m) is the predicted value of the kth indicator; c k are the predicted values ​​s1,s2,...,s m The kth value in the sequence according to a certain standard (the present invention is sorted in descending order); k is the kth weight, indicating the contribution of the corresponding independent prediction value to the final result.

[0074] The mapping relationship constructed in this embodiment is:

[0075]

[0076] in, and They are the similarity index scores based on CN algorithm, LRW algorithm and KATZ algorithm respectively. About and The mapping function, c k for and The kth value in the sequence according to some criteria; w k is the kth weight.

[0077] The similarity-based link prediction algorithm in this embodiment obtains a similarity matrix by calculating node similarity or path similarity, and then uses performance measurement indicators such as AUC to calculate in the similarity matrix to evaluate the prediction performance of the algorithm. Therefore, it is a good choice to integrate the three different types of algorithms selected and use the OWA operator. The OWA operator can sort the importance (weight) of the input values ​​according to demand. Because the three algorithms CN, LRW, and KATZ consider different network information when making link predictions, they will have different similarity scores, so they can be sorted according to the similarity scores, and the algorithms with high similarity scores, that is, with good prediction performance, are assigned greater weights. This is also in line with the laws of life.

[0078] Step 4: Based on the maximum entropy method, the mapping relationship in step 3 is converted into an optimization problem, and the score weight of each similarity index is solved;

[0079] O'Hagan's Maximum Entropy Method (MEM) transforms the solution of OWA into the following optimization problem:

[0080]

[0081] Among them, the objective function represents the degree to which each indicator is used on average; θ represents the degree to which the integration is similar to the "or" operation. In the present invention, θ is called the optimistic factor, and θ∈[0,1]. The weight vector w=(w1,w2,w3) of the integration algorithm can be solved.

[0082] Step 5: Based on the multiple similarity index scores in step 2 and the weight of each similarity index score in step 4, the comprehensive similarity score of the node pair is solved; and link prediction is performed based on the comprehensive similarity score of the node pair;

[0083] Sort the normalized scores obtained in step 2 to get c k (k=1,2,3); then c k (k=1,2,3) and the weight vector w obtained in step 4 are substituted into step 3 to obtain the similarity score between node i and node j, which is:

[0084]

[0085] Using the above formula, we can find the similarity between nodes of the OCLK integrated algorithm, which can be used to complete the link prediction task in complex networks.

[0086] Step 6: Verify the link prediction performance based on the AUC value.

[0087] The AUC (Area Under the Receiver Operating Characteristic Curve) value is selected as the link prediction algorithm performance measurement indicator. The AUC indicator is defined as:

[0088]

[0089] From the above formula, we can see that when n1=n2=n / 3, AUC=0.5, that is, the link prediction score is completely random. Therefore, the degree to which the AUC value exceeds 0.5 indicates the degree to which the algorithm is superior to the pure random algorithm. By calculating the AUC values ​​of the three independent algorithms and the OCLK integrated algorithm, the performance of the OCLK integrated algorithm can be verified.

[0090] In this embodiment, five real networks from different fields are selected, namely, INT network, GRID network, PB network, PPI network and USAir network. The basic information and topological structure information of these five networks are shown in Table 1 and Table 2 respectively.

[0091] Table 1. Basic information of five real networks

[0092]

[0093] Table 2. Topological information of five real networks

[0094] Serial number network Number of nodes Number of links Average Average clustering coefficient Network density Average path length 1 INT 5022 6258 2.492 0.0231 0.0010 3.973 2 GRID 4940 6594 2.669 0.1602 0.0011 2.8 3 PB 1222 19021 27.355 0.036 0.051 3.39 4 PPI 2375 11693 9.847 0.6115 0.0083 4.147 5 USAir 332 2126 12.807 1.2504 0.039 2.564

[0095] Subsequent experiments were conducted in the same settings. For the LRW algorithm, as shown in Table 2, the average path lengths of the five real networks are all less than 5, so the random walk step size is set to 5; for the KATZ algorithm, the damping factor β is set to 0.01. For the optimistic factor θ, its impact on the performance of the OCLK integrated algorithm is tested, and 15 optimistic factors θ are randomly set to be 0.55, 0.60, 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97 and 0.98.

[0096] The link prediction scores of the three independent algorithms are normalized and sorted. The weights corresponding to 15 different optimistic factors θ are calculated by combining the MEM method. The link prediction is performed using the OCLK algorithm. The specific results are shown in Table 3 and Figure 2 shown. Figure 2 The variation trend of AUC value of OCLK integrated algorithm in five real networks with the change of optimistic factor θ is shown, which verifies the feasibility and effectiveness of OCLK integrated algorithm.

[0097] Table 3. OWA operator weights corresponding to different optimism factors θ

[0098]

[0099]

[0100] Furthermore, the present invention also selects different training set ratios for prediction on the PB network to test the stability of the OCLK algorithm and the three independent algorithms. The specific results are as follows: Figure 3 .Depend on Figure 3 It can be seen that the OCLK integrated algorithm has higher prediction accuracy and stronger stability than the three independent algorithms.

[0101] 10% of the links of the five real networks are selected to form the test set, and 90% of the links are selected to form the training set. The AUC values ​​of link prediction using the CN algorithm, LRW algorithm and KATZ algorithm on the above five real networks are shown in Table 4. The AUC data in Table 4 reflects the accuracy of the algorithm in link prediction of real networks.

[0102] Table 4 AUC values ​​of three independent algorithms on five real networks

[0103]

[0104] In Table 4, for link prediction of each real network, the AUC value of the KATZ algorithm is mostly the highest. The link prediction scores of the three independent algorithms are normalized and sorted, and the OCLK algorithm is used for link prediction in combination with the weights in Table 3. Table 5 shows the AUC values ​​of the OCLK algorithm proposed in the present invention for link prediction on five real networks when the optimism factor θ takes 15 different values.

[0105] Table 5 AUC values ​​of OCLK integrated algorithm under different optimistic factors θ

[0106]

[0107]

[0108] In Table 5, no matter which case, the accuracy of the OCLK algorithm link prediction is very high, reaching more than 90%. Figure 2 In the figure, the AUC value trend of the OCLK integrated algorithm under different optimistic factors θ is shown. For each real network, Table 5 and Figure 2All of them show that the larger the optimistic factor θ of the OCLK link prediction algorithm, the higher the AUC value. This shows that to obtain higher prediction accuracy, a larger optimistic factor θ is required. Moreover, using the same OCLK algorithm, among the five real networks, the prediction accuracy of the PB network is always the smallest, and the prediction accuracy of the INT network is always the highest.

[0109] It can be seen from Table 5 that when the optimistic factor θ takes different values, the OCLK algorithm will have different link prediction accuracies. Figure 4 The AUC values ​​of the OCLK algorithm and three independent algorithms on five real networks are shown as the optimism factor θ changes. Figure 4 In the figure, since the CN algorithm, LRW algorithm and KATZ algorithm are not affected by the optimistic factor θ, their change curves are all horizontal lines; while the AUC value of the OCLK algorithm will change significantly as the optimistic factor θ increases. As with the results in Table 5, among the three independent algorithms, the link prediction accuracy of the KATZ algorithm is mostly the best, with the exception of the link prediction accuracy on the USAir network. Therefore, below we mainly compare the prediction accuracy of the OCLK algorithm and the KATZ algorithm. On the INT and Grid networks (see Figure 4 (a) and (b)), the AUC values ​​of the OCLK algorithm and the KATZ algorithm are similar, and when the optimistic factor θ approaches 1, that is, when the value of w1 approaches 1, the AUC value of the OCLK algorithm will be higher than that of the KATZ. Figure 4 (d)), as the optimistic factor θ increases, the AUC value of the OCLK algorithm gradually increases; until the optimistic factor θ approaches 1, the AUC value of the OCLK algorithm will be higher than that of the KATZ algorithm. Figure 4 (c)), when θ>0.85, the AUC value of the OCLK algorithm is higher than that of the KATZ algorithm. On the USAir network (see Figure 4 (e)), when θ>0.78, the OCLK algorithm performs better than the CN algorithm.

[0110] In this embodiment, four different test set ratios are selected to test the stability of the proposed OCLK integrated algorithm, which are 10%, 14%, 18% and 22% respectively. Each algorithm is performed on the same test set ratio. For the OCLK integrated algorithm, when conducting experiments on five real networks, the optimal optimistic factor θ is selected for each experiment, that is, the predicted AUC value of the OCLK algorithm is the highest. Table 6 shows the AUC values ​​of the four algorithms on five real networks when the test set ratio takes the above four different values. According to Table 6, Figure 4 The corresponding trend of change is shown. The first column of Table 6 contains the proportion of the test set in brackets; the black bold AUC is the maximum value.

[0111] Table 6. AUC values ​​of the four algorithms under different test set ratios

[0112]

[0113] Since Table 6 and Figure 4 Consistent. Figure 4 In the figure, as the proportion of the test set increases, on the five real networks, the AUC values ​​of the CN and LRW algorithms fluctuate greatly, and the stability is poor; while maintaining a high AUC value, the KATZ algorithm is less affected by the change in the proportion of the test set and has better stability; the AUC value of the OCLK integrated algorithm is higher than that of the independent algorithm, and is not greatly affected by the proportion of the test set, and has better stability. This is because the OCLK integrated algorithm combines the advantages of multiple independent algorithms and reduces the fluctuations that may occur in independent algorithms in certain specific scenarios. Different algorithms may perform differently under different graph structures. By combining these algorithms, the integrated algorithm performs more balanced in different scenarios, thereby improving the overall stability.

[0114] Example 2

[0115] A specific embodiment of the present invention also provides a computer-readable medium.

[0116] The computer readable medium is a server workstation;

[0117] The server workstation stores a computer program executed by an electronic device. When the computer program runs on the electronic device, the electronic device executes the steps of an integrated link prediction method based on multiple similarity indicators according to an embodiment of the present invention.

[0118] The above is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed in the present application should be covered within the protection scope of the present application.

[0119] It should be understood that parts not elaborated in detail in this specification belong to the prior art.

[0120] It should be understood that the above description of the preferred embodiment is relatively detailed, and it cannot be considered as limiting the scope of protection of the patent of the present invention. Under the enlightenment of the present invention, ordinary technicians in this field can also make substitutions or modifications without departing from the scope of protection of the claims of the present invention, which fall within the scope of protection of the present invention. The scope of protection of the present invention shall be based on the attached claims.

Claims

1. An integrated link prediction method based on multiple similarity indicators, characterized in that: The following steps are involved: Step 1: Sample the complex network to obtain node pairs; Step 2: Based on multiple similarity algorithms, similarity indices between the node pairs are calculated respectively, and similarity indices between any node pairs are normalized to obtain multiple similarity index scores; Step 3: Based on the OWA operator, multiple similarity index scores are integrated to construct a mapping relationship; Step 4: Based on the maximum entropy method, the mapping relationship in step 3 is converted into an optimization problem, and the score weight of each similarity index is solved; Step 5: Based on the multiple similarity index scores in step 2 and the weight of each similarity index score in step 4, solving the comprehensive similarity score of the node pair; Link prediction is performed based on the comprehensive similarity scores of node pairs.

2. The integrated link prediction method based on multiple similarity indicators according to claim 1, characterized in that: The method also includes step 6: verifying the link prediction performance based on the AUC value.

3. The integrated link prediction method based on multiple similarity indicators according to claim 1, characterized in that: The multiple similarity algorithms in step 1 include: CN algorithm, LRW algorithm and KATZ algorithm.

4. The integrated link prediction method based on multiple similarity indicators according to claim 3 is characterized in that: The similarity index s between node pairs calculated based on the CN algorithm ij CN for: Among them, Γ(i) is the set of neighbors of node i, Γ(j) is the set of neighbors of node j, and N is the total number of nodes in the complex network.

5. The integrated link prediction method based on multiple similarity indicators according to claim 4, characterized in that: Similarity index between node pairs calculated based on LRW algorithm for: Among them, k i is the degree of node i, k j is the degree of node j, E = E train ∪E test is the set of links in the complex network G, E train is the training set, E test is the test set, π ij (t) represents the probability that a random walker at node i will be at node j after t steps, π ji (t) represents the probability that a random walker at node j will be at node i after t steps.

6. The integrated link prediction method based on multiple similarity indicators according to claim 5, characterized in that: Similarity index between node pairs calculated based on KATZ algorithm for: in, is the set of all paths of length l connecting node i and node j; β is a free parameter that controls the path weight, A ij is an element of the adjacency matrix A of the complex network G; if node i and node j are linked, A ij is 1 if the value is true, otherwise it is 0.

7. The integrated link prediction method based on multiple similarity indicators according to claim 6, characterized in that: The mapping relationship constructed in step 3 is: in, and are the similarity index scores calculated based on the CN algorithm, LRW algorithm and KATZ algorithm respectively. For about and The mapping function, c k for and The kth value in the sequence according to some criteria; w k is the kth weight.

8. The integrated link prediction method based on multiple similarity indicators according to claim 7, characterized in that: The optimization problem in step 4 is: Among them, θ is the optimistic factor, θ∈[0,1], m represents the number of similarity index scores, max is the maximum value, st is the constraint condition, ln is the natural logarithm, and ∑ represents the sum.

9. The integrated link prediction method based on multiple similarity indicators according to claim 8, characterized in that: The comprehensive similarity score of the node pair in step 5 is: in, is the comprehensive similarity score between node i and node j.

10. A computer-readable medium, characterized in that The computer readable medium is a server workstation; The server workstation stores a computer program executed by an electronic device, and when the computer program runs on the electronic device, the electronic device executes the steps of the integrated link prediction method based on multiple similarity indicators according to any one of claims 1 to 9.

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