A recommendation system matrix filling method fusing social network graph and hypergraph information

Abstract

The application discloses a kind of fusion social network graph and hypergraph information recommendation system matrix filling method, comprising the following steps: S1, using generative model modeling generation social network graph information and hypergraph information;S2, the generation and input of incomplete recommendation matrix;S3, through three-stage algorithm, using social network hypergraph information and incomplete matrix information are carried out matrix filling, output the recommendation matrix after completion, and then complete recommendation task;S4, collect user feedback information, optimize recommendation algorithm: according to the feedback of user, improve social network information and then optimize recommendation algorithm.Compared with prior art, the present application uses mixed graph and more complex hypergraph for modeling, can better make full use of complex social network data, on this basis, through three-stage algorithm, using social network hypergraph information auxiliary matrix filling, can carry out more accurate matrix reply, and then enable recommendation system to realize more efficient recommendation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of recommendation systems, and particularly relates to a recommendation system matrix filling method fusing social network graph and hypergraph information. BACKGROUND

[0002] In the current era of high development of the Internet, people's behaviors on the Internet are increasingly diverse, involving shopping, browsing, consulting, social activities and other aspects, and the demand for personalized recommendation is increasing. The recommendation system can provide personalized content or product recommendations for users based on their historical behavior, preferences, social network relationships and other related information, and thus has received extensive attention and development.

[0003] Matrix completion is a widely used method in recommendation systems, which aims to handle the missing values in the user-item rating matrix. In recommendation systems, some users may not rate certain items, resulting in a large number of missing values in the rating matrix. The goal of matrix completion is to predict these missing ratings using existing rating data and fill in the blanks, thereby obtaining a complete rating matrix.

[0004] Traditional matrix completion methods use a single incomplete matrix as input to predict the values of missing items based on known items in the incomplete matrix, and this method has been widely studied, with many algorithms proposed, including matrix decomposition, convex optimization, and semi-definite programming. However, using only the information of the incomplete matrix can limit the performance of the recommendation system. In today's big data era, available data not only includes people's ratings and preferences for items, but also includes relationships between people, or social network data. For example, when two people are friends on a shopping platform, they tend to get closer ratings when rating a product.

[0005] In addition to traditional methods, some studies have reported the combination of recommendation systems and social networks, and research has shown that using simple social network data can significantly improve the performance of recommendations and effectively solve the "cold start" problem. The "cold start" problem refers to the situation when new users or new items appear, and there is a lack of historical data to make recommendations. With the help of social network data, recommendations can be made based on the community information of users or items, thereby solving the "cold start" problem to some extent.

[0006] The prior art uses simple undirected graphs to model social networks, however, due to the diversity of information, social networks exhibit complex and diverse topological structures, for example, hypergraph structures can be used to model various group chats. The main difference between hypergraph structure and graph structure is that the hyperedge in the hypergraph can connect more than two nodes, while the edge in the graph structure can only connect two nodes. The group chat on various social media can be regarded as a hyperedge, because the people in the group do not necessarily have a connection with each other, the existence of the group only proves that all nodes are in a hyperedge, therefore, using graph and hypergraph structures to model social network information is more realistic.

[0007] In view of this, the present application proposes to use mixed graph and hypergraph structure for modeling, and on this basis, to use matrix completion method for recommendation. SUMMARY

[0008] In view of the problems existing in the prior art, the purpose of the present application is to provide a recommendation system matrix filling method fusing social network graph and hypergraph information.

[0009] In order to achieve the above-mentioned purpose, the present application adopts the following technical scheme:

[0010] The first aspect of the present application provides a recommendation system matrix filling method fusing social network graph and hypergraph information, comprising the following steps:

[0011] S1, generating social network graph information and hypergraph information using generative model modeling;

[0012] S2, generation and input of the to-be-completed recommendation matrix;

[0013] S3, filling the matrix using social network hypergraph information and to-be-completed matrix information through a three-stage algorithm, outputting the completed recommendation matrix, and then completing the recommendation task;

[0014] S4, collecting user feedback information and optimizing the recommendation algorithm: according to the feedback of the user, improving the social network information and optimizing the recommendation algorithm.

[0015] Preferably, in step S1, the social network graph information and hypergraph information are generated using generative model modeling, comprising the following steps: collecting user data, using generative model modeling to generate social network graph information and hypergraph information according to the relationship between users; if the relationship between users is a binary relationship, using a probabilistic graph generation model to generate social network graph information using graph structure modeling; if the relationship between users is a multi-element relationship, using a probabilistic graph generation model to generate social network hypergraph information using hypergraph structure modeling.

[0016] Preferably, the probabilistic graph generation model is used to generate social network hypergraph information using hypergraph structure, and the specific steps are as follows:

[0017] The probabilistic graph generation model, i.e. "random block model", assumes that all n user groups are divided into k different communities, and the probability of the existence of a hyperedge between people in the same community is p, and the probability of the existence of a hyperedge between people in different communities is q, and p>q; in addition, when generating the social hypergraph information, the degree d of the hyperedge in the hypergraph also needs to be determined, i.e. how many nodes each hyperedge can contain, and here d takes a value of 2 to W; for different d, the corresponding p and q are given, denoted as p d and q d ; when the values of p d and q d are given, a random hyperedge generation is performed on any d users in n users with the probabilities of p d and q d , i.e. a social network hypergraph information can be generated; in addition, when d is taken as 2, a social network graph information can be generated.

[0018] Preferably, in step S2, the generation of the to-be-completed recommendation matrix comprises the following steps: generating a complete recommendation matrix according to the historical data of the user and the community information, and then flipping or losing each item in the complete recommendation matrix with the same probability, thereby obtaining a to-be-completed noise-controllable recommendation matrix.

[0019] Preferably, in step S3, the matrix filling by using the social network hypergraph information and the to-be-completed matrix information through the three-stage algorithm outputs a completed recommendation matrix, and then completes the recommendation task, which comprises the following steps:

[0020] Stage one, partial recovery of the community in the hypergraph is performed, and a spectral clustering algorithm is used to obtain an initial community recovery;

[0021] Stage two, on the basis of the partial recovery in stage one, a majority voting method is used to obtain the general preference of each community for the item;

[0022] Stage three, according to the current community attribution and the item rating of each user, the community division attribution of each user is re-adjusted.

[0023] Preferably, in the stage one, the partial recovery of the community in the hypergraph information comprises the following specific steps: a graph and hypergraph calculation weighted adjacency matrix A is used according to the following formula (1):

[0024]

[0025] In the formula, H d represents a plurality of hypergraphs obtained by decomposing the hypergraph H according to the degree of the hyperedge, which also includes a graph structure; d represents the degree of each edge in the hypergraph H, and d takes a value of 2 to W; represents the representation of H dThe matrix obtained after performing the transpose operation.

[0026] Preferably, in the second stage, when using majority voting to obtain the rating matrix for each community, it is assumed that people within the community have the same tendency when rating items.

[0027] Preferably, in stage three, the community affiliation of each user is readjusted based on their current community affiliation and item rating, specifically including the following steps:

[0028] Iterate through each user, and based on each user's current community affiliation and item ratings, fine-tune the user's community using social network information and rating matrix information to achieve precise community division; among which, for the th Each user is assigned to a community based on the following formula (2):

[0029]

[0030] In the formula, For the final output user The meaning of d in the club or organization is the same as in formula (1); For hyperparameters, This represents the set of users initially assigned to community k. This represents the number of users initially assigned to community k. Indicates user With club members The number of existing superedges, Indicates user The number of user ratings obtained in community k through the maximum voting method is the same.

[0031] Preferably, it also includes: evaluation and verification of the three-stage algorithm:

[0032] If the hypergraph data fully conforms to the generation rules of the "random block model", then the hyperparameters can be accurately estimated by the following equations (3)-(5). This ensures the optimality of the algorithm, where hyperparameters... It is represented as shown in the following formula (3):

[0033]

[0034] in, and Represents the hypergraph H after decomposition d The parameters can be accurately estimated using the following equations (4) and (5):

[0035]

[0036] Wherein, K is the number of communities, is a hypergraph H d The number of all hyperedges in the hypergraph H.

[0037] The present application has the following beneficial effects:

[0038] Compared with the prior art, the present application uses mixed graphs and more complex hypergraphs for modeling, can better make full use of complex social network data, and on this basis, through a three-stage algorithm, uses social network hypergraph information to assist matrix filling, can perform more accurate matrix recovery, and further enables a recommendation system to realize more efficient recommendation. BRIEF DESCRIPTION OF DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0040] Figure 1 is a structural schematic diagram of a graph and a hypergraph;

[0041] Figure 2 is a flow schematic diagram of a recommendation system matrix filling method provided by the present application, which fuses social network graph and hypergraph information;

[0042] Figure 3 is a flow schematic diagram of a three-stage algorithm;

[0043] Figure 4 is an experimental result of a simulation data set;

[0044] Figure 5 is contact-high-school dataset Experimental results. DETAILED DESCRIPTION

[0045] In the following description, specific details are set forth in order to provide a thorough understanding of embodiments of the present application. However, persons of ordinary skill in the art will readily appreciate that embodiments of the present application can be practiced without these specific details.

[0046] Embodiment 1

[0047] Referring to Figure 2 A recommendation system matrix filling method fusing social network graph and hypergraph information is provided by the embodiment of the present application, which comprises the following steps:

[0048] S1, using a generative model to model to generate social network graph information and hypergraph information;

[0049] Specifically, the process includes the following steps: collecting user data, and generating social network graphs and hypergraph information based on the relationships between users; if the relationship between users is binary, such as the friendship relationship in social software, then a probabilistic graph generation model is used to generate social network graph information using graph structure modeling; if the relationship between users is multi-faceted, such as the group chat relationship in social software, then a probabilistic graph generation model is used to generate social network hypergraph information using hypergraph structure modeling.

[0050] The specific steps for generating social network hypergraph information using a probabilistic graphical generation model with hypergraph structure modeling are as follows:

[0051] The probabilistic graph generation model, also known as the "random block model," assumes that all n user groups are divided into k distinct communities, and the probability of a hyperedge existing between members of the same community is p, and the probability of a hyperedge existing between members of different communities is q, where p > q. Furthermore, when generating social hypergraph information, it is necessary to determine the degree d of the hyperedges in the hypergraph, i.e., how many nodes each hyperedge can contain; here, d takes values ​​from 2 to W. For different d values, corresponding p and q need to be provided, denoted as p and q respectively. and When given and After setting the value, for any d users out of n users, with... and By generating random hyperedges with a probability of d, a social hypergraph can be generated; in addition, when d is set to 2, social graph information can be generated.

[0052] For existing social graph or hypergraph data, p can also be estimated based on this data. d and q d The value of this value is then used in the next step of the calculation. If the data perfectly matches the generation pattern of the "random block model," it can be proven that the three-stage algorithm is optimal.

[0053] S2. Generation and input of the recommendation matrix to be completed;

[0054] The recommendation matrix to be completed, i.e. the recommendation matrix with controllable noise to be completed, is generated by the following steps: generating a complete recommendation matrix based on users' historical data and community information, and then flipping or losing each item in the complete recommendation matrix with the same probability to obtain the recommendation matrix with controllable noise to be completed.

[0055] S3. Using a three-stage algorithm, matrix filling is performed using information from the social network hypergraph and the matrix to be filled, and the completed recommendation matrix is ​​output to complete the recommendation task.

[0056] The three-stage algorithm herein is derived using local maximum likelihood estimation. Maximum likelihood estimation is a method of estimating the parameters of a probability model given the observed data. This method attempts to find a set of parameter values for which the probability of observing the current data is maximized. In the present invention, local maximum likelihood estimation refers to assigning a community to each user such that the probability of observing the graph and hypergraph data associated with the user and the observed rating vector of the user for all item pairs is maximized.

[0057] In the present invention, the three-stage algorithm is the key to efficiently utilizing social hypergraph information, and specifically includes the following steps:

[0058] Stage One, partial recovery of communities in the hypergraph, using a spectral clustering algorithm to obtain initial community recovery;

[0059] Stage Two, based on the partial recovery in Stage One, using majority voting to obtain the general preference of each community for an item;

[0060] Stage Three, re-adjusting the community division of each user according to the current community affiliation and item rating of each user.

[0061] Referring to Figure 3 , the specific process is as follows:

[0062] Stage One, partial recovery of communities in the hypergraph information, using a spectral clustering algorithm to obtain initial community recovery ;

[0063] Among them, the partial recovery of communities in the hypergraph information, the specific steps are: according to the following formula (1), using the graph and hypergraph , calculate the weighted adjacency matrix A of the graph and hypergraph data:

[0064]

[0065] In the formula, H d represents a plurality of hypergraphs obtained by decomposing the hypergraph H according to the degree of hyperedge, which also includes graph structure; d represents the degree of each edge in the hypergraph H, d takes a value from 2 to W; represents the matrix obtained after the transpose operation on H d ;

[0066] Stage Two, assuming that people within a community have the same tendency when rating an item, using majority voting to obtain the rating matrix of each community ;

[0067] Phase three, traversing each user, according to each user's current community affiliation and item ratings, using social network information and rating matrix information to fine-tune the community where the user is located, and then realize the accurate division of the community; wherein, for the first user, according to the following formula (2) to determine the community where it is located:

[0068]

[0069] In the formula, is the final output of the user The community where it is located, d has the same meaning as formula (1); is a hyperparameter, represents the initial division of the user set in community k, represents the number of users initially divided in community k, represents the number of hyperedges between user and community members , represents the number of users The ratings of the users are the same as the ratings of the users in community k obtained by the maximum voting method.

[0070] The above formula (2) shows that if a user has the most contact with a certain community and the most similar ratings, then the user tends to belong to this community.

[0071] Also includes: evaluation and verification of the three-stage algorithm:

[0072] If the hypergraph data completely conforms to the generation rule of the "random block model", then the hyperparameter can be accurately estimated by the following formula, and then the optimality of the algorithm is guaranteed, wherein the hyperparameter is represented by the following formula (3):

[0073]

[0074] Among them, and represent the parameters about the decomposed hypergraph H d , which can be accurately estimated by the following formulas (4) and (5):

[0075]

[0076] Among them, K is the number of communities, is the number of all hyperedges in the hypergraph H d .

[0077] S4, collect user feedback information, optimize the recommendation algorithm: according to the user's feedback, improve the social network information and then optimize the recommendation algorithm. ​

[0078] Example 2

[0079] (1) For generating simulation dataset, i.e. social hypergraph information, using "random block model", the method (MCH) of the present application is compared with two representative existing methods which only use social graph data for assistance, which are respectively the method of "K. Ahn, K. Lee, H. Cha, and C. Suh, "Binary rating estimation with graph side information," Advances in neural information processing systems, vol. 31, 2018." and the hyperedge-added version of the method (after adding hyperedges, all hyperedges are converted into fully connected normal edges for processing), which are respectively recorded as Ahn et al. '18 and Ahn et al. '18 HG. The experimental results are as follows Figure 4 .

[0080] (2) For the real social hypergraph dataset contact-high-school, which is derived from “P. S. Chodrow, N. Veldt, and A. R. Benson, “Hypergraph clustering: from blockmodels to modularity,” Science Advances, 2021.”, the present method (MCH) and seven common matrix filling methods, namely user KNN, item KNN, svd++ (Y. Koren, “Factorization meets the neighborhood: a multifaceted collaborative filtering model,” in Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining, 2008, pp. 426-434.), SocialMF (M. Jamali and M. Ester, “A matrix factorization technique with trust propagation for recommendation in social networks,” in Proceedings of the fourth ACM conference on Recommender systems, 2010, pp. 135-142.), SocialReg (H. Ma, D. Zhou, C. Liu, M. R. Lyu, and I. King, “Recommender systems with social regularization,” in Proceedings of the fourth ACM international conference on Web search and data mining, 2011, pp. 287-296.), GraphRec (W. Fan, Y. Ma, Q. Li, Y. He, E. Zhao, J. Tang, and D.Yin, “Graph neural networks for social recommendation,” in The world wide web conference, 2019, pp. 417-426.) and the Ahn et al. ’18 method in the previous experiment. The experiment counts the running time and accuracy of the method. The relevant data of the experimental dataset and the experimental results are as follows. Figure 5 and Table 1-2.

[0081] Table 1

[0082] dataset user item hyperedge degree community hyperedge generation probability SBM-HG 300 100 3 3 0~0.08 dataset user hyperedge edge community hyperedge maximum degree contact-high-school 327 2320 5498 9 5

[0083] Table 2

[0084] method GraphRec socialMF soialReg svd++ user k-NN item k-NN Ahn et al. ’18 MCH runtime / s 291.93 301.33 33.28 22.52 3.15 3.45 5.3 5.7

[0085] The above experimental results fully prove the effectiveness of the method of the present application, especially for social network data with complex topological structure. Compared with existing methods, the present application uses more complex hypergraphs for modeling, which can better utilize social network data, and then perform more accurate matrix recovery, enabling the recommendation system to achieve more efficient recommendation.

[0086] The present application is not limited to the above specific embodiments, and various modifications made by those skilled in the art based on the above concept without creative labor are within the scope of the present application.

Claims

1. A recommendation system matrix filling method fusing social network graph and hypergraph information, comprising the following steps: S1. Generating social network graph information and hypergraph information using a generative model; including the following steps: collecting user data, modeling and generating social network graph and hypergraph information according to the relationship between users; if the relationship between users is a binary relationship, using a probabilistic graph generation model to generate social network graph information using hypergraph structure; if the relationship between users is a multi-element relationship, using a probabilistic graph generation model to generate social network hypergraph information using hypergraph structure; The specific steps of using a probabilistic graph generation model to generate social network hypergraph information using hypergraph structure are as follows: The probability graph generation model assumes that all n user groups are divided into k different communities, and the probability of the existence of a hyperedge between people in the same community is p, and the probability of the existence of a hyperedge between people in different communities is q, and p>q; in addition, when generating social hypergraph information, it is also necessary to determine the degree d of the hyperedge in the hypergraph, that is, how many nodes each hyperedge can contain, here d takes a value of 2 to W; for different d, the corresponding p and q are given, denoted as and ; when the values of and are given, for any d users in n users, a random hyperedge generation is performed with the probability of and , that is, a social network hypergraph information can be generated; in addition, when d is taken as 2, a social network graph information can be generated; S2. Generation and input of the recommendation matrix to be completed; including the following steps: generating a complete recommendation matrix according to the historical data and community information of the user, and then flipping or losing each item in the complete recommendation matrix with the same probability, thereby obtaining a noise-controllable recommendation matrix to be completed; S3. Fill the matrix using social network hypergraph information and matrix information to be completed through a three-stage algorithm, output the completed recommendation matrix, and then complete the recommendation task; including the following steps: First stage, according to the following formula (1), use graph and hypergraph to calculate the weighted adjacency matrix A, and partially recover the community in the hypergraph; use the spectral clustering algorithm to obtain the initial community recovery; the calculation formula of the weighted adjacency matrix A is as follows: where H d represents a plurality of hypergraphs obtained by decomposing hypergraph H according to the degrees of hyperedges, which also includes graph structures; d represents the degree of each edge in hypergraph H, and d takes values from 2 to W; represents a matrix obtained by performing a transpose operation on H d . Second stage, on the basis of the partial recovery in the first stage, use the majority voting method to obtain the general preference of each community for the item; Third stage, according to the current community affiliation and item rating of each user, readjust the community division affiliation of each user; In the second stage, when the majority voting method is used to obtain the rating matrix of each community, it is assumed that the people in the community have the same tendency when rating the item; In the third stage, according to the current community affiliation and item rating of each user, readjust the community division affiliation of each user, which includes the following steps: Traverse each user, according to each user's current community affiliation and item rating, using social network information and rating matrix information to fine-tune the community where the user is, and then realize the accurate division of the community; wherein, for the first user, determine the community where it is according to the following formula (2): In the formula, For the final output user The club I belong to For hyperparameters, This represents the set of users initially assigned to community k. This represents the number of users initially assigned to community k. Indicates user With club members The number of existing superedges, Indicates user The number of ratings is the same as the number of user ratings obtained in community k using the maximum voting method: It also includes evaluation and verification of the three-stage algorithm: If the hypergraph data completely conforms to the generation rule of the "random block model", the hyperparameters are accurately estimated by the following equations (3)-(5) , thereby ensuring the optimality of the algorithm, wherein the hyperparameters are represented as shown in the following equation (3): wherein with denotes the parameters of the decomposed hypergraph H d which can be accurately estimated by the following equations (4) and (5): wherein K is the number of communities, is a hypergraph H d the number of all hyperedges in H. S4. Collect user feedback information and optimize the recommendation algorithm: according to the user's feedback, improve the social network information and optimize the recommendation algorithm.

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