Graph neural network recommendation method based on fusion enhancement of social graph, knowledge graph and time decay mechanism

By integrating social graphs, knowledge graphs and time decay mechanisms into graph neural networks, dynamically modeling user-project interactions has solved the problem of existing recommendation systems being difficult to deal with dynamic changes in user preferences and data sparsity, and achieved more accurate and personalized recommendation effects.

CN120045791APending Publication Date: 2025-05-27ZHEJIANG UNIV OF TECH
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Patent Information

Application Number
CN202510218122.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-02-26
Publication Date
2025-05-27

AI Technical Summary

Technical Problem

Existing recommendation systems are difficult to effectively deal with the dynamic changes in user preferences and data sparsity, especially in dealing with dynamically changing user preferences and real-time interactive data. Traditional methods lack the application of time decay mechanisms.

Method used

Integrate social graphs, knowledge graphs and time attenuation mechanisms into graph neural networks, and form an ISKG-TD model through steps such as node coding, feature fusion, propagation iteration and scoring prediction to dynamically model user-project interaction.

Benefits of technology

By integrating the time decay mechanism, the model can more accurately capture the dynamic characteristics of user preferences, improve the accuracy and personalization of the recommendation system, especially in dealing with dynamically changing user preferences and real-time interactive data.

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Abstract

A graph neural network recommendation method based on fusion enhancement of a social graph, a knowledge graph and a time decay mechanism comprises the steps that node coding is conducted, an initial embedding layer is dedicated to coding user, project and entity nodes, attribute information of users, projects and entities is preprocessed, and the embedding technology is applied; converting the attributes into vector representation in a high-dimensional space; feature fusion: fusing features from different sources to enhance the characterization capability of the model; propagation iteration: effective propagation and iterative updating of information are realized through a multi-layer structure of the graph neural network; in each layer, the representation of the nodes is updated according to the information of the neighbor nodes, and each node can indirectly acquire and fuse wider network information through multi-round iteration; splicing and synthesizing: integrating and splicing the node representations after multiple rounds of iteration updating to form comprehensive feature representations; score prediction and optimization: predicting a matching score through an inner product embedded by a user and a project; performing parameter optimization by adopting a Bayesian personalized ranking (BPR) loss function, and covering embedding and convolution weights; in consideration of the change of user interests along with time, introducing a time decay function to improve the weight of recent rating, and calculating mean square error MSE loss through time weighted rating; and finally, combining the loss function with the BPR loss and the time weighted MSE loss to optimize the model performance.
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Description

Technical Field

[0001] The present invention belongs to the technical field of graph neural network recommendation systems, and particularly relates to a graph neural network recommendation method enhanced by the fusion of a social graph, a knowledge graph, and a time decay mechanism. Background Art

[0002] In the era of the explosive growth of Internet information, the recommendation system (RS), as a tool for filtering information of user interest, has been widely applied in multiple fields due to its powerful functions such as helping users make reasonable decisions, improving data processing efficiency, and alleviating the problem of information explosion. The recommendation system (RS) enhances the social recommendation process by aggregating and guiding user recommendations, and uses implicit evaluations such as reading duration and bookmark lists to filter content and highlight significant items, considering not only technological innovation but also incentive mechanisms and personal privacy impacts.

[0003] Traditional recommendation system methods mainly rely on user preferences and behavior patterns to predict and recommend interesting items or content, including content-based recommendation, collaborative filtering recommendation, and knowledge-based recommendation.

[0004] However, due to the problem of data sparsity, it is difficult to implement recommendations based on weaker user association information. Therefore, scholars have tried to adopt deep learning methods.

[0005] With the development of deep learning technology, convolutional neural networks (CNNs), recurrent neural networks (RNNs), and attention mechanisms are considered to be able to effectively process and learn complex features in large-scale unstructured data.

[0006] In deep learning technology, the application of graph neural networks (GNNs) mainly focuses on mining potential complex interactions between users and items as well as between items. By constructing user-item interaction data into a graph structure, GNNs can effectively capture high-order connection information between users and items, thereby learning more accurate user and item representations. This method of dealing with complex node relationships between users and items utilizes the powerful representation learning ability of GNNs on graph data to understand users' interests and preferences more deeply, thereby improving the accuracy and personalization of the recommendation system.

[0007] In addition, in the field of recommendation systems, the concept of time decay has been used to enhance deep neural network (DNN) models to achieve more accurate and personalized recommendations. Although time decay has been proven to be effective in DNNs, it has not been applied to graph neural networks (GNNs). Given the unique advantages of GNNs in dealing with complex relationships between users and items and their attribute features, integrating time decay into GNNs can further improve the performance of the recommendation system, especially in dealing with dynamically changing user preferences and real-time interaction data.

[0008] Meanwhile, social enhancement and knowledge graph enhancement use social connections and domain knowledge to improve the accuracy and interpretability of RS. Although both methods have achieved certain success independently in recommendation systems, their combined use has been relatively less explored in existing research.

[0009] Based on the above discussion, this paper proposes a new method - integrating social graph, knowledge graph, and time decay mechanism into a graph neural network (GNN), aiming to shift from traditional static modeling to dynamic temporal modeling of user-item interactions in recommendation systems. Summary of the Invention

[0010] The present invention aims to overcome the above-mentioned drawbacks of the prior art and provides a graph neural network recommendation method based on the fusion and enhancement of social graph, knowledge graph, and time decay mechanism.

[0011] The graph neural network recommendation method based on the fusion and enhancement of social graph, knowledge graph, and time decay mechanism of the present invention includes the following steps:

[0012] Step 1, Node Encoding: The initial embedding layer is dedicated to encoding user, item, and entity nodes. By preprocessing the attribute information of users, items, and entities and applying embedding techniques, these attributes are converted into vector representations in a high-dimensional space.

[0013] Step 2, Feature Fusion: Fuse features from different sources to enhance the model's representation ability.

[0014] Step 3, Propagation Iteration: Through the multi-layer structure of the graph neural network, effective propagation and iterative update of information are achieved. In each layer, the representation of a node will be updated according to the information of its neighbor nodes. Through multiple rounds of iteration, each node can indirectly obtain and fuse more extensive network information.

[0015] Step 4, Concatenation Synthesis: Integrate and concatenate the node representations after multiple rounds of iterative updates to form a comprehensive feature representation.

[0016] Step 5, Score Prediction and Optimization: Predict the matching score through the inner product of user and item embeddings. Use the Bayesian Personalized Ranking (BPR) loss function for parameter optimization, covering embeddings and convolutional weights. Considering that user interests change over time, introduce a time decay function to increase the weight of recent ratings, and calculate the mean square error (MSE) loss through time-weighted ratings. The final loss function combines the BPR loss and the time-weighted MSE loss to optimize the model performance.

[0017] Further, in the above-mentioned Step 1, the node encoding includes:

[0018] In the initial embedding layer, convert the input data into R dLow - dimensional embedding vectors, and correspond to users, items, and entities respectively. These embedding vectors are then represented by embedding matrices P, Q, and O. By integrating the dimensions of P, Q, and O, a three - dimensional space can be formed in the ISKG - TD framework, which serves as the basis for further updates through aggregation and propagation. As Figure 2 shown, the present invention utilizes the time - series information and node interactions in these graphs, aiming to capture the nuances of users' long - term preferences and their temporal dynamics, providing a more refined and effective recommendation system.

[0019] Furthermore, in the second step, the feature fusion includes:

[0020] Input the vector into the fusion layer. For each user a, the fusion layer combines the user's embedding vector p a with its associated feature vector x a to produce

[0021]

[0022] where W a is a transformation matrix and g(x) is a non - linear transformation function.

[0023] Similarly, for item embeddings and item - entity associations, and are calculated in the same way as used above.

[0024] Furthermore, in the third step, the propagation iteration includes:

[0025] In this framework, the embeddings of users items and entities are refined in the iteration. Starting from k = 0, the embeddings are propagated through the propagation function until reaching depth K.

[0026] For any given item i and its embedding at the k - th layer, construct the embedding of the next layer I as follows:

[0027]

[0028]

[0028] Here, I i represents the set of users who rate item i, is the embedding of user a at the k - th layer. The aggregation weight is represented by and the updated embedding of each item combines the aggregated neighbor embeddings with the previous - layer embedding of the item.

[0029] For merging knowledge from the knowledge graph, the formula for updating the embedding is similar, and we can obtain

[0030] Adopt an attention mechanism to calculate the weight η ia and η if , and use the following attention function:

[0031]

[0032] The attention network adopts a multi-layer perceptron (MLP). The subsequent attention weight normalization operation is as follows:

[0033]

[0034] The exponential function ensures the non-negativity of the attention weights. Using the exponential function guarantees that each calculated attention weight is greater than zero.

[0035] For each user a, their latent representation at the k-th layer is symbolized by For the social structure G S and the interest graph G I , the embedding of the user at the (k + 1)-th layer absorbs the influence of these two networks: the influence diffusion within G S and the interest propagation within G I . The term encapsulates the composite embedding from social proximity, while aggregates the embeddings based on item-centered interests in subsequent layers. Therefore, the evolution of each user embedding is expressed as follows:

[0036]

[0037] is calculated in a similar way by

[0038]

[0039] .

[0040] where and represent the scores reflecting social and interest influences respectively. The former is calculated as follows:

[0041]

[0042] After calculating the attention weights of specific nodes, these are input into the graph attention framework, allowing the formation of graph attention weights as follows:

[0043]

[0044] Similarly, in the enhancement phase involving the knowledge graph,

[0045] Furthermore, in step four, the splicing and synthesis includes:

[0046] After the K-level propagation process, collect the embeddings of users, items, and entities, represented by and at all levels up to k = K. For each user, construct as their cumulative embedding, which combines their representations at each level. Within the framework of the knowledge graph, the final item embedding is formulated as Similarly, for entities, construct as their cumulative embedding. Within the framework of the knowledge graph, the final item embedding is formulated as This method combines the functions of social graph and knowledge graph enhancement, simplifying the representations of users, items, and entities at multiple levels.

[0047] Therefore, the connection layer enables the synthesis of a set of features reflecting social and knowledge graph enhancement:

[0048]

[0049] Use vector splicing to obtain the final feature vector as follows:

[0050]

[0051] Furthermore, in step five, the score prediction and optimization includes:

[0052] Finally, take the inner product of the final user and item embeddings to predict their matching score:

[0053]

[0054] Adopt the Bayesian Personalized Ranking (BPR) loss to optimize all trainable parameters, including embeddings and convolutional weights. The loss function is defined as:

[0055]

[0056] where I = {(a, i, j) ∣ (a, i) ∈ I + , (a, j) ∈ I -} represents the training set, I + represents the set of positive instances (known user-item interactions), while I- Represents negative instances (user-item pairs not observed and thus sampled from the set I).

[0057] Users' interests change over time. Therefore, to give higher weight to recent ratings, a time decay function is added to the ratings. These time functions determine appropriate time weights and provide high weights for items with recent ratings. Table 1 gives a list of time decay functions.

[0058] Table 1

[0059]

[0060] Here, μ, α, β, ω, γ, and λ are tuning parameters, and t is the difference between the most recent timestamp and the timestamp when the item was rated.

[0061] The time-weighted ratings can be retrieved as follows:

[0062]

[0063] Then, the loss is obtained using the MSE loss with respect to the time decay as follows:

[0064]

[0065] where I a represents the labels of the training set.

[0066] In summary, the final loss is defined as:

[0067] L = L origin + L time (17)

[0068] The model ISKG-TD proposed by the present invention aims to capture the dynamic characteristics of user preferences by incorporating time information into user-item interactions, thus solving the limitations of static models. By leveraging the social graph connected by users and the knowledge graph of entity attributes, the present invention utilizes rich context information to improve the recommendation quality. At the same time, the integration of the time decay mechanism allows for discrimination of interactions over time, ensuring that the model remains sensitive to changing user preferences. Verified through comprehensive experiments conducted on the sampled Yelp dataset, the present invention is superior to traditional and state-of-the-art models in terms of recommendation accuracy and relevance, and the results highlight the effectiveness of the multi-graph method of the present invention and the potential of time-sensitive modeling in recommendation systems.

[0069] The present invention has the following beneficial effects:

[0070] 1. A novel method for a graph neural network-based recommendation system is proposed. Based on the integration of user-item graphs, social graphs, and knowledge graphs, a time decay mechanism is added to consider the evolving characteristics of user preferences, thereby achieving a more accurate temporal dynamic representation in user-item interactions.

[0071] 2. Extensive experiments on diverse datasets have demonstrated the superior performance of the present invention in capturing dynamic user preferences and outperforming existing recommendation systems.

[0072] In addition to the purposes, features, and advantages described above, the present invention has other purposes, features, and advantages. The present invention will be described in further detail below with reference to the accompanying drawings. Description of the Drawings

[0073] Figure 1 It is an explanatory diagram of the ISKG-TD model of the present invention. The left sub-diagram is the model framework of ISKG-TD, and the right sub-diagram is the embedding propagation layer of ISKG-TD.

[0074] Figure 2 It is a representation of temporal information in the user-item interaction graph and item-entity interaction graph of the present invention. The yellow node u i represents the user, and the blue node v i represents the item, and the green node e i represents the entity. Detailed Embodiment

[0075] Reference will now be made in detail to the exemplary embodiments of the present disclosure, examples of which are illustrated in the accompanying drawings. Like reference numerals in the drawings and the description indicate the same or similar parts. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0076] This embodiment relates to a recommendation method for an online teacher community (OTCs) applying the graph neural network recommendation method based on the fusion and enhancement of social graphs, knowledge graphs, and time decay mechanisms of the present invention. As Figure 1 shown, its steps include:

[0077] Step S1: Acquisition and processing of data, and acquisition of label difference E;

[0078] Specifically, in an application scenario of a recommendation system, taking online teacher communities (OTCs) as an example, the task of the graph neural network recommendation method is to classify the teacher interactions and educational content needs of target teacher users, so as to dynamically recommend corresponding types of educational content and realize teacher interactions, which belongs to the node classification task. Each client obtains data related to the online teacher community OTCs in various ways, converts teachers, educational resources (ERs), and entities into vector representations, and encodes these relationships into a matrix, representing the complex interaction network within the OTCs.

[0079] The model is constructed based on three basic sets: the teacher set U = {u 1 , u 2 ,..., u m}, where m = |U| represents the number of teachers, and each teacher is described by an attribute vector such as age and teaching preferences; the ER set I = {i 1 , i 2 ,..., i n}, where n = |I| represents the number of educational resources, and each ER is described by features such as subject and grade; and the entity set E = {e 1 , e 2 ,..., e k}, where k = |E|, the ERs are associated with entities, and their representations are enriched through relation tuples such as (textbook, belongs to, mathematics). This multi-dimensional model effectively captures the complex relationships among teachers, ERs, and entities.

[0080] Step S2: In the online teacher community, to achieve precise and dynamic recommendation of educational resources, a social graph, a knowledge graph, and a time decay mechanism are integrated. When a new teacher joins or a teacher's behavior changes, the relevant information is input into the fusion layer in vector form.

[0081] For teacher a, the fusion layer combines its embedding vector p a based on the social graph and the feature vector x a associated with the knowledge graph to generate an initial teacher embedding vector The formula is where W a is the transformation matrix, and g(x) is the non-linear transformation function.

[0082] For example, Teacher Wang is a newly joined English teacher in the community. His communication behavior in the social graph forms p a , and the information such as his teaching style and areas of expertise recorded in the knowledge graph constitutes x a . The initial embedding vector suitable for him can be obtained through the formula.

[0083] Similarly, for educational resource items and knowledge entities, the initial item embedding vector and the embedding vectors of knowledge entities A similar method is also used for calculation. Subsequently, by combining the time decay mechanism and considering the time variation of the teacher's interests, suitable educational resources can be accurately recommended to the teacher.

[0084] Step S3: To achieve the accurate and dynamic recommendation of educational resources and meet the educational resources suitable for the teacher's own needs. Starting from the initial state k = 0, the system will educational resource items and knowledge entities are continuously iteratively refined until the preset depth K is reached.

[0085] For an educational resource item i, its embedding at the k-th layer is The system starts from the interest graph G I and constructs the embedding of the next layer where I i is the set of teachers who have evaluated this item. The weight η ia is calculated through the attention mechanism and is ensured to be positive after normalization.

[0086] Under the influence of the social structure G S and the interest graph G I the embedding of teacher a evolves according to During the knowledge graph enhancement stage, we can also obtain By combining the time decay mechanism and considering the change of the teacher's interests, the system can accurately recommend suitable educational resources for the teacher.

[0087] After achieving the K-level propagation, collect the embeddings of teachers, educational resource items, and knowledge entities at each level and

[0088] Through system integration, their embeddings at each layer are constructed into cumulative embeddings as a comprehensive personalized ability profile provided for the teacher. The same applies to educational resource items and knowledge entities, obtaining and

[0089] Subsequently, the connection layer synthesizes the feature set: The final feature vector is obtained by vector concatenation:

[0090] By combining the time decay mechanism and considering the change of the teacher's interests, the system can accurately recommend resources for the teacher based on these and find high-quality materials that meet the teaching needs of the teacher.

[0091] Step S5: After completing the embedding construction and feature integration, start predicting the matching degree between teachers and resources.

[0092] When the system takes the inner product of the final embeddings of teachers and resource items, the matching score is obtained: To optimize the model parameters, the Bayesian Personalized Ranking (BPR) loss is adopted: where the training set I contains positive and negative instances.

[0093] Considering that teachers' interests change over time, a time decay function is introduced to assign higher weights to recently evaluated resources. The time-weighted rating is calculated as follows: Then, the mean squared error (MSE) loss is combined with the time decay to obtain L time . The final loss function is: L = L origin + L time . By minimizing this loss, the system combines various aspects of information to accurately recommend current applicable educational resources for teachers.

[0094] Step S6: Input new user features into the model to achieve dynamic recommendation of educational content and teacher interaction;

[0095] When the client obtains a new user network or adds new nodes to the original network, the newly constructed graph neural network is input into the trained model to obtain the classification results of the new nodes, and then the corresponding types of educational content are recommended.

[0096] The data acquisition and processing module collects OTCs data in the online teacher community, converts teachers, educational resources, and entities into vectors and encodes them into matrices, constructs a multi-dimensional model, and obtains the label difference E to capture the complex relationships among the three.

[0097] The fusion mechanism module inputs relevant information vectors into the fusion layer when a new teacher joins or a teacher's behavior changes. It fuses social and knowledge graph features to generate initial embedding vectors for teachers, educational resources, and knowledge entities, and considers interest changes in combination with the time decay mechanism.

[0098] The embedding iteration module continuously iterates the embeddings of teachers, educational resources, and knowledge entities, and refines them to a preset depth based on the interest graph, social structure, knowledge graph enhancement results, and time decay mechanism.

[0099] The construction and integration module, after achieving K-level propagation, collects the cumulative embeddings of each layer to construct the embedding, synthesizes and splices the feature vectors, and combines the time decay to provide data for accurate recommendation.

[0100] The prediction and recommendation module calculates the matching scores between teachers and resource embeddings, optimizes the model using the BPR loss and the time decay function, and minimizes the loss to achieve accurate recommendations. When the client obtains a new network or node, it inputs the graph neural network into the model to obtain the classification results, completing dynamic recommendations and teacher interactions.

[0101] The embodiments described above are only descriptions of the preferred embodiments of the present invention and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A graph neural network recommendation method based on the fusion enhancement of social graph, knowledge graph and time decay mechanism includes the following steps: Step 1, node encoding: The initial embedding layer is dedicated to encoding user, item, and entity nodes; by preprocessing the attribute information of users, items, and entities and applying embedding techniques, these attributes are converted into vector representations in a high-dimensional space; Step 2: Feature fusion: Fusion of features from different sources to enhance the representation capability of the model; Step 3: Propagation and iteration: Through the multi-layer structure of the graph neural network, effective information propagation and iterative update are achieved; in each layer, the representation of the node will be updated according to the information of its neighboring nodes. Through multiple rounds of iterations, each node can indirectly obtain and integrate more extensive network information; Step 4: splicing and synthesis: Integrate and splice the node representations after multiple rounds of iterative updates to form a comprehensive feature representation; Step 5: Rating prediction and optimization: predict the matching score through the inner product of user and item embeddings; use the Bayesian personalized ranking BPR loss function for parameter optimization, covering embedding and convolution weights; considering that user interests change over time, introduce the time decay function to increase the weight of recent ratings, and calculate the mean square error MSE loss through time-weighted ratings; the final loss function combines the BPR loss and the time-weighted MSE loss to optimize the model performance.

2. The method according to claim 1, characterized in that The node encoding described in step 1 includes: In the initial embedding layer, the input data is transformed into R d Embedding vectors of medium and low dimensions, and Corresponding to users, items and entities respectively; these embedding vectors are then represented by embedding matrices P, Q and O; by integrating the dimensions of P, Q and O, a three-dimensional space is formed in the ISKG-TD framework, which serves as the basis for further updating through aggregation and propagation; utilizing time series information and node interactions to capture the nuances of users' long-term preferences and their temporal dynamics.

3. The method according to claim 1, characterized in that The feature fusion described in step 2 includes: The vector is input into the fusion layer. For each user a, the fusion layer embeds the user’s vector p a The eigenvector x associated with it a Combined, it produces Where W a is a transformation matrix, g(x) is a nonlinear transformation function; Similarly, for item embeddings and item-entity associations, and The calculation method of is the same as used above.

4. The method according to claim 1, characterized in that The propagation iteration described in step 3 includes: In this framework, users project and entities The embedding of is refined in iterations; starting from k=0, the embedding is performed through the propagation function until the depth K is reached; For any given item i and its embedding at layer k From the interest graph G I Construct the next layer of embedding As shown below: Here, I i represents the set of users who provide ratings for item i, is the embedding of user a at layer k; the aggregation weight is given by Indicates that each item's update is embedded in Combines aggregated neighbor embeddings with the previous layer embeddings of items; For merging knowledge from the knowledge graph, the formula for updating the embedding is similar, which can be obtained The weight η in the calculation formula is calculated using the attention mechanism ia and η if , using the following attention function: The attention network uses a multi-layer perceptron (MLP); the subsequent attention weight normalization operation is as follows: The exponential function ensures the non-negativity of the attention weights. Using the exponential function ensures that each calculated attention weight is greater than zero. For each user a, their latent representation at layer k is given by Symbolization; for social structure G S and interest graph G I , the user’s embedding at layer k+1 Absorbing the influence of these two networks: in G S The influence of the diffusion within and in G I Propagation of interest within; terminology encapsulates a composite embedding from social proximity, while The embeddings based on the central interest of the items are aggregated in the subsequent layers; therefore, each user embedding The evolution of is expressed as follows: Calculated by The calculation method is similar to; in and They represent the scores reflecting social and interest influence respectively, the former is calculated as follows: After calculating the attention weights for specific nodes, these are fed into the graph attention framework, allowing the formation of graph attention weights as follows: Similarly, in the enhancement phase involving the knowledge graph, we obtain 5. The method according to claim 1, characterized in that The splicing synthesis described in step 4 includes: After the K-level propagation process, the embeddings of users, items, and entities are collected and given by and At all levels until k = K; for each user, construct This merges her representations at each level as their cumulative embedding; within the framework of the knowledge graph, the final item embedding is formulated as Similarly, for entities, construct as their cumulative embeddings; within the framework of knowledge graphs, the final item embedding is formulated as This approach combines the enhanced capabilities of social graphs and knowledge graphs to simplify the representation of users, items, and entities at multiple levels; Thus, the concatenation layer enables the synthesis of a feature set that reflects social and knowledge graph enhancements: The final feature vector obtained by vector concatenation is as follows:

6. The method according to claim 1, characterized in that The score prediction and optimization described in step 5 include: Finally, the inner product of the final user and item embedding is performed to predict its matching score: Bayesian personalized ranking (BPR) loss is used to optimize all trainable parameters, including embeddings and convolution weights; the loss function is defined as: where I={(a,i,j)∣(a,i)∈I + ,(a,j)∈I - } represents the training set, I + represents the set of positive instances (known user-item interactions), and I - represents negative instances (unobserved user-item pairs, hence sampled from set I); Users’ interests change over time; therefore, in order to give higher weights to recent ratings, a time decay function is added to the ratings; these time functions determine the appropriate time weights and give high weights to recently rated items; Table 1 gives a list of time decay functions; Here, μ, α, β, ω, γ, and λ are tuning parameters, and t is the difference between the most recent timestamp and the timestamp when the item was rated; Time-weighted ratings can be retrieved as follows: Then the MSE loss is used to decay with respect to time to obtain the loss as follows: Among them, I a Represents the label of the training set; The final loss in summary is defined as: L=L origin +L time (17)

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