CN116896510B - Link prediction method based on odd-length paths and oriented to two-way network - Google Patents

Link prediction method based on odd-length paths and oriented to two-way network Download PDF

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CN116896510B
CN116896510B CN202310090795.9A CN202310090795A CN116896510B CN 116896510 B CN116896510 B CN 116896510B CN 202310090795 A CN202310090795 A CN 202310090795A CN 116896510 B CN116896510 B CN 116896510B
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赵志立
吴思敏
胡阿慧
张娜娜
谢济全
孙越
杜子豪
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Lanzhou University
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Abstract

A link prediction method based on odd-length paths for a binary network comprises the following steps of: initializing accuracy AUC of the bipartite network, and step 2: dividing a known connected edge set E in a bipartite network into a training set and a testing set; step 3: respectively constructing adjacent matrixes of corresponding networks aiming at the training set and the testing set; then, calculating the basic similarity between any two nodes of the binary network by using a basic link prediction method LPOP based on an odd-length path; step 4: for any two nodes of the bipartite network, calculating the increment part of the similarity; step 5: adding the basic similarity matrix and the incremental matrix to obtain a final similarity value of the two nodes, and step 6: calculating LPOPE the accuracy of the method by using the training set, the testing set and the basic similarity matrix; step 7: the LPOPE method is returned to the accuracy and similarity matrix on the bipartite network. The method and the device improve the accuracy of the binary network link prediction.

Description

Link prediction method based on odd-length paths and oriented to two-way network
Technical Field
The invention belongs to the technical field of complex network analysis, and particularly relates to a link prediction method based on an odd-length path for a binary network.
Background
The main problem of the traditional link prediction method is that the method is proposed for a general network, and unknown links in a binary network cannot be accurately predicted. In addition, the node similarity index based on the local and semi-local information is relatively simple, has relatively high prediction efficiency, and is relatively suitable for link prediction in medium-scale and large-scale complex networks. However, these metrics typically rely on the common neighbors of two nodes, i.e. they typically calculate the connection probability between two nodes based on the number of common neighbors or the topology of the common neighbors. However, since there are only two different node sets in the bipartite network, and the connected edge of a node can only exist between two nodes belonging to the different node sets, it is impossible for a common neighbor to exist between two nodes having connected edges. If there are indirect links between two nodes belonging to two different sets, there are at least two nodes from the different sets between them. In other words, if there is no edge between two nodes belonging to different sets in the bipartite network, the shortest path length between two nodes should be an odd length of three, five or seven. Therefore, the existing link prediction method is not suitable for the link prediction of the binary network.
Disclosure of Invention
In order to overcome the technical problems, the invention aims to provide the link prediction method based on the odd-length paths for the binary network, which not only considers paths with odd-length paths in the binary network, but also calculates the similarity between two nodes belonging to the same set based on the number of common neighbors, thereby improving the accuracy of the link prediction of the binary network.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
A link prediction method based on odd-length paths facing to a two-way network comprises the following steps of;
Step 1: initializing an AUC, setting auc=0; AUC is the accuracy of the link prediction method on a bipartite network with n nodes;
Step 2: dividing a known connected edge set E in a bipartite network into a training set E T and a testing set E P;
Step 3: for a training set E T and a test set E P, respectively constructing adjacent matrixes A T and A P of corresponding networks; then, calculating the basic similarity between any two nodes of the binary network by using a basic link prediction method LPOP based on an odd-length path;
step 4: for any two nodes x and y of the bipartite network, calculating an increment part M xy of the similarity;
Step 5: the base similarity matrix S LPOP calculated by using the LPOP method is added to the incremental matrix M to be the final similarity value of the two nodes, that is:
SLPOPE＝SLPOP+M
Step 6: using training set E T, test set E P and base similarity matrix S LPOPE, calculating LPOPE the accuracy AUC lpope of the method;
Step 7: the method LPOPE is returned to accuracy AUC avg and similarity matrix S LPOPE on the bipartite network.
In the step 2, ninety percent of edges are randomly selected from the known edge set E as a training set E T, and the remaining edges are used as a test set E P, and a test is performed, where e=e T∪EP,ET∩EP =Φ.
In the step 3, the process steps of the basic link prediction method LPOP include:
Step 3.1: let β=0, AUC *＝0,SLPOP* =0, where β e (0, 1) is the super parameter for calculating the basic similarity between any two nodes of the bipartite network, AUC * is the optimal accuracy of the link prediction model under different β, and S LPOP* is the basic similarity matrix for generating AUC *;
Step 3.2: calculating basic similarity between any two nodes of the bipartite network according to the beta value, and storing the result in a basic similarity matrix S LPOP;
The LPOP method considers all paths with odd-numbered binary network length, and an example of the odd-numbered paths between two nodes in a binary network is shown in fig. 4.LPOP the calculation process is as follows:
step 3.3: using training set E T, test set E P and base similarity matrix S LPOP, the accuracy index AUC lpop of the β -value downlink prediction model is calculated. The calculation process of AUC is shown in figure 5;
Step 3.4: if AUC lpop is greater than AUC *, S LPOP*＝SLPOP;
Step 3.5: this is done for β: beta = beta +0.01;
Step 3.6: and judging whether beta is larger than 1. If not greater than 1, return to step 3.2, otherwise LPOP the algorithm ends, return to S LPOP.
In the step 4, the calculating process of the M xy includes:
Step 4.1: let sim 1＝1,sim2 = 1;
Step 4.2: finding all paths x-z 1-z2 -y of length three between the two nodes, wherein x and z 2 belong to one set of the bipartite network and z 1 and y belong to the other set;
step 4.3: if there is no path of length three between x and y, then M xy =1 is returned.
Otherwise, executing the step 4.4;
Step 4.4: for each path of length three between x and y, the similarity based on the number of common neighbors, namely the similarity sim 1 and sim 2 of x and z 2 and z 1 and y, respectively, is calculated. The calculation formula is as follows:
Where k is the number of paths between nodes x and y with a length of three. i is the ith path of length three between nodes x and y, and z i1 and z i2 are the two intermediate nodes on the path. R (x) represents the neighbor node set of node x, |r (x)/(z i2) | represents the number of common neighbors of nodes x and z i2, |r (z i1) |r (y) | represents the number of common neighbors of nodes z i1 and y;
Step 4.5: the incremental portion M xy of node x and y similarity is calculated. The reason for calculating the increment portion M xy is shown in FIG. 6; the calculation formula of M xy is as follows:
Mxy＝sim1*sim2
Step 4.6: and returning an increment matrix M epsilon R n×n of the similarity between the two network nodes.
In the step 7, the similarity matrix S LPOPE includes the possibility of generating a connection between two nodes that are not yet connected in the bipartite network, and the larger the value of a certain position in the similarity matrix S LPOPE, the larger the possibility of generating a connection between two nodes corresponding to the position is, and the size of the possibility of generating a connection between two nodes that are not connected in the bipartite network is predicted according to the similarity matrix S LPOPE.
The invention has the beneficial effects of.
The invention provides a link prediction method based on odd-length paths and oriented to a binary network. The method comprises the steps of firstly calculating the basic similarity S LPOP between any two nodes of a binary network based on an odd-length path, secondly calculating the increment part M of the similarity between two nodes belonging to the same set of the binary network based on the number of common neighbors, and finally adding the basic similarity and the increment part to be used as a final similarity value of the two nodes, namely S LPOPE＝SLPOP +M, so that the accuracy of binary network link prediction is improved. The method can be used for not only the link prediction of the binary network, but also a recommendation system.
Description of the drawings:
FIG. 1 is a schematic illustration of the calculation process of the method LPOPE of the present invention.
Fig. 2 is a calculation process of the method LPOP of the present invention.
Fig. 3 is a schematic diagram of a calculation process of the node similarity increment matrix M according to the present invention.
Fig. 4 is an example of path lengths between two and no edge nodes in a two-way network for a user and a movie. Node 1 and node 7 have a path 1, -6-2-7 with a path length of three; there are two paths 3-8-5-10 and 3-8-4-9-5-10 between node 3 and node 10, with path lengths of three and five, respectively.
Fig. 5 is a schematic diagram of a process for calculating the accuracy index AUC of the link prediction method according to the present invention.
Fig. 6 shows the reason why the present invention calculates the incremental part of the similarity between two nodes belonging to the same set of two-way networks based on the common neighbor number based on LPOP algorithm.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Specific embodiments of the present invention applied in the field of user movie recommendation are given below.
There are several pieces of user-viewed movie history data (<u1,m1>,<u2,m2>,<u3,m3>,…,<u1,m3>,<u3,m1>,…<un,ms>), in which u and m represent a user and a movie, respectively, one user can view a plurality of movies, and one movie can be viewed by a plurality of users. When a binary network is constructed for a user to watch a movie, the user and the movie can be regarded as nodes in the binary network, and a user watching a movie can form a continuous edge between the two nodes. After the binary network is constructed, the steps of recommending movies to the user using LPOPE method are as follows:
Step 1: AUC is initialized, set auc=0. AUC is the accuracy of the link prediction method on the user movie bipartite network; the calculation process is shown in figure 1.
Step 2: the known connected edge set E in the user film bipartite network is divided into a training set E T and a test set E P, namely ninety percent of edges are randomly selected from the known connected edge set E to be used as the training set E T, and the rest edges are used as the test set E P for testing. E=e T∪EP,ET∩EP =Φ;
Step 3: adjacency matrices a T and a P of their corresponding networks are constructed for training set E T and test set E P, respectively. Then, a base link prediction method LPOP based on the odd-length path is used to calculate the base similarity between any two nodes of the bipartite network. The process of the basic link prediction method LPOP is shown in fig. 2, and the steps include:
Step 3.1: let β=0, auc *＝0,SLPOP* =0. Wherein, β∈ (0, 1) is a super parameter for calculating the basic similarity between any two nodes of the user film bipartite network, AUC * is the optimal accuracy of the link prediction model under different β, and S LPOP* is a basic similarity matrix for generating AUC *;
step 3.2: and calculating the basic similarity between any two nodes of the user film bipartite network according to the beta value, and storing the result in a basic similarity matrix S LPOP. The LPOP method considers a full path with an odd number of binary network lengths. An example of an odd length path between two nodes in a two-part network is shown in figure 4.LPOP the calculation process is as follows:
step 3.3: using training set E T, test set E P and base similarity matrix S LPOP, the accuracy index AUC lpop of the β -value downlink prediction model is calculated. The calculation process of AUC is shown in figure 5;
Step 3.4: if AUC lpop is greater than AUC *, S LPOP*＝SLPOP;
Step 3.5: this is done for β: beta = beta +0.01;
Step 3.6: and judging whether beta is larger than 1. If not, returning to the step 3.2, otherwise, ending LPOP algorithm, and returning to the step S LPOP;
step 4: for any two nodes x and y of the user movie bipartite network, the process of calculating the increment part M xy.Mxy of the similarity is shown in fig. 3, and the steps include:
Step 4.1: let sim 1＝1,sim2 = 1;
Step 4.2: all paths x-z 1-z2 -y of length three between the two nodes are found. Wherein x and z 2 belong to one set of the bipartite network and z 1 and y belong to the other set;
step 4.3: if there is no path of length three between x and y, then M xy =1 is returned.
Otherwise, executing the step 4.4;
Step 4.4: for each path of length three between x and y, the similarity based on the number of common neighbors, namely the similarity sim 1 and sim 2 of x and z 2 and z 1 and y, respectively, is calculated. The calculation formula is as follows:
Where k is the number of paths between nodes x and y with a length of three. i is the ith path of length three between nodes x and y, and z i1 and z i2 are the two intermediate nodes on the path. R (x) represents the neighbor node set of node x, |r (x)/(z i2) | represents the number of common neighbors of nodes x and z i2, |r (z i1) |r (y) | represents the number of common neighbors of nodes z i1 and y;
Step 4.5: the incremental portion M xy of node x and y similarity is calculated. The reason for calculating the increment portion M xy is shown in FIG. 6; the calculation formula of M xy is as follows:
Mxy＝sim1*sim2
Step 4.6: and returning an increment matrix M epsilon R n×n of the similarity between the two network nodes of the user film.
Step 5: the base similarity matrix S LPOP calculated by using the LPOP method is added to the incremental matrix M to be the final similarity value of the two nodes, that is:
SLPOPE＝SLPOP+M
Step 6: using training set E T, test set E P and base similarity matrix S LPOPE, calculating LPOPE the accuracy AUC lpope of the method;
step 7: the method returns LPOPE the accuracy AUC avg and the similarity matrix S LPOPE on the user movie network.
The similarity matrix S LPOPE may then be used to recommend movies to the user. The greater the value of a certain position in the similarity matrix S LPOPE, the greater the likelihood that the user corresponding to that position views the relevant movie. For a certain user, a corresponding data row can be found from the similarity matrix S LPOPE, and then a movie which is not watched and has higher similarity is recommended according to the size of the data value.
Figure 5 depicts an odd length path between two nodes in a bipartite network. As shown in fig. 5, node 1 and node 7 have a path 1, -6-2-7 with a path length of three; there are two paths 3-8-5-10 and 3-8-4-9-5-10 between node 3 and node 10, with path lengths of three and five, respectively.
Fig. 6 depicts the reason for calculating the delta portion in the LPOPE method. If the delta portion is not calculated, as shown in FIG. 6, according to LPOP algorithm, there is only one path of length three between node 1 and node 7 of the left and right graphs: 1-6-2-7, so the LPOP algorithm has the same likelihood of having a border between node 1 and node 7 in the left and right graphs. However, since the nodes 1 and 2 and the nodes 6 and 7 of the right graph have multiple common neighbors, the probability of edge connection between the nodes 1 and 7 of the right graph should be greater than that of the left graph, that is, the incremental portions of the similarity between two nodes belonging to the same set of two binary networks need to be calculated based on the number of common neighbors to increase the probability of edge connection.

Claims (3)

1. A link prediction method based on odd-length paths for a binary network is characterized by comprising the following steps of;
Step 1: initializing an AUC, setting auc=0; AUC is the accuracy of the link prediction method on a bipartite network with n nodes;
Step 2: dividing a known connected edge set E in a bipartite network into a training set E T and a testing set E P;
Step 3: for a training set E T and a test set E P, respectively constructing adjacent matrixes A T and A P of corresponding networks; then, calculating the basic similarity between any two nodes of the binary network by using a basic link prediction method LPOP based on an odd-length path;
step 4: for any two nodes x and y of the bipartite network, calculating an increment part M xy of the similarity;
Step 5: the base similarity matrix S LPOP calculated by using the LPOP method is added to the incremental matrix M to be the final similarity value of the two nodes, that is:
SLPOPE＝SLPOP+M
Step 6: using training set E T, test set E P and base similarity matrix S LPOPE, calculating LPOPE the accuracy AUC lpope of the method;
Step 7: returning LPOPE to the accuracy AUC avg and similarity matrix S LPOPE of the method on the bipartite network;
In the step 3, the process steps of the basic link prediction method LPOP include:
Step 3.1: let β=0, AUC *＝0,SLPOP* =0, where β e (0, 1) is the super parameter for calculating the basic similarity between any two nodes of the bipartite network, AUC * is the optimal accuracy of the link prediction model under different β, and S LPOP* is the basic similarity matrix for generating AUC *;
Step 3.2: calculating basic similarity between any two nodes of the bipartite network according to the beta value, and storing the result in a basic similarity matrix S LPOP;
LPOP the calculation process is as follows:
Step 3.3: calculating an accuracy index AUC lpop of the beta-value downlink prediction model by using the training set E T, the test set E P and the basic similarity matrix S LPOP;
Step 3.4: if AUC lpop is greater than AUC *, S LPOP*＝SLPOP;
Step 3.5: this is done for β: beta = beta +0.01;
Step 3.6: judging whether beta is larger than 1, returning to the step 3.2 if beta is not larger than 1, otherwise, ending LPOP algorithm, and returning to the step S LPOP;
In the step 4, the calculating process of the M xy includes:
Step 4.1: let sim 1＝1,sim2 = 1;
Step 4.2: finding all paths x-z 1-z2 -y of length three between the two nodes, wherein x and z 2 belong to one set of the bipartite network and z 1 and y belong to the other set;
step 4.3: if there is no path with length of three between x and y, returning to M xy =1, otherwise executing step 4.4;
step 4.4: for each path of length three between x and y, the similarity based on the number of common neighbors, namely the similarity sim 1 and sim 2 of x and z 2 and z 1 and y, is calculated as follows:
Wherein k is the number of paths with the length of three between the nodes x and y, i is the path with the length of three between the nodes x and y, z i1 and z i2 are two intermediate nodes on the path, r (x) represents the neighbor node set of the node x, r (x) r (z i2) r represents the number of common neighbors of the nodes x and z i2, r (z i1) r (y) r represents the number of common neighbors of the nodes z i1 and y;
Step 4.5: the calculation formula of the increment part M xy;Mxy for calculating the similarity of the nodes x and y is as follows:
Mxy＝sim1*sim2
Step 4.6: and returning an increment matrix M epsilon R n×n of the similarity between the two network nodes.
2. The method according to claim 1, wherein in the step 2, ninety percent of the edges from the known edge set E are randomly selected as the training set E T, the remaining edges are used as the test set E P, and the test is performed, where e=e T∪EP,ET∩EP =Φ.
3. The method for predicting a link based on an odd-numbered path for a bipartite network according to claim 1, wherein in the step 7, the similarity matrix S LPOPE includes a probability of generating a link between two nodes that are not yet connected in the bipartite network, and the larger the value of a certain position in the similarity matrix S LPOPE is, the greater the probability of generating a link between two nodes corresponding to the certain position is, and the size of the probability of generating a link between two nodes that are not connected in the bipartite network is predicted according to the similarity matrix S LPOPE.
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