A cross-domain recommendation method based on multi-layer recurrent graph convolutional network

Abstract

The present invention provides a cross-domain recommendation method based on a multi-layer cyclic graph convolutional network. The method designs a pseudo-overlapping judgment mechanism, calculates the modularity gain generated by moving a user into the community where all neighboring users are located, and then moves the user into the community that enables the user to obtain the maximum modularity gain, so as to achieve community set transformation, thereby obtaining an optimal community network, which can fully explore the trust relationship of users and similar user communities, improve the adaptability of clustering algorithms to cross-domain recommendations, and solve the problem of low accuracy of clustering results. In addition, when aggregating node embedding, the multi-layer cyclic graph convolutional network module replaces the fixed graph learning in traditional graph convolution with a dynamic cyclic graph structure. In this way, aggregation embedding can make full use of data information in different domains, consider the weight relationship from the perspective of intra-domain / inter-domain, enhance the high-order connectivity of the model, and utilize the combined feature vector aggregated by the gated network layer to improve data utilization and alleviate the problem of data sparsity.

Description

Technical Field

[0001] The present invention relates to the field of data processing technology, and in particular to a cross-domain recommendation method based on a multi-layer cyclic graph convolutional network. Background Art

[0002] Cross-Domain Recommendation (CDR) can alleviate the cold start phenomenon by migrating the user-item rating pattern in the densely rated auxiliary domain to the sparsely rated target domain, and has been widely studied. However, the clustering methods based on single-domain recommendation adopted by most CDRs do not effectively utilize overlapping information and cannot fully adapt to cross-domain recommendations, resulting in inaccurate clustering results.

[0003] In cross-domain recommendation, the Graph Convolution Network (GCN) method can make full use of the associations between nodes to improve the accuracy of recommendations. However, cross-domain recommendations based on GCN often use static graphs to learn node embeddings, ignoring the fact that user preferences change with recommendation scenarios, resulting in poor performance of the model when facing different recommendation tasks and inability to effectively alleviate data sparsity. Summary of the invention

[0004] To this end, an embodiment of the present invention proposes a cross-domain recommendation method based on a multi-layer recurrent graph convolutional network to solve the problem that the clustering results of the prior art are inaccurate and cannot effectively alleviate data sparsity.

[0005] A cross-domain recommendation method based on a multi-layer cyclic graph convolutional network according to an embodiment of the present invention is applied to a cross-domain recommendation system, wherein the cross-domain recommendation system includes a pseudo-overlap determination module, a multi-layer cyclic graph convolutional network module, and a prediction module;

[0006] The method comprises:

[0007] In the pseudo-overlapping determination module, the initial similarity between users and the initial similarity between projects are calculated based on the user-project rating matrix of the source domain and the target domain, each user is initialized as a community, and an improved modularity-based community discovery algorithm is used to perform inter-domain community clustering. In the clustering process, the initial similarity between users is used to calculate the internal weight sum of the community and the weight sum of the edges connected to the nodes in the community, and then the modularity gain generated by moving the user into the community where all neighboring users are located is calculated in combination with the weights of overlapping users in the community, and then the user is moved into the community that obtains the maximum modularity gain to achieve community set transformation, and then the internal weight sum of the community after the community set transformation and the weight sum of the edges connected to the nodes in the community are recalculated. After a preset number of iterations, the modularity gain of the overall community network is maximized, thereby obtaining an optimal community network, and then the final similarity between users and the final similarity between projects are calculated based on the common neighbors in the optimal community network, and finally the user similarity matrix and the project similarity matrix are obtained based on the final similarity between users and the final similarity between projects;

[0008] The multi-layer recurrent graph convolutional network module includes an embedding layer, a graph learning layer and a gated network layer. In the multi-layer recurrent graph convolutional network module, a user similarity matrix and a project similarity matrix are used as inputs of the embedding layer, and a user embedding vector and a project embedding vector are output through the embedding layer. The user embedding vector and the project embedding vector are used as inputs of the graph learning layer, and a user-project preference weight is output through the graph learning layer. In the graph learning layer, an adaptive amplitude pruning strategy is used to dynamically adjust the user-project preference weight, and a domain-specific node embedding vector of a source domain, a domain-specific node embedding vector of a target domain, and a domain-shared node embedding vector are generated based on the user-project preference weight. Finally, the domain-specific node embedding vector of the source domain and the domain-shared node embedding vector are combined by using the gated network layer to generate a combined feature vector of the source domain, and the domain-specific node embedding vector and the domain-shared node embedding vector of the target domain are combined to generate a combined feature vector of the target domain.

[0009] The combined feature vector of the source domain and the combined feature vector of the target domain are input into the prediction module, and a multi-layer perceptron is used to model the user-item interaction of the source domain and the target domain respectively, and the final predicted interaction score is output, and according to the final predicted interaction score, a list of project recommendations is provided to users of the source domain and the target domain respectively.

[0010] The cross-domain recommendation method based on a multi-layer cyclic graph convolutional network according to an embodiment of the present invention has the following beneficial effects:

[0011] (1) The present invention makes full use of overlapping data and designs a pseudo-overlapping judgment mechanism based on the traditional modularity-based community discovery algorithm (Louvain). By calculating the modularity gain generated by moving a user into the community where all neighboring users are located, and then moving the user into the community that achieves the maximum modularity gain, the community set transformation is achieved, and the optimal community network is obtained. The trust relationship between users and similar user communities can be fully explored, thereby improving the adaptability of the clustering algorithm to cross-domain recommendations and solving the problem of low accuracy of clustering results.

[0012] (2) The multi-layer recurrent graph convolutional network module proposed in the present invention replaces the fixed graph learning in traditional graph convolution with a dynamic recurrent graph structure when aggregating node embedding. In this way, the aggregation embedding can make full use of data information from different domains, consider the weight relationship from the perspective of intra-domain / inter-domain, enhance the high-order connectivity of the model, and use the combined feature vector aggregated by the gated network layer to improve data utilization and alleviate the data sparsity problem.

[0013] (3) The present invention uses a multi-layer perceptron to model user-item interactions, obtains the final predicted interaction rating, and optimizes the total loss function by combining the loss functions of the source domain and the target domain, which can effectively improve the generalization ability and improve the recommendation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The above and / or additional aspects and advantages of the embodiments of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0015] Figure 1 is a schematic diagram of the structure of a cross-domain recommendation system according to an embodiment of the present invention;

[0016] Figure 2 It is a flowchart of a cross-domain recommendation method based on a multi-layer cyclic graph convolutional network according to an embodiment of the present invention. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0018] The embodiment of the present invention proposes a cross-domain recommendation method based on a multi-layer recurrent graph convolutional network, which is applied to a cross-domain recommendation system. Figure 1 The cross-domain recommendation system includes a pseudo-overlapping determination module, a multi-layer cyclic graph convolutional network module and a prediction module.

[0019] See also Figure 2 , the method comprises steps S1 to S3:

[0020] S1, in the pseudo-overlapping determination module, the initial similarity between users and the initial similarity between projects are calculated based on the user-project rating matrix of the source domain and the target domain, each user is initialized as a community, and the improved modularity-based community discovery algorithm is used to perform inter-domain community clustering. In the clustering process, the initial similarity between users is used to calculate the internal weight sum of the community and the weight sum of the edges connected to the nodes in the community, and then combined with the weights of overlapping users in the community, the modularity gain generated by moving the user into the community where all neighboring users are located is calculated, and then the user is moved into the community that obtains the maximum modularity gain to achieve community set transformation, and then the internal weight sum of the community after the community set transformation and the weight sum of the edges connected to the nodes in the community are recalculated. After a preset number of iterations, the modularity gain of the overall community network is maximized, thereby obtaining an optimal community network, and then the final similarity between users and the final similarity between projects are calculated based on the common neighbors in the optimal community network. Finally, based on the final similarity between users and the final similarity between projects, a user similarity matrix and a project similarity matrix are obtained.

[0021] Among them, given two domains, the source domain S and target domain T , source domain S and target domain T The user sets in the source domain / target domain partially overlap, and the item sets do not overlap. The source domain / target domain user sets and the source domain / target domain item sets are respectively recorded as and . Source domain-target domain joint similarity matrix W As shown below:

[0022] ;

[0023] in, represents the source domain matrix, represents the target domain matrix.

[0024] In order to better realize the transmission of information in different domains, the present invention starts from the user group, models the user relationship, mines the user group with high similarity, and calculates the similarity between users by combining the user-item rating matrix of the source domain and the target domain. Specifically, the following formula is used to calculate the initial similarity between users:

[0025] ;

[0026] in, Indicates user u and users vThe initial similarity of r u,i Indicates user u About Project i Ratings, r v,i Is a user v About Project i Ratings, and For users u ,user v The average rating of the interactive items, I uv Represents user u and users v The same method can be used to obtain the initial similarity between items.

[0027] During the clustering process, the modularity-based community discovery algorithm (Louvain) uses modularity gain to dynamically adjust the clustering results by moving nodes into the neighboring community that maximizes the modularity gain. At this time, the overall community network modularity is maximized and the similarity community division also presents the best effect.

[0028] However, the traditional Louvain algorithm cannot adapt well to clustering between different domains. The present invention considers using overlapping users as a bridge to unite domains and improves the Louvain algorithm. In order to make full use of the inter-domain relationship and give full play to the role of overlapping users, the present invention proposes a pseudo-overlapping judgment mechanism, the principle of which is to expand the overlapping user area through a similarity judgment mechanism. u As an overlapping user, the user v As a non-overlapping user, a non-overlapping user v With users u If there is a high degree of similarity, the user v It is also approximately an overlapping user. In this way, the overlapping user area is expanded, and finally the overlapping user area is maximized. Specifically, the modularity gain is calculated using the following formula:

[0029] ;

[0030] in, Indicates that the user u The corresponding node moves from the current community to the community where each neighbor node is located. c The resulting modularity gain, Representing the community c Internal and User u The weight and the weight of the associated edges of the corresponding nodes, m is the sum of the weights of all edges in the community network, Representation and Community c The sum of the weights of the edges connecting the midpoint nodes, Represents user u The corresponding node weight, represents overlapping user sets, is the overlapping user weight.

[0031] Through the above formula, a pseudo-overlapping user community with a maximized overlapping area can be formed, making full use of the updated pseudo-overlapping user information, so that the Louvain algorithm for a single network can connect the dual-domain networks through the pseudo-overlapping user community. The specific implementation process of the clustering method based on the pseudo-overlapping judgment mechanism is as follows:

[0032] Step 1: Calculate the modularity gain of all nodes. u The corresponding node is calculated to u The corresponding node moves from the current community to the community where each neighbor node is located. c The resulting modularity gain First, the user vectors in the source and target domains are randomly initialized to the same dimension, and the user vectors in these domains are regarded as the user joint domain ST , and use it as the input of the improved Louvain algorithm; secondly, the inter-domain user similarity is used in combination with the improved Louvain algorithm to obtain preliminary community results; finally, since community clustering involves multiple data domains and the amount of information is too large, in order to reduce clustering bias, modularity gain is used to dynamically adjust the clustering results.

[0033] To the user u After all neighbor nodes of the user are calculated, u Move to the community that can obtain the maximum modularity gain. If the modularity gain is not positive, the user u Remain in the original community.

[0034] Step 2: Construct a hypergraph based on the community clustering results. Each community is compressed into a supernode with a self-loop edge, and the weight of the self-loop edge is the sum of the weights within the community. The weight of the edge between supernodes is the sum of the edge weights between nodes in each community.

[0035] Repeat steps 1 and 2 until the modularity gain of the overall community network reaches the maximum and the optimal community network is obtained. By weighting the neighboring nodes in the same community of each node, a more meaningful node representation can be obtained.

[0036] In a community network, the number of common neighbors can reflect the similarity of interests between users. If two users have many common friends, they are likely to have similar interests and behaviors. Therefore, the present invention uses the common neighbors in the community network graph to re-measure the similarity between users. Specifically, the following formula is used to calculate the final similarity between users:

[0037] ;

[0038] in, Indicates user u and users v The final similarity is represents the common neighbor weight, Indicates user u With users k The initial similarity of Indicates user v With users k The initial similarity.

[0039] Similarly, the final similarities between items can be obtained. The user similarity matrix is ​​formed by the final similarities between all users, and the project similarity matrix is ​​formed by the final similarities between all items.

[0040] S2, the multi-layer recurrent graph convolutional network module includes an embedding layer, a graph learning layer and a gating network layer. In the multi-layer recurrent graph convolutional network module, the user similarity matrix and the project similarity matrix are used as inputs of the embedding layer, and the user embedding vector and the project embedding vector are output through the embedding layer. The user embedding vector and the project embedding vector are used as inputs of the graph learning layer, and the user-project preference weights are output through the graph learning layer. In the graph learning layer, an adaptive amplitude pruning strategy is used to dynamically adjust the user-project preference weights. Based on the user-project preference weights, a domain-specific node embedding vector of the source domain, a domain-specific node embedding vector of the target domain, and a domain-shared node embedding vector are generated. Finally, the gated network layer is used to combine the domain-specific node embedding vector of the source domain and the domain-shared node embedding vector to generate a combined feature vector of the source domain, and the domain-specific node embedding vector and the domain-shared node embedding vector of the target domain are combined to generate a combined feature vector of the target domain.

[0041] Among them, a multi-layer recurrent graph convolutional network (GCN) is used in the embedding layer to effectively learn node embedding based on neighborhood aggregation. Specifically, the embedding layer satisfies the following conditional formula:

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] in, and They are x The user embedding matrix and item embedding matrix obtained by the embedding propagation layer are and They are x +1 embedding propagation layer to obtain the user embedding matrix and item embedding matrix, represents the activation function, and They represent the user adjacency matrix and item adjacency matrix with self-connection, respectively. represents the user similarity matrix, represents the item similarity matrix, I u is the user's identity matrix, I i is the identity matrix of the project, D u and D i They are the degree matrix of users and the degree matrix of items respectively. The degree matrix of users indicates the number of neighbor nodes with non-zero similarity between each user and other users, and the degree matrix of items indicates the number of neighbor nodes with non-zero similarity between each item and other items. and They are x The user weight matrix and item weight matrix of the embedding propagation layer.

[0047] Among them, the graph learning layer satisfies the following conditional formula:

[0048] ;

[0049] in, Indicates x +1 embedding propagation layer to obtain the user-item preference weights, express sigmoid function, and They are x +1 embedding propagation layer to obtain the user embedding vector and item embedding vector, F 1 and F 2 is the trainable matrix, represents the vector inner product operation, Represents vector modulo operation.

[0050] When the input data dimension is large, the result matrix obtained above will be too dense. Combined with the pseudo-overlapping judgment mechanism used in the previous article, the calculation time and memory usage will increase exponentially. For large-scale data sets, the memory consumption will be high, which may lead to insufficient memory of the computing device. Therefore, it cannot be directly applied to GCN, and the obtained user-item preferences need to be sparsely processed.

[0051] Many models use the Magnitude Pruning (MaP) method in the sparsification process, but MaP focuses on local information and ignores the relationship between global structure and weights. In addition, data pruning with small similarity may also lead to a decrease in model performance. To address this problem, the present invention uses an adaptive method to set the corresponding threshold based on the magnitude of similarity, and dynamically adjusts it during the training process so that the preference matrix is ​​not too dense. The preference for each user's corresponding project and the threshold of the previous round together constitute the prediction threshold of this layer.

[0052] In order to make better use of graph data and avoid performance degradation caused by excessive pruning, a dynamic adjustment mechanism is used during training to adaptively adjust to different users or different situations, so as to more flexibly respond to changes in local information and global structure. At the same time, in order to balance the relationship between rounds during pruning and ensure that the pruning threshold of each round is more independent and reasonable, weight parameters are set so that the pruning ratio of each round is gradually reduced, thereby reducing the impact of previous rounds on subsequent rounds.

[0053] Among them, in the process of dynamically adjusting the user-item preference weights using the adaptive amplitude pruning strategy, the following conditional formula is met:

[0054] ;

[0055] ;

[0056] in, Indicates x The user-item preference weights obtained by embedding propagation layers, Indicates x A dynamic threshold embedded in the propagation layer, Indicates x - 1 dynamic threshold embedded in the propagation layer, is the weight parameter, Indicates x -1 embedding propagation layer to obtain the user-item preference weights.

[0057] Each layer has u All item preferences are calculated to obtain the corresponding preference vectors. X After step aggregation propagation, the final embedding vector is obtained.

[0058] In this embodiment, the domain-specific node embedding vector of the source domain includes the domain-specific user node embedding vector of the source domain , domain-specific item node embedding vector of the source domain , the domain-specific node embedding vector of the target domain includes the domain-specific user node embedding vector of the target domain , the domain-specific item node embedding vector of the target domain , the domain shared node embedding vector includes the domain shared node embedding vector of the user and the domain of the project share the node embedding vector , the combined feature vector of the source domain includes the user combined feature vector of the source domain and the source domain's project portfolio feature vector , the combined feature vector of the target domain includes the user combined feature vector of the target domain and the project portfolio feature vector of the target domain ;

[0059] To effectively combine users, we need to balance the commonality of joint domains and the characteristics of single domains. u The shared embedding vector and the unique embedding vector of the source domain are generated by the gated network layer that shares some parameters. , the project portfolio feature vector of the source domain , user combination feature vector of target domain and the project portfolio feature vector of the target domain .

[0060] Specifically, the gated network layer satisfies the following conditional formula:

[0061] ;

[0062] ;

[0063] in, represents the domain-shared weight matrix of the gated network layer, represents the source domain-specific weight matrix of the gated network layer, represents the target domain-specific weight matrix of the gated network layer, Represents the dot product operation.

[0064] Similarly, we can get the project portfolio feature vector of the source domain: and the project portfolio feature vector of the target domain .

[0065] S3, inputting the combined feature vector of the source domain and the combined feature vector of the target domain into the prediction module, using a multi-layer perceptron to model the user-item interaction of the source domain and the target domain respectively, outputting the final predicted interaction score, and providing item recommendation lists to users of the source domain and the target domain respectively according to the final predicted interaction score.

[0066] The final predicted interaction score includes the final predicted interaction score of the source domain and the final predicted interaction score of the target domain ;

[0067] The prediction module satisfies the following conditional formula:

[0068] ;

[0069] ;

[0070] ;

[0071] in, X represents the total number of embedding propagation layers, represents the output result of the first embedding propagation layer, Indicates X The output of the embedding propagation layer is Indicates X -1 output result of the embedding propagation layer, represents the activation function of the first embedding propagation layer, Indicates X The activation function of the embedding propagation layer, represents the trainable matrix of the first embedding propagation layer, Indicates X A trainable matrix for embedding propagation layer, represents the bias term of the first embedding propagation layer, Indicates X A bias term embedded in the propagation layer, Indicates that Mapped to a prediction function for the score.

[0072] In the prediction module, the loss function of the source domain is And the loss function of the target domain They are:

[0073] ;

[0074] ;

[0075] in, and denote the user-item interaction pairs selected in the source domain and the target domain, respectively. represents the true value of the interaction score in the source domain, represents the true value of the interaction score of the target domain;

[0076] The total loss function of the prediction module for:

[0077] ;

[0078] in, for The weight coefficient of for The weight coefficient of To control the regularization weight coefficient, represents the network parameters, represents the L2 norm.

[0079] Considering the inconsistency of the sparsity of the data sets in the two domains, the present invention adjusts and Balance the samples in the source domain and the target domain to control the sample balance. For example, if the data in the target domain is more sparse, you can set a larger , to increase the impact of target domain data on the total loss. and Together they form a regularization term to prevent the model from overfitting.

[0080] According to the above cross-domain recommendation method based on multi-layer cyclic graph convolutional network, the following beneficial effects are achieved:

[0081] (1) The present invention makes full use of overlapping data and designs a pseudo-overlapping judgment mechanism based on the traditional modularity-based community discovery algorithm (Louvain). By calculating the modularity gain generated by moving a user into the community where all neighboring users are located, and then moving the user into the community that achieves the maximum modularity gain, the community set transformation is achieved, and the optimal community network is obtained. The trust relationship between users and similar user communities can be fully explored, thereby improving the adaptability of the clustering algorithm to cross-domain recommendations and solving the problem of low accuracy of clustering results.

[0082] (2) The multi-layer recurrent graph convolutional network module proposed in the present invention replaces the fixed graph learning in traditional graph convolution with a dynamic recurrent graph structure when aggregating node embedding. In this way, the aggregation embedding can make full use of data information from different domains, consider the weight relationship from the perspective of intra-domain / inter-domain, enhance the high-order connectivity of the model, and use the combined feature vector aggregated by the gated network layer to improve data utilization and alleviate the data sparsity problem.

[0083] (3) The present invention uses a multi-layer perceptron to model user-item interactions, obtains the final predicted interaction rating, and optimizes the total loss function by combining the loss functions of the source domain and the target domain, which can effectively improve the generalization ability and improve the recommendation accuracy.

[0084] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0085] Although the embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the claims and their equivalents.

Claims

1. A cross-domain recommendation method based on a multi-layer recurrent graph convolutional network, characterized in that: Applied to a cross-domain recommendation system, the cross-domain recommendation system includes a pseudo-overlapping determination module, a multi-layer cyclic graph convolutional network module and a prediction module; The method comprises: In the pseudo-overlapping determination module, the initial similarity between users and the initial similarity between projects are calculated based on the user-project rating matrix of the source domain and the target domain, each user is initialized as a community, and an improved modularity-based community discovery algorithm is used to perform inter-domain community clustering. In the clustering process, the initial similarity between users is used to calculate the internal weight sum of the community and the weight sum of the edges connected to the nodes in the community, and then the modularity gain generated by moving the user into the community where all neighboring users are located is calculated in combination with the weights of overlapping users in the community, and then the user is moved into the community that obtains the maximum modularity gain to achieve community set transformation, and then the internal weight sum of the community after the community set transformation and the weight sum of the edges connected to the nodes in the community are recalculated. After a preset number of iterations, the modularity gain of the overall community network is maximized, thereby obtaining an optimal community network, and then the final similarity between users and the final similarity between projects are calculated based on the common neighbors in the optimal community network, and finally the user similarity matrix and the project similarity matrix are obtained based on the final similarity between users and the final similarity between projects; The multi-layer recurrent graph convolutional network module includes an embedding layer, a graph learning layer and a gated network layer. In the multi-layer recurrent graph convolutional network module, a user similarity matrix and a project similarity matrix are used as inputs of the embedding layer, and a user embedding vector and a project embedding vector are output through the embedding layer. The user embedding vector and the project embedding vector are used as inputs of the graph learning layer, and a user-project preference weight is output through the graph learning layer. In the graph learning layer, an adaptive amplitude pruning strategy is used to dynamically adjust the user-project preference weight, and a domain-specific node embedding vector of a source domain, a domain-specific node embedding vector of a target domain, and a domain-shared node embedding vector are generated based on the user-project preference weight. Finally, the domain-specific node embedding vector of the source domain and the domain-shared node embedding vector are combined by using the gated network layer to generate a combined feature vector of the source domain, and the domain-specific node embedding vector and the domain-shared node embedding vector of the target domain are combined to generate a combined feature vector of the target domain. The combined feature vector of the source domain and the combined feature vector of the target domain are input into the prediction module, a multi-layer perceptron is used to model the user-item interaction of the source domain and the target domain respectively, a final predicted interaction score is output, and an item recommendation list is provided to users of the source domain and the target domain respectively according to the final predicted interaction score; The initial similarity between users is calculated using the following formula: ； in, Indicates user u and users v The initial similarity of r u,i Indicates user u About Project i Ratings, r v,i Is a user v About Project i Ratings, and For users u ,user v The average rating of the interactive items, I uv Represents user u and users v The set of items that interact with each other; The user u As an overlapping user, the user v As a non-overlapping user, the modularity gain is calculated using the following formula: ； in, Indicates that the user u The corresponding node moves from the current community to the community where each neighbor node is located. c The resulting modularity gain, Representing the community c Internal and User u The weight and the weight of the associated edges of the corresponding nodes, m is the sum of the weights of all edges in the community network, Representation and Community c The sum of the weights of the edges connecting the midpoints, Represents user u The corresponding node weight, represents overlapping user sets, is the overlapping user weight; The final similarity between users is calculated using the following formula: ； in, Indicates user u and users v The final similarity is represents the common neighbor weight, Indicates user u With users k The initial similarity of Indicates user v With users k The initial similarity of The embedding layer satisfies the following conditional formula: ； ； ； ； in, and They are x The user embedding matrix and item embedding matrix obtained by the embedding propagation layer are and They are x +1 embedding propagation layer to obtain the user embedding matrix and item embedding matrix, represents the activation function, and They represent the user adjacency matrix and item adjacency matrix with self-connection, respectively. represents the user similarity matrix, represents the item similarity matrix, I u is the user's identity matrix, I i is the identity matrix of the project, D u and D i are the degree matrix of the user and the degree matrix of the item respectively, and They are x A user weight matrix and an item weight matrix embedded in the propagation layer; The graph learning layer satisfies the following conditional formula: ； in, Indicates x +1 embedding propagation layer to obtain the user-item preference weights, express sigmoid function, and They are x +1 embedding propagation layer to obtain the user embedding vector and item embedding vector, F 1 and F 2 is the trainable matrix, represents the vector inner product operation, Represents vector modulus operation; In the process of dynamically adjusting the user-item preference weights using the adaptive amplitude pruning strategy, the following conditions are met: ； ； in, Indicates x The user-item preference weights obtained by embedding propagation layers, Indicates x A dynamic threshold embedded in the propagation layer, Indicates x - 1 dynamic threshold embedded in the propagation layer, is the weight parameter, Indicates x -1 user-item preference weight obtained by embedding propagation layer; The domain-specific node embedding vector of the source domain includes a domain-specific user node embedding vector of the source domain , domain-specific item node embedding vector of the source domain , the domain-specific node embedding vector of the target domain includes the domain-specific user node embedding vector of the target domain , the domain-specific item node embedding vector of the target domain , the domain shared node embedding vector includes the domain shared node embedding vector of the user and the domain of the project share the node embedding vector , the combined feature vector of the source domain includes the user combined feature vector of the source domain and the source domain's project portfolio feature vector , the combined feature vector of the target domain includes the user combined feature vector of the target domain and the project portfolio feature vector of the target domain ; The gated network layer satisfies the following conditional formula: ； ； in, represents the domain-shared weight matrix of the gated network layer, represents the source domain-specific weight matrix of the gated network layer, represents the target domain-specific weight matrix of the gated network layer, Represents the dot product operation; The final predicted interaction score includes the final predicted interaction score of the source domain and the final predicted interaction score of the target domain ; The prediction module satisfies the following conditional formula: ； ； ； in, X represents the total number of embedding propagation layers, represents the output result of the first embedding propagation layer, Indicates X The output of the embedding propagation layer is Indicates X -1 output result of the embedding propagation layer, represents the activation function of the first embedding propagation layer, Indicates X The activation function of the embedding propagation layer, represents the trainable matrix of the first embedding propagation layer, Indicates X A trainable matrix for embedding propagation layer, represents the bias term of the first embedding propagation layer, Indicates X A bias term embedded in the propagation layer, Indicates that Mapping to a prediction function for ratings; In the prediction module, the loss function of the source domain is And the loss function of the target domain They are: ； ； in, and denote the user-item interaction pairs selected in the source domain and the target domain, respectively. represents the true value of the interaction score in the source domain, represents the true value of the interaction score of the target domain; The total loss function of the prediction module for: ； in, for The weight coefficient of for The weight coefficient of To control the regularization weight coefficient, represents the network parameters, represents the L2 norm.

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