Federal recommendation method combining aspect-level emotion embedding and two-stage graph aggregation

Abstract

The invention provides a federal recommendation method combining aspect-level emotion embedding and two-stage graph aggregation, and belongs to the technical field of recommendation systems. According to the method, the interpretability of a model is improved by constructing aspect-level emotion embedding, and joint training under privacy protection is realized by adopting a two-stage graph aggregation mechanism: firstly, user and article embedding is constructed at each client based on comments, and a user-article interaction graph is constructed in combination with local interaction information; obtaining personalized article embedding through first-order graph aggregation; the server side constructs a user relation graph through similarity analysis, implements second-order graph aggregation to reconstruct cross-client association and captures popular preferences; and the client performs iterative training according to the return parameters and the designed joint loss function. According to the method, on the premise of protecting user privacy, the convergence speed, recommendation precision and interpretability of a recommendation model are effectively improved through fusion of emotion semantics and a graph structure, and the key technical problems of data islands and relation missing in a federated scene are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of recommendation systems, and particularly relates to a federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation. Background Art

[0002] In the prior art, traditional recommendation systems based on centralized data storage have significant privacy leakage risks, and their paradigm of constructing a unified model by aggregating user behavior data no longer meets the requirements of increasingly strict data security regulations. Although the federated learning framework can achieve privacy protection through distributed training, the existing federated recommendation methods still have the following problems: First, at the level of representation learning, existing solutions mostly use random initialization strategies to model users / items, lacking in-depth mining of fine-grained semantic features in review texts, resulting in limited model convergence speed and being prone to falling into local optima; Second, at the level of relationship modeling, existing methods are based on the independent and identically distributed assumption for local training, failing to effectively construct a cross-client user association graph, causing fragmentation of user preference modeling and the data island effect.

[0003] Graph neural network technology has demonstrated powerful relationship reasoning capabilities in centralized recommendation scenarios, while existing federated recommendation systems have not effectively solved the following key problems: (1) Existing solutions only process user review data at the bag-of-words model or shallow semantic representation level, failing to effectively extract fine-grained aspect-level sentiment features, resulting in a lack of transparency support in the recommendation decision-making process; (2) How to construct a cross-domain graph topology under distributed privacy constraints and achieve collaborative optimization of client local graph learning and server global graph aggregation.

[0004] This technical solution solves the following problems in the federated recommendation scenario by constructing a collaborative mechanism of aspect-level sentiment embedding and two-stage graph aggregation: (1) Aspect-level sentiment modeling based on deep semantic parsing effectively solves the semantic sparsity problem in traditional representation learning; (2) The client-server collaborative two-stage graph aggregation architecture innovatively realizes the compatibility of privacy protection and relationship reasoning, providing a new technical path for the practical application of federated recommendation systems. Summary of the Invention

[0005] The present invention aims to provide a federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation, which improves the training efficiency and recommendation accuracy of the model under the federated framework while ensuring user privacy.

[0006] Step 1: The federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation includes the following steps: Step S10: Each client constructs aspect-level sentiment embeddings for users and items based on local review data respectively, and establishes a user-item interaction graph by combining user interaction information; Step S20: Perform first-order graph aggregation on the embeddings of users and items according to the user-item interaction graphs established by each client, obtain user embeddings with first-order neighbor information and item embeddings with user personalized features, and upload the user personalized item embeddings to the server; Step S30: The server obtains the user personalized item embeddings from different clients, performs similarity analysis on them, constructs a user relationship graph according to the analysis results, and performs second-order graph aggregation to obtain user relationship enhanced item embeddings. Then, perform popularity preference calculation on all user relationship enhanced item embeddings to obtain globally shared item embeddings, and then distribute each user relationship enhanced item embedding and the globally shared item embedding to the corresponding client; Step S40: The client uses the user relationship enhanced item embedding as the regularization term of the loss function and uses the globally shared item embedding as the initial vector for the next round of training until the model converges.

[0007] Step 2: According to the federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation described in Step 1, in Step S10, the client divides the comment data into user private comments and item public comments, and then uses the LDA (Latent Dirichlet Allocation) topic model to extract aspect features from the comment data, identify the item attribute dimensions concerned by the user, and take the top L aspect words with the highest probability to form the aspect set A; design the polarity set P according to the sentiment polarity type, and design the corresponding template T as the prompt word of the pre-trained language model according to the different fields involved in the data, and perform aspect-level sentiment analysis on the comments, which is formalized as: Among them, represents the u th comment of user x , and respectively represent the aspect and sentiment polarity corresponding to the u th comment of user x , represents the prompt template composed of the elements in the aspect set A and the elements in the polarity set P, a l represents the l th aspect word in the aspect set A, p k represents the k th sentiment polarity in the polarity set P, F represents the pre-trained language model; Construct the embeddings of users and items according to the aspect-level sentiment polarity obtained from the analysis, which is formalized as: Among them,e u and e i respectively represent the aspect-level sentiment embeddings of the user and the item, a 1 , a 2 and a L respectively represent the 1st, 2nd, and Lth aspect words in the aspect word set A, represents the item i of the y th comment corresponding aspect word, and are the sentiment weighting coefficients of the user and item comments respectively, and are defined as: where represents the sentiment polarity corresponding to the i th comment of the item y , and a user-item interaction graph is formed by constructing the user and item aspect-level sentiment embeddings and user interaction information.

[0008] Step 3: According to the federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation described in Step 1, in the step S20, the client uses the constructed user-item interaction graph for first-order graph aggregation, formalized as: where and are the user embedding aggregating the first-order neighbor information and the item embedding with user personalized features respectively, W is the shared learnable parameter matrix, LeakyReLU is the non-linear activation function, α ui is the attention weight coefficient of each neighbor node u of the user i , α iu is the attention weight coefficient of each neighbor node i of the item u , and is defined as: Then, each client sends the user personalized item embedding encrypted by LDP to the server, and the encryption method adopts local differential privacy, formalized as: where is the encrypted personalized item embedding, is the zero-mean Laplace noise, δis the noise intensity, and the privacy protection ability increases with δ the increase, and the embedding finally uploaded by the client m is: where represents the item embedding of random sampling.

[0009] Step 4: According to the federated recommendation method that combines aspect-level sentiment embedding and two-stage graph aggregation described in Step 1, in Step S30, the server obtains the user personalized item embeddings from different clients, and uses cosine similarity as the similarity metric for item embeddings. The similarity m between n and is defined as: where q m and q n are the item embeddings of two clients; According to the similarity metric select users with high similarity as neighbors to construct the user relationship adjacency matrix , which is formalized as: where ζ is the proportionality factor for setting the similarity threshold, and the similarity mean is used as the reference value; Then perform second-order graph aggregation on all users to obtain the user relationship enhanced item embedding, which is formalized as: where Q is the initial item embedding matrix, and its m row represents the item embedding received from the client m , R is the aggregated item embedding matrix, C represents the number of aggregation layers, A is the adjacency matrix; Next, average all the user personalized item embeddings to obtain the global shared item embedding , which is formalized as: where D is the C = 1 degree matrix when A .

[0010] Step 5: According to the federated recommendation method that combines aspect-level sentiment embedding and two-stage graph aggregation described in Step 1, in the said Step S40, the client receives the globally shared item embedding and the user relationship-enhanced item embedding, and designs the following optimization objective for the local model: where λ 1 and λ 2 are the weight decay coefficients, L BPR is the Bayesian personalized ranking loss, specifically: where , N u represents the neighbor set of user u , σ represents the sigmoid activation function, and respectively represent the predicted scores of user u for item i and j ; is a regularization term that constrains the predicted score of the item to be close to the true score, specifically: where represents the neighbor set of user u with rating records, is the true rating of user u for item i ; is a regularization term that constrains the similarity between the user's personalized item embedding and the user relationship-enhanced item embedding, specifically: where t represents the number of interactive items, represents the user's personalized embedding of item i , represents the user relationship-enhanced embedding of item i .

[0011] The beneficial effects of the present invention are as follows: Aiming at the problem of sparse semantic representation caused by random initialization in existing federated recommendation systems, the present invention designs an aspect-level sentiment embedding method based on deep semantic parsing, specifically: through dual feature extraction of the LDA topic model and the pre-trained language model, jointly model the fine-grained aspect features and sentiment polarities in the review text locally on the client side. Compared with the traditional word vector averaging method, experiments on the Yelp dataset show that this technology reduces the number of training rounds required for the model to converge by 38.6%; the embedding construction process has clear physical interpretability, and the contribution degree of specific aspect features to the recommendation decision can be traced (such as the weight ratio of "service quality" in restaurant recommendations is 0.26).

[0012] Different from the traditional federated recommendation training method, the client-server two-stage graph aggregation method designed by the present invention has the following advantages: (1) On the client side, the first-order neighbor aggregation is completed through the local graph attention network protected by differential privacy to ensure that the user interaction data does not leave the domain; (2) On the server side, an algorithm for constructing a cross-client user relationship graph based on embedding similarity is proposed, and the user association topology is reconstructed by using the shared item embedding. In the Amazon-CDs dataset test, this method can achieve performance comparable to that of the interaction-based graph; (3) Through the second-order graph aggregation mechanism based on the user relationship graph, while maintaining user privacy, the recommendation accuracy can be significantly improved. The NDCG@10 index reaches 29.12% on the Amazon-CDs dataset, which is 7.5% higher than the best baseline model. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a processing flow chart of a federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation provided by an embodiment of the present invention; Figure 2 It is a schematic architecture diagram of a federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation provided by an embodiment of the present invention; Figure 3 It is an embedding construction algorithm diagram of a federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation provided by an embodiment of the present invention; Figure 4 It is a comparison chart of the performance experiment effects on each dataset provided by an embodiment of the present invention; Figure 5 It is a loss curve graph of the ablation experiment on the Yelp dataset provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0014] The following describes the embodiments of the present invention in detail with reference to the accompanying drawings. However, the present invention can be implemented in many different ways defined and covered by the claims.

[0015] First, introduce the technical terms involved in the embodiments of this application: Federated Recommendation System: A distributed recommendation system designed based on the federated learning architecture. Its core features are as follows: ① The original user data (including interaction records, review texts, etc.) always stays on the local client device and is not transmitted to the server; ② By uploading the item embeddings trained locally to transfer the commonalities between users, and reconstructing the user relationship graph on the server to achieve cross-client collaborative training; ③ Meeting differential privacy constraints to ensure that user privacy cannot be reverse-inferred. In the present invention, the client refers to the user terminal device (such as a smart phone, personal computer), and the server refers to the central coordination node.

[0016] LDA Topic Model: An unsupervised text generation model used to mine potential aspect topics from review texts. In the present invention, each review document is regarded as a mixed distribution of aspect topics. First, preprocess the review text to construct a bag-of-words vector, and then set the hyperparameters α = 50 / L and β = 0.1, and iteratively optimize the document-topic distribution θ and topic-word distribution φ through the variational EM algorithm, and finally extract the top L topics with the highest probabilities as aspect features.

[0017] Next, the implementation steps of the invention will be further explained in detail: Step 1: Refer to Figure 1 , and the processing flow of the federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation includes the following steps: Step S10: Each client constructs aspect-level sentiment embeddings for users and items respectively based on local review data, and establishes a user-item interaction graph in combination with user interaction information; Step S20: Perform first-order graph aggregation on the embeddings of users and items according to the user-item interaction graphs established by each client to obtain user embeddings with first-order neighbor information and item embeddings with user personalized features, and upload the user personalized item embeddings to the server; Step S30: The server obtains the user personalized item embeddings from different clients, performs similarity analysis on them, constructs a user relationship graph according to the analysis results, and performs second-order graph aggregation to obtain user relationship enhanced item embeddings. Then, perform popularity preference calculation on all user relationship enhanced item embeddings to obtain globally shared item embeddings, and then distribute each user relationship enhanced item embedding and the globally shared item embedding to the corresponding client; Step S40: The client uses the user relationship enhanced item embedding as the regularization term of the loss function and uses the globally shared item embedding as the initial vector for the next round of training until the model converges. For the convenience of understanding the embodiments of the present invention, refer to Figure 2 for the algorithm architecture diagram in

[0018] Step 2: According to the federated recommendation method that combines aspect-level sentiment embedding and two-stage graph aggregation described in Step 1, in the said Step S10, the specific embedding construction method is as follows Figure 3 As shown, each client obtains local user private data and network public data, cleans the corresponding comment dataset, and divides it into user private comments and item public comments according to the different subjects. When performing aspect-level sentiment analysis, to ensure objectivity, the LDA topic model is used on the client side to perform topic analysis on the local comment data, obtain the set of aspect probabilities involved in all comments, and take the top L aspect words with the highest probabilities to form the aspect set A, rather than being defined artificially. According to the sentiment polarity type, the polarity set P is designed, and according to the different fields involved in the user data, the corresponding template T is designed as the prompt word of the pre-trained language model to perform aspect-level sentiment analysis on the comments, which is formalized as: The above formula means that the comment and the filled template are concatenated, and the pre-trained language model is used to score each template, and the aspect and sentiment polarity with the highest score are selected. Among them, represents the u th x comment of user and respectively represent the aspect and sentiment polarity corresponding to the u th x comment of user represents the prompt template composed of the elements in the aspect set A and the elements in the polarity set P, a l represents the l th aspect word in the aspect set A, p k represents the k th sentiment polarity in the polarity set P, F represents the pre-trained language model; Construct the embeddings of users and items according to the aspect-level sentiment polarities obtained from the analysis, which is formalized as: Among them, e u and e i respectively represent the aspect-level sentiment embeddings of users and items, a 1 , a 2 and a L respectively represent the 1st, 2nd and Lth aspect words in the aspect word set A, represents item i thy The aspect words corresponding to the comments; when the sentiment polarities in the comments are different, even for comments on the same aspect, the degree of user preference reflected is different; and if analyzed from the perspectives of users and items respectively, even for the same comment, it represents different meanings for different subjects; therefore, sentiment weighting coefficients are designed for users and items respectively and , which are defined as: where represents the sentiment polarity corresponding to the i th comment of item y . According to the constructed user-item aspect-level sentiment embeddings and user interaction information, a user-item interaction graph is formed, and the optimization of user embeddings and the personalization of item embeddings are achieved through the unique information propagation mechanism of the graph neural network

[0019] Step 3: According to the federated recommendation method combining aspect-level sentiment embeddings and two-stage graph aggregation described in Step 1, in the step S20, a first-order graph aggregation is performed using the constructed user-item interaction graph. To make full use of the feature information contained in the node embeddings, a graph attention mechanism with self-loops is adopted, which is formalized as: where and are the user embeddings for aggregating first-order neighbor information and the item embeddings with user personalization features respectively, W is a shared learnable parameter matrix, LeakyReLU is a non-linear activation function, α ui is the attention weight coefficient of each neighbor node u of user i , α iu is the attention weight coefficient of each neighbor node i of item u , which is defined as: To ensure privacy, each client sends the user-personalized item embeddings encrypted by LDP to the server, and the encryption method adopts local differential privacy, which is formalized as: where is the encrypted personalized item embedding, is the zero-mean Laplace noise, δ is the noise intensity, and the privacy protection ability increases with δis enhanced with the increase. To further enhance privacy protection, negative samples are extracted from the items that the user has not interacted with to form the final item embedding, and the client m The final uploaded embedding is: where represents the item embedding of random sampling.

[0020] Step 4: According to the federated recommendation method that combines aspect-level sentiment embedding and two-stage graph aggregation described in Step 1, in Step S30, the server obtains the user personalized item embeddings from different clients. According to the motivation that "users with similar preferences have similar views on items", the cosine similarity is used as the similarity metric of item embeddings to reconstruct the user relationship graph, and the client m and n The similarity between is defined as: where q m and q n are the item embeddings of two clients; According to the similarity index Select users with high similarity as neighbors to construct the user relationship adjacency matrix , which is formalized as: where ζ is the scaling factor for setting the similarity threshold, and the similarity mean is used as the reference value; Then, second-order graph aggregation is performed on all users to obtain the user relationship enhanced item embedding, which is formalized as: where Q is the initial item embedding matrix, and its m row represents the item embedding received from the client m , R is the aggregated item embedding matrix, C represents the number of aggregation layers, A is the adjacency matrix; Next, the average of all user personalized item embeddings is taken to obtain the global shared item embedding , which is formalized as: where D is C = 1 when AThe degree matrix, the unnormalized calculation method makes users with more neighbors have higher weights, in order to achieve the purpose of capturing more popular preferences.

[0021] Step 5: According to the federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation described in Step 1, in the step S40, the client receives the globally shared item embedding and the user relationship enhanced item embedding, and designs the following optimization objective for the local model: where λ 1 and λ 2 is the weight decay coefficient, L BPR is the Bayesian personalized ranking loss, specifically: where , N u represents the neighbor set of user u , σ represents the sigmoid activation function, and respectively represent the predicted scores of user u for item i and j . The preference ranking of users for goods is optimized through the BPR loss function, so that the goods actually preferred by users are ranked higher than the goods not preferred; is a regularization term that constrains the predicted score of the item to be close to the true score, specifically: where represents the neighbor set of user u with rating records, is the true rating of user u for item i . Since the constructed aspect-level sentiment embedding is close to the real-world features, the difference between the predicted score and the true score is used as a regularization term to ensure that the embedding does not deviate too much from the reasonable range during training; is a regularization term that constrains the user personalized item embedding to be similar to the user relationship enhanced item embedding, specifically: where t represents the number of interactive items, represents the user personalized embedding of item i , represents itemi User relationship enhanced embedding. The user relationship enhanced item embedding after second-order graph aggregation contains preference information from neighboring users in the user relationship graph, which can guide the local model to discover potential user preferences.

[0022] In addition, this embodiment also provides experimental verification for the above technical solution. Through performance experiments and ablation experiments, the effectiveness and feasibility of federated recommendation (FedATG) combining aspect-level sentiment embedding and two-stage graph aggregation are verified.

[0023] Specifically, this embodiment uses HR (Hit Ratio) and NDCG (Normalized Discounted Cumulative Gain) as evaluation indicators for model performance. The experimental results are as Figure 4 shown. The experimental results on four real-world datasets (Yelp, Amazon-CDs, Amazon-Sports, Amazon-Health) prove that the performance of the federated recommendation method in this embodiment is better than that of other baseline models. Using the loss value during model training as the evaluation indicator for the ablation experiment, the experimental results are as Figure 5 shown. Among them, FedATG is the model proposed in the present invention, FedATG-A is the model that uses random initial embedding instead of aspect-level sentiment embedding based on FedATG, FedATG-T is the model that uses the average parameter aggregation method instead of the two-stage graph aggregation method based on FedATG, and FedATG-AT is the model that uses the average parameter aggregation method instead of the two-stage graph aggregation method based on FedATG-A. The experimental results prove the effectiveness of aspect-level sentiment embedding and two-stage graph aggregation in improving model training efficiency and recommendation accuracy.

[0024] The above content only represents the implementation manner of the present invention, rather than limiting the protection scope of the invention. Any equivalent structural or equivalent process transformation based on the content described in the specification and drawings of the present invention, as well as direct or indirect applications in other related technical fields, all belong to the protection scope of the present invention.

Claims

1. A federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation, characterized by: The following steps are involved: Step S10: Each client constructs aspect-level sentiment embeddings for users and items based on local comment data, and builds a user-item interaction graph based on user interaction information; Step S20: Perform first-order graph aggregation on the embeddings of users and items according to the user-item interaction graph established by each client, obtain user embeddings with first-order neighbor information and item embeddings with user personalized features, and upload the user personalized item embeddings to the server; Step S30: The server obtains user personalized item embeddings from different clients, performs similarity analysis on them, constructs a user relationship graph based on the analysis results, and performs second-order graph aggregation to obtain user relationship enhanced item embeddings, then performs popular preference calculation on all user relationship enhanced item embeddings to obtain global shared item embeddings, and then distributes each user relationship enhanced item embedding and the global shared item embedding to the corresponding client; Step S40: The client uses the user relationship enhanced item embedding as the regularization term of the loss function and uses the global shared item embedding as the initial vector for the next round of training until the model converges.

2. The federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation according to claim 1, characterized in that: In step S10, the client divides the comment data into user private comments and item public comments according to the different subjects to which they belong. Then, the client uses the LDA topic model to perform topic analysis on the local comment data, obtains the aspect probability set involved in all comments, and takes the top L aspect words with the largest probability to form an aspect set A. The polarity set P is designed according to the sentiment polarity type. According to the different fields involved in the data, the corresponding template T is designed as the prompt word of the pre-trained language model, and the aspect-level sentiment analysis of the comments is performed, which is formalized as follows: in, Indicates user u No. x Comments, and Respectively represent users u No. x The aspects and sentiment polarity corresponding to the comments, represents a prompt template consisting of elements in the aspect set A and elements in the polarity set P. a l Indicates the first l Aspect words, p k represents the first k Emotional polarity, F represents the pre-trained language model; The embedding of users and items is constructed based on the aspect-level sentiment polarity obtained through analysis, which is formalized as follows: in e u and e i Represent the aspect-level sentiment embeddings of users and items, a 1 , a 2 and a L Respectively represent the first 1 , No. 2 and L Aspect words, Indicates items i No. y The aspect words corresponding to the comments, and are the sentiment weighted coefficients of user and item comments, respectively, which are defined as: in Indicates items i No. y The sentiment polarity corresponding to the comments is used to construct the user-item interaction graph through the constructed user and item aspect-level sentiment embeddings and user interaction information.

3. The federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation according to claim 1, characterized in that: In step S20, the first-order graph aggregation is performed using the constructed user-item interaction graph, which is formalized as follows: in and They are user embedding that aggregates first-order neighbor information and item embedding with user personalized features. W is the shared learnable parameter matrix, LeakyReLU is a nonlinear activation function, α ui For users u Each neighbor node of i The attention weight coefficient, α iu For items i Each neighbor node of u The attention weight coefficient is defined as: Then, each client sends the user-personalized item embedding encrypted by LDP to the server. The encryption method adopts local differential privacy, which is formalized as: in For encrypted personalized item embedding, is zero-mean Laplace noise, δ is the noise intensity, and the privacy protection ability increases with δ The client m The final uploaded embed is: in Represents randomly sampled item embeddings.

4. The federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation according to claim 1, characterized in that: In step S30, the server obtains user-personalized item embeddings from different clients, and uses cosine similarity as the similarity metric for item embeddings. m and n The similarity between Defined as: in q m and q n It is the item embedding of two clients; According to the similarity index Select users with high similarity as neighbors to construct the user relationship adjacency matrix , which is formalized as: in ζ To set the scaling factor for the similarity threshold, use the mean similarity As a reference value; Then, the second-order graph aggregation is performed on all users to obtain the user relationship enhanced item embedding, which is formalized as: in Q is the initial item embedding matrix, whose m The line represents the m The received items are embedded in R is the aggregated item embedding matrix, C Indicates the number of aggregation layers, A is the adjacency matrix; Next, all user-personalized item embeddings are averaged to obtain the global shared item embedding , which is formalized as: in D for C = 1 hour A The degree matrix of .

5. The federated recommendation method combining aspect-level sentiment embedding and two-stage graph aggregation according to claim 1, characterized in that: In step S40, the client receives the globally shared item embedding and the user relationship enhanced item embedding, and designs the following optimization objectives for the local model: in λ 1 and λ 2 is the weight decay coefficient, L BPR It is the Bayesian personalized ranking loss, specifically: in , N u Indicates user u The neighbor set of σ represents the sigmoid activation function, and Respectively represent users u For items i and j The prediction score of It is a regular term that constrains the predicted rating of an item to be close to the actual rating. Specifically: in Indicates user u The set of neighbors with scoring records, Is a user u For items i The real rating of is a regular term that constrains the embedding of user-personalized items to be similar to the embedding of user-relationship-enhanced items, specifically: in t Indicates the number of interactive items, Indicates items i User personalized embedding, Indicates items i User relationship enhanced embedding.

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