CN108847993B - Link prediction method based on multi-order path intermediate node resource allocation - Google Patents

Link prediction method based on multi-order path intermediate node resource allocation Download PDF

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CN108847993B
CN108847993B CN201810805798.5A CN201810805798A CN108847993B CN 108847993 B CN108847993 B CN 108847993B CN 201810805798 A CN201810805798 A CN 201810805798A CN 108847993 B CN108847993 B CN 108847993B
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CN108847993A (en
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吴云洋
黄虎
胡金晖
魏晓龙
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Smart City Research Institute Of China Electronics Technology Group Corp
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Abstract

The invention discloses a link prediction method based on multi-order path intermediate node resource allocation, which selects any two unconnected links in a network G by establishing a network model GTaking the node x and the node y as a node pair to be predicted, and calculating similarity values L2 of the node pair to be predicted under the resource allocation action of all second-order path intermediate nodesx，y(ii) a Secondly, calculating the similarity value L3 of the node pair under the resource transfer allocation action of two intermediate nodes of all the third-order pathsx，y(ii) a And finally, calculating the final similarity value S of any two unconnected node pairs in the network G by combining the resource allocation effect of the intermediate nodes of the second-order path and the third-order pathxyAccording to the final similarity value SxyAnd carrying out network link prediction on the node pair to be predicted. The invention fully excavates the structural characteristics of the network path, deeply describes the function of the key node and has high network link prediction accuracy.

Description

Link prediction method based on multi-order path intermediate node resource allocation
Technical Field
The invention relates to the technical field of network science and technology and network link prediction, in particular to a link prediction method based on multi-order path intermediate node resource allocation.
Background
In recent years, a great deal of research is carried out to understand the properties of complex systems such as society, biology, information and the like from the perspective of network structures, and along with the increasing development and popularization of network science, people know the complex networks more deeply and clearly. Link prediction is an important branch of network science, and mainly researches two aspects: on one hand, the method predicts some actually existing continuous edges which are not detected due to information loss, and on the other hand, the method predicts the continuous edges which are possibly linked in the future in the network evolution process.
In the field of computers, a link prediction method mainly utilizes external information such as node attributes and the like to carry out similarity characterization based on machine learning and Markov chains. Because the acquisition of information such as node attributes is difficult, for example, the information is confidential or the information itself is not trusted, the traditional method for analyzing the link by using the node attributes has a limited effect in practical application. Therefore, the link prediction based on the topological structure of the connection relation network has more important research and application values. The most classical and simple same-genus common neighbor algorithm (CN) in the two nodes considers that the more the two nodes have common neighbor nodes, the more the two nodes are similar; for another example, an adaptive-Adar Algorithm (AA) and a resource allocation algorithm (RA) both consider the value information of the common neighbors of two unconnected nodes and give different weights to different neighbor nodes. There are also e.g. local path algorithms (LP), which take into account the influence of the third order path on the basis of common neighbors. The advantage of these conventional prediction algorithms based on local structure information is that they are less computationally complex. However, the information examined by the algorithms is too limited to be highlighted in a large complex network. The traditional link prediction method has the defects of insufficient extraction and excavation of a network structure, insufficient excavation of the reasonable resource distribution problem of the intermediate node, and no deep excavation of the important role of the intermediate node in two unconnected nodes; some consider only the neighbor nodes and do not continue to discuss the influence of the third-order or even higher-order nodes, and once two unconnected nodes do not have a common neighbor node, they are considered to have no similarity, which is obviously not strict enough.
Disclosure of Invention
In order to overcome the problem that the prediction precision is not high due to limited information considered by the existing link prediction method based on local structure information, the invention provides a link prediction method based on the multi-order path intermediate node resource allocation function with high prediction precision.
In order to achieve the above object, the present invention provides a link prediction method based on multi-order path intermediate node resource allocation, which comprises the following steps:
s1, establishing an undirected network model G (V, E), wherein V represents a node set, and E represents an edge set;
s2, selecting any two unconnected nodes x and y in the network G as node pairs to be predicted, and calculating similarity values L2 of the node pairs to be predicted under the resource allocation effect of all second-order path intermediate nodes according to the resource allocation of all second-order path intermediate nodes of the node pairs to be predictedx,yThe calculation process is as follows:
s21, randomly selecting one second-order path from all second-order paths, marking the middle node of the second-order path as w, and calculating the distribution value of the node x connected to the node y through the middle node w:
Figure GDA0002784395710000021
where k (w) represents the value of node w, | OwyL represents the number of common adjacent nodes of the node w and the node y;
s22, calculating the assigned value that node y is connected to node x through intermediate node w:
Figure GDA0002784395710000022
Figure GDA0002784395710000023
wherein, | OwxL represents the number of common neighbor nodes of the node w and the node x;
s23, according to the centrality of the second-order path intermediate node w selected in the step S21 in the network G, the centrality index of the intermediate node w is calculated:
Figure GDA0002784395710000024
wherein N represents the total number of nodes of the network model;
s24, calculating the similarity value of the node to be predicted under the resource allocation action of the intermediate node w of the second-order path selected in the step S21:
Figure GDA0002784395710000025
s25, repeating the steps S21-S24, and calculating the similarity value of the node to be predicted under the resource allocation action of all second-order path intermediate nodes w:
Figure GDA0002784395710000026
wherein (l)2)x,yRepresenting a path set with the length of 2 between the node pairs (x, y) to be predicted, and w representing an intermediate node passing through any path in the path set;
s3, according to the resource allocation of all third-order path intermediate nodes of the node pair to be predicted, calculating the similarity value of the node pair under the resource transfer allocation action of two intermediate nodes of all third-order paths:
Figure GDA0002784395710000031
wherein (l)3)x,yRepresenting a path set with the length of 3 between the node pair (x, y) to be predicted, (a, b) representing two intermediate nodes passing through any path in the path set, and alpha representing a third-order path pair similarity value L3x,yThe contribution of (1), alpha > 0;
s4, constructing a first link prediction algorithm model by combining the resource allocation effect of the intermediate nodes of the second-order path and the third-order path, calculating the final similarity value of any two unconnected node pairs in the network G through the first link prediction algorithm model, and performing network link prediction on the two unconnected node pairs according to the final similarity value of the two unconnected node pairs; the first link prediction algorithm model is constructed by the following process:
s41, calculating the final similarity value of the node pair (x, y) to be predicted by combining the resource allocation effect of the intermediate node of the second-order path and the third-order path:
Figure 5
s42, calculating the corresponding final similarity values of all unconnected node pairs in the network G, arranging the obtained final similarity values according to a descending order, combining the corresponding node pairs together to obtain a first similarity-node pair list, and predicting the link in the network G according to the first similarity-node pair list. Wherein the first similarity is the final similarity S of node pairs further ahead in the node pair listxyThe larger the size of the tube is,indicating that the node pair is more likely to generate a link.
Preferably, the method further comprises the following steps: s5, constructing a second link prediction algorithm model by combining the resource allocation effect of the intermediate node from the second-order path to the n-order path, calculating the final similarity value of any two unconnected node pairs in the network G through the second link prediction algorithm model, and performing network link prediction on the two unconnected node pairs according to the final similarity value of the two unconnected node pairs; the second link prediction algorithm model is constructed as follows:
s51, calculating the final similarity value of the node pair (x, y) to be predicted by combining the final similarity value of the node pair (x, y) to be predicted under the resource allocation effect of the intermediate node from the second-order path to the n-order path:
Figure 6
wherein (a, b, c, d, …, mu, lambda) represents n-1 intermediate nodes passing through any one path in the n-order path set, alphan-2Represents the final similarity value S of the n-order path pairn xyThe degree of contribution of (c);
s52, pressing S for all unconnected node pairs in the network Gn xyThe calculation formula calculates the corresponding final similarity values of all unconnected node pairs, the obtained final similarity values are arranged according to a descending order, the corresponding node pairs are combined together to obtain a second similarity-node pair list, and the link in the network G is predicted according to the second similarity-node pair list. Wherein the second similarity is the final similarity S of node pairs further forward in the node pair listn xyThe larger the number, the more likely it is that the node pair is to generate a link.
The network link prediction method provided by the invention fully excavates the resource allocation effect of the intermediate node of the unconnected node pair on the network link, considers the three-order or even higher-order path, considers the centrality of different nodes and distinguishes the importance of the nodes. Compared with the traditional method, the link prediction method provided by the invention further expands the network structure information to the global structure information of the network, more deeply excavates the network path structure characteristics, and more deeply describes the effect of the key node, thereby effectively improving the link prediction precision.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a flow diagram of the present invention;
FIG. 2 is a flow chart of an embodiment of the present invention;
the objects, features and advantages of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
The invention provides a link prediction method based on multi-order path intermediate node resource allocation.
Referring to fig. 1-2, fig. 1 is a flow chart of the present invention, and fig. 2 is a flow chart of the present invention.
As shown in fig. 1-2, in the embodiment of the present invention, the link prediction method includes the following steps:
and S1, establishing an undirected network model G ═ V, E, wherein V represents a node set, E represents an edge set, and the total number of nodes in the network is marked as N.
S2, selecting any two unconnected nodes x and y in the network G as node pairs to be predicted, and calculating similarity values L2 of the node pairs to be predicted under the resource allocation effect of all second-order path intermediate nodes according to the resource allocation of all second-order path intermediate nodes of the node pairs to be predictedx,y. Specifically, the similarity value L2x,yThe calculation process of (2) is as follows:
s21, randomly selecting one second-order path from all second-order paths, marking the middle node of the second-order path as w, and calculating the branch of the node x connected to the node y through the middle node wMatching value:
Figure GDA0002784395710000051
where k (w) represents the value of node w, | OwyL represents the number of common adjacent nodes of the node w and the node y;
s22, calculating the assigned value of node y connected to node x through intermediate node w, taking into account the asymmetry in network G:
Figure GDA0002784395710000052
wherein, | OwxL represents the number of common neighbor nodes of the node w and the node x;
s23, according to the centrality of the second-order path intermediate node w selected in the step S21 in the network G, the centrality index of the intermediate node w is calculated:
Figure GDA0002784395710000053
n represents the total number of nodes of the network model, and the importance degree of different nodes is distinguished by using a centrality index;
s24, calculating the similarity value of the node to be predicted under the resource allocation action of the intermediate node w of the second-order path selected in the step S21:
Figure GDA0002784395710000054
s25, repeating the steps S21-S24, and calculating the similarity value of the node to be predicted under the resource allocation action of all second-order path intermediate nodes w:
Figure GDA0002784395710000055
wherein (l)2)x,yAnd (3) representing a path set with the length of 2 between the node pairs (x, y) to be predicted, and w representing an intermediate node passing through any path in the path set.
S3, analogizing the resource allocation effect of the middle nodes of the second-order path in the step S2, further considering the resource allocation effect of the two middle nodes of the third-order path, and calculating according to the resource allocation of the middle nodes of all the third-order paths of the node pair to be predictedThe node pair has similarity under the resource transfer and allocation action of two intermediate nodes of all third-order paths:
Figure GDA0002784395710000056
Figure GDA0002784395710000061
(l3)x,yrepresenting a path set with the length of 3 between the node pair (x, y) to be predicted, (a, b) representing two intermediate nodes passing through any path in the path set, and alpha representing a third-order path pair similarity value L3x,yThe contribution of (1), alpha > 0.
In step S3, in consideration of the resource transfer allocation role of the two intermediate nodes of the 3 rd order path, the adjacent nodes are connected by product method during transfer. In addition, because the contribution degree of the third-order path is lower than that of the second-order path, an adjusting parameter alpha is added before the accumulated value of the similarity values under the resource transfer allocation action of two intermediate nodes of all the third-order paths, and alpha is a small positive decimal and is used for reducing the similarity value L3x,yAt the final similarity value SxyThe weight in (1).
S4, a first link prediction algorithm model is constructed by combining the resource allocation effect of the second-order path and the third-order path intermediate nodes, the final similarity value of any two unconnected node pairs in the network G is calculated through the first link prediction algorithm model, and network link prediction is carried out on the two unconnected node pairs according to the final similarity value of the two unconnected node pairs.
Specifically, the first link prediction algorithm model is constructed as follows:
s41, calculating the final similarity value of the node pair (x, y) to be predicted by combining the resource allocation effect of the intermediate node of the second-order path and the third-order path:
Figure 9
s42, calculating the final similarity values corresponding to all the unconnected node pairs in the network G, and arranging the obtained final similarity values in descending orderAnd combining the corresponding node pairs together to obtain a first similarity-node pair list, and predicting the link in the network G according to the first similarity-node pair list. Wherein the first similarity is the final similarity S of node pairs further ahead in the node pair listxyThe larger the number, the more likely it is that the node pair is to generate a link.
Further, in this embodiment, in order to include a larger amount of network structure information, and consider global information of the network, the link prediction method further includes: s5, combining the resource allocation function of the intermediate node from the second-order path to the n-order path, constructing a second link prediction algorithm model, calculating the final similarity value of any two unconnected node pairs in the network G through the second link prediction algorithm model, and performing network link prediction on the two unconnected node pairs according to the final similarity value of the two unconnected node pairs.
Specifically, the second link prediction algorithm model is constructed as follows:
s51, calculating the final similarity value of the node pair (x, y) to be predicted by combining the final similarity value of the node pair (x, y) to be predicted under the resource allocation effect of the intermediate node from the second-order path to the n-order path:
Figure 6
wherein (l)n)x,yRepresents a path set with the length of n between the node pairs (x, y) to be predicted, (a, b, c, d, …, mu, lambda) represents n-1 intermediate nodes passing through any path of the n-order path set, alphan-2Represents the final similarity value S of the n-order path pairn xyThe degree of contribution of (c);
s52, pressing S for all unconnected node pairs in the network Gn xyThe calculation formula calculates the corresponding final similarity values of all unconnected node pairs, the obtained final similarity values are arranged according to a descending order, the corresponding node pairs are combined together to obtain a second similarity-node pair list, and the link in the network G is predicted according to the second similarity-node pair list. Wherein the second similarity is the final similarity S of node pairs further forward in the node pair listn xyThe larger the size, the larger the sectionThe point pair is more likely to be linked.
In step S5, the method is extended to the n-order path according to the same node resource allocation operation principle disclosed in steps S1 to S4, and the intermediate node resource allocation operations of the paths of different orders are considered in combination, and similarly, the network asymmetry phenomenon is considered. In addition, when the order of the path is one order per liter, the relative contribution of the path is relatively reduced, and an adjustable parameter alpha is added to each order of the pathn-2The contribution degree of different paths is adjusted, namely the weight of the multi-order paths is reduced. Thus, the accuracy of link prediction in the network G is improved by taking the above-described comprehensive factors into consideration.
The method has the advantages that the important effect of the intermediate nodes which are not connected with the node pairs on network link is fully excavated, and the reasonable resource distribution effect of the intermediate nodes and the centrality difference of the nodes are considered on the basis of the traditional node-based prediction method considering the number and the value of the nodes and the like. Meanwhile, the defects that the distribution condition of the fraction values of the similarity values in the second-order path calculation is concentrated and the discrimination degree is very limited are also considered, the influence effect of intermediate nodes on the third-order path and even higher-order paths is considered, the similarity which is not distinguished by the second-order path is distinguished again, the network structure information is further expanded, the network structure is deeply mined and the key nodes in the network are depicted by focusing on the global structure information of the network, and the link prediction precision is effectively improved.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all modifications and equivalents of the present invention, which are made by the contents of the present specification and the accompanying drawings, or directly/indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (2)

1. A multi-order path intermediate node resource allocation-based link prediction method is characterized by comprising the following steps:
s1, establishing an undirected network model G (V, E), wherein V represents a node set, and E represents an edge set;
s2, selecting any two unconnected nodes x and y in the network G as node pairs to be predicted, and calculating similarity values L2 of the node pairs to be predicted under the resource allocation effect of all second-order path intermediate nodes according to the resource allocation of all second-order path intermediate nodes of the node pairs to be predictedx,yThe calculation process is as follows:
s21, randomly selecting one second-order path from all second-order paths, marking the middle node of the second-order path as w, and calculating the distribution value of the node x connected to the node y through the middle node w:
Figure FDA0002784395700000011
Figure FDA0002784395700000012
where k (w) represents the value of node w, | OwyL represents the number of common adjacent nodes of the node w and the node y;
s22, calculating the assigned value that node y is connected to node x through intermediate node w:
Figure FDA0002784395700000013
Figure FDA0002784395700000014
wherein, | OwxL represents the number of common neighbor nodes of the node w and the node x;
s23, according to the centrality of the second-order path intermediate node w selected in the step S21 in the network G, the centrality index of the intermediate node w is calculated:
Figure FDA0002784395700000015
wherein N represents the total number of nodes of the network model;
s24, calculating the similarity value of the node to be predicted under the resource allocation action of the intermediate node w of the second-order path selected in the step S21:
Figure FDA0002784395700000016
Figure FDA0002784395700000017
s25, repeating the steps S21-S24, and calculating the similarity value of the node to be predicted under the resource allocation action of all second-order path intermediate nodes w:
Figure FDA0002784395700000018
wherein (l)2)x,yRepresenting a path set with the length of 2 between the node pairs (x, y) to be predicted, and w representing an intermediate node passing through any path in the path set;
s3, according to the resource allocation of all third-order path intermediate nodes of the node pair to be predicted, calculating the similarity value of the node pair under the resource transfer allocation action of two intermediate nodes of all third-order paths:
Figure FDA0002784395700000019
wherein (l)3)x,yRepresenting a path set with the length of 3 between the node pair (x, y) to be predicted, (a, b) representing two intermediate nodes passing through any path in the path set, and alpha representing a third-order path pair similarity value L3x,yThe contribution of (1), alpha > 0;
s4, constructing a first link prediction algorithm model by combining the resource allocation effect of the intermediate nodes of the second-order path and the third-order path, calculating the final similarity value of any two unconnected node pairs in the network G through the first link prediction algorithm model, and performing network link prediction on the two unconnected node pairs according to the final similarity value of the two unconnected node pairs; the first link prediction algorithm model is constructed by the following process:
s41, calculating the final similarity value of the node pair (x, y) to be predicted by combining the resource allocation effect of the intermediate node of the second-order path and the third-order path:
Figure 1
s42, calculating the corresponding final similarity values of all unconnected node pairs in the network G, arranging the obtained final similarity values according to a descending order, combining the corresponding node pairs together to obtain a first similarity-node pair list, and predicting the link in the network G according to the first similarity-node pair list.
2. The method for link prediction based on multi-order path intermediate node resource allocation according to claim 1, further comprising: s5, constructing a second link prediction algorithm model by combining the resource allocation effect of the intermediate node from the second-order path to the n-order path, calculating the final similarity value of any two unconnected node pairs in the network G through the second link prediction algorithm model, and performing network link prediction on the two unconnected node pairs according to the final similarity value of the two unconnected node pairs; the second link prediction algorithm model is constructed as follows:
s51, calculating the final similarity value of the node pair (x, y) to be predicted by combining the final similarity value of the node pair (x, y) to be predicted under the resource allocation effect of the intermediate node from the second-order path to the n-order path:
Figure DEST_PATH_6
wherein (a, b, c, d, …, mu, lambda) represents n-1 intermediate nodes passed on any one path in the n-th order path set; alpha is alphan-2Represents the final similarity value S of the n-order path pairn xyThe degree of contribution of (c);
s52, pressing S for all unconnected node pairs in the network Gn xyThe calculation formula calculates the corresponding final similarity values of all unconnected node pairs, the obtained final similarity values are arranged according to a descending order, the corresponding node pairs are combined together to obtain a second similarity-node pair list, and the link in the network G is predicted according to the second similarity-node pair list.
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