Fairness recommendation method based on meta-learning and feature enhancement

Abstract

This invention discloses a fair recommendation method based on meta-learning and feature enhancement. This method extracts features from user features and item features using graph neural networks and Gaussian mixture models, respectively. Then, an MLP network is used to generate the final predicted value. The entire model is trained using a meta-learning MAML model. Finally, the fairness of the recommendation system is optimized from both individual and group fairness perspectives. This invention fuses and enhances the user embedding representation in the recommendation process, and models, learns, and extracts features from the item embedding representation separately. It effectively integrates user interaction information with traditional recommendation methods, captures fine-grained user interests and preferences, improves recommendation performance, and ensures fairness to users within the recommendation system.

Description

Technical Field

[0001] This invention belongs to the field of meta-learning and fusion feature enhancement. It proposes a meta-learning-based sequence recommendation method to ensure the fairness of the recommendation system while alleviating the cold start problem. Background Technology

[0002] In recent years, few-shot and meta-learning techniques have developed rapidly. Meta-learning and few-shot learning enable models to learn and tune parameters, allowing them to quickly learn new tasks based on existing knowledge. Therefore, at the model level, meta-learning can effectively alleviate the cold start problem. Specifically, meta-learning first learns on each task, acquiring prior knowledge, and then quickly adjusts and optimizes on new tasks based on a small amount of prior knowledge and training data. The cold start problem is a data sparsity problem, with limited user interaction information, and each task is to recommend relevant items to the user. The model first learns generalization ability through prior knowledge during the meta-training phase, enabling it to quickly fine-tune and adapt to new tasks during meta-testing. Meta-learning has achieved certain results, and many models incorporate the MAML (Mean Interaction and Learning) concept. This method can obtain relatively good generalization parameters, but it also has a certain risk of overfitting and does not effectively incorporate user interaction information.

[0003] Meanwhile, during the cold start phase of a recommender system, fairness issues arise, encompassing both individual and group fairness. Individual fairness primarily addresses user data privacy, while group fairness aims to mitigate group bias. Currently, to alleviate fairness issues, Alex et al. proposed an unbiased measurement method for recommender system ranking fairness, which allows relevant bias data to be exposed. However, this method may fail to provide optimal recommendations when data is limited. Therefore, in environments with scarce data, user fairness needs to be prioritized. Summary of the Invention

[0004] The purpose of this invention is to propose a meta-learning-based model framework to address the cold start and fairness issues existing in current recommender systems. The cold start solution combines fusion feature enhancement techniques and a meta-learning model, while also using side information to supplement user features, thereby improving recommendation accuracy. Regarding the fairness issue, generative adversarial learning is proposed to address the fairness problem in recommender systems, effectively mitigating fairness concerns. The technical solution of this invention is as follows:

[0005] S1: Split the dataset into a support set and a query set, using a 7:3 weighting. Then integrate the input data; first, embed user attributes and project attributes are represented separately.

[0006] S2: A Gaussian Mixture Model (GMM) and a Graph Convolutional Neural Network (GCN) are used to capture user input features. The Gaussian Mixture Model focuses on probabilistic modeling of user behavior patterns, which mainly involves statistically analyzing and classifying users' personal and sensitive information. The GCN mainly studies the relationships between user-interacting items. Through these relationships, the GCN can extract better embedding representations. Finally, the information from the two modules is concatenated to obtain a high-quality final fused embedding representation.

[0007] S3: The fused and enhanced embedding representation, along with the candidate items, is fed into the MLP. The MLP contains multiple fully connected layers that can output the user's rating information for the items. Using the predicted rating information, the loss function of the model can be obtained through the mean error function.

[0008] S4: Fairness of the recommender system. Two discriminators are designed and added to the model. Their functions are to identify sensitive information of users and to determine user clusters, respectively. They are used to judge the user's input features and the final predicted embedding representation, thereby ensuring the fairness of the system. This invention focuses on individual fairness and group fairness.

[0009] S5: The entire model is trained using the MAML algorithm. MAML is a model-independent meta-learning algorithm, but to address fairness concerns, adjustments are made to both global and local updates. Adjustments to the global update require considering the discriminator's parameter updates, necessitating parameter updates for both discriminators. Adjustments to the local update do not require considering the discriminator's parameters for user cluster fairness; therefore, only the parameters of the recommender and the discriminator for user-sensitive information need to be updated.

[0010] Furthermore, specific step S1 includes the following steps:

[0011] S11: Select a dataset and partition it. The dataset contains user information u, user interaction information uvi, and item information v. Therefore, the supported set partitioning is as follows: Supported set St = {(u1, x1), ..., (u...} k x k )}}, where k represents the number of support sets. The query set is also defined similarly as Qt={(u1,x1),...,(u m x m )}}.

[0012] The support set St and the query set Qt are disjoint and are both composed of subsets of the entire dataset T.

[0013]

[0014] S12: In the model of this invention, U = {u1, u2, ... u...} is used respectively. n} and X = {x1, x2, ..., x} m Let} represent all users and items, where n and m are the number of users and items, respectively. The embedding layer primarily contains the embedded representations of items and users.

[0015] Given a project x i Its embedded representation can be expressed using its attribute ai. Since projects often have multiple different attributes, ai = {at1, at2, ..., at...} s}, at i Let represent the i-th attribute of the project, and S represent the number of attributes contained in the project.

[0016] User embeddings are represented using interactive item information. Since different item attributes are often heterogeneous and have varying impacts on user preference decisions, this invention employs an attention mechanism to obtain preference weights for different attributes. The attention network γi for item i is calculated as follows.

[0017] γi = softmax(w f ai+b f )

[0018] Among them, w f and b f All of them are learnable parameter matrices.

[0019] S13: Let user u i The embedding is represented as {l1, l2, ... l T}, where l i Let l represent the information for the i-th item that the user has interacted with, and T represent the total number of items the user has interacted with. An attention mechanism is introduced for the item information l. i The following formula can be used to calculate it.

[0020] l i =γiai

[0021] Furthermore, specific step S2 includes the following steps:

[0022] S21: Constructing user interaction codes. First, based on the user's own coding, a Gaussian mixture model is used to model it, generating the corresponding user interaction codes. The Gaussian mixture model is a weighted set of Gaussian densities of the S components, as shown in the following equation:

[0023]

[0024] In the formula, S represents the number of single Gaussian distributions, s is the formal parameter, l is the feature vector of the item attribute, and β s The mixed weights represent the probability of being selected from a Gaussian distribution, g(l|μ) s , ∑ s ) represents the component Gaussian density, where each component density is a bivariate Gaussian function, in form:

[0025]

[0026] Where μ s Let ∑ be the average eigenvector. s For covariance, use the average eigenvector, covariance matrix, and the mixing weight β of each mixture component. s Parameterizing the Gaussian mixture model Used to represent these parameters,

[0027] For a specific user u i Given a set of user's historical interaction item attribute information, where T is the total number of items the user has interacted with, and user u i The embedding is represented as {l1, l2, ..., l... T}, that is u i ={l1, ..., l T The likelihood of the GMM is given by the following formula:

[0028]

[0029] This invention uses the expectation-maximization algorithm to estimate the parameters. After constructing the GMM for user u, given...

[0030] Project preference information The preference of user u for item b is given.

[0031] S22: Construct project-related coding. The correlation between projects is modeled using a graph G = (V, E), where V represents each project, and E are the weighted edges representing the similarity between two projects with the same attributes. G is represented by an adjacency matrix A, where A... i，j =sim(x i x j ).

[0032] Graph Convolutional Networks (GCNs) are defined on adjacency graphs, allowing the extraction and aggregation of neighborhood information for each vertex. Graph convolution is defined as:

[0033]

[0034] Where I is the identity matrix, included to capture the project's own attribute characteristics. Matrix D is... The degree matrix is ​​Wβ, which is the weight matrix of the β-th layer in the GCN, and Hβ is the output of the β-th layer.

[0035] Specifically, H 0 =X, In the formula, X is the initial vertex feature matrix, and Z is the final output of the GCN. Indicates the number of layers in the GCN.

[0036] S23: After modeling the user interaction code and project-related code, they are jointly output. This design uses MLP to fuse the outputs of these two modules, as shown in the following formula:

[0037]

[0038] Fi represents the output of the fusion feature enhancement layer, which consists of two connected modules. The Concat function is designed to connect the two modules.

[0039] Furthermore, specific step S3 includes the following steps:

[0040] S31: In order to capture user preference information, the input of the prediction layer includes the output of the fusion feature enhancement module and the item embedding representation. This invention connects these two embedding representations together and inputs them into a fully connected layer for the final calculation of user preferences for items.

[0041]

[0042] Where Fi represents the fused feature enhancement representation of the user UI, and ai represents the embedded representation of item i. f represents the recommendation model.

[0043] In the entire recommendation model, the mean absolute error (MAE) is used as the loss function. The mean absolute error loss is calculated as the average of the sum of the absolute differences between the actual and predicted values. Therefore, the overall loss of the recommendation model is shown in the following equation.

[0044]

[0045] In the above formula, fθ r Represents the expression by θ r The initial recommendation model f, at θ r In this context, 'r' represents the recommender, and 'm' represents the total number of items. This represents the user's predicted rating for the item, while y ui That is the actual rating information.

[0046] Furthermore, specific step S4 includes the following steps:

[0047] S41: Individual fairness primarily addresses implicit user protection, meaning minimizing the possibility of implicit data theft by eavesdroppers. This is achieved by generating embedded representations unrelated to sensitive user information, using an individual fairness discriminator. The discriminator takes the user's fused feature-enhanced embedded representation as input and outputs the user's sensitive attributes, aiming to maximize the difference between the two to protect privacy. Therefore, the loss function of the individual fairness discriminator is as follows:

[0048]

[0049] Where g represents the discriminator, which is the component used to obtain the user's sensitive information, and a... u This represents the user's sensitive information, which has many categories. i This is the embedded representation of user i, l D This represents the loss function of the discriminator. Unlike traditional adversarial games, it also introduces external information F. g To achieve better performance. D The loss function for each fairness level is shown in the following equation:

[0050]

[0051] In the above formula, l D In the function, since the discriminator needs to consider the generation of the recommender, f is represented by θ. r θ d Initialization: Here, r and d represent the parameters of the recommender and discriminator, respectively. c represents the user's sensitive information category. This represents the probability that the sensitive information of user u is predicted by the discriminator to be of class c. When When the value is 1, it means that this is a real class;

[0052] S42: Group fairness primarily addresses the preferences of user groups, requiring that the recommendation system perform similarly across different groups. This necessitates generating predicted values ​​that closely approximate the true values, achieved through a group fairness discriminator. The group fairness discriminator takes the recommender's output as its input and outputs sensitive group-specific information, aiming to maximize the difference between the two to achieve similar recommendation results. Therefore, the loss function of the group fairness discriminator is shown in the following equation.

[0053]

[0054] Where h is the discriminator, E hThis is external information; the embedding of the project data is presented as supplementary information in the text. Besides the reasons mentioned above, project data often contains sensitive information. For example, men tend to borrow science fiction novels, while women may prefer romance novels. This approach helps eliminate coding biases in the project data.

[0055] To comprehensively alleviate the fairness issue, this invention employs representation-level and prediction-level adversarial learning for multi-task learning, as shown in the following equation:

[0056]

[0057] Among them, the hyperparameters λ and ξ are mainly used to balance these two types of losses, while l D This will be combined with the recommendation loss function l R For co-training, this design uses two hyperparameters to more flexibly control the loss function.

[0058] Furthermore, specific step S5 includes the following steps:

[0059] S51: This design uses the meta-learning MAML algorithm for parameter training and updating. The MAML algorithm mainly optimizes the parameters of the entire recommendation model and the discriminant model. The model parameters consist of two parts, θ={θ r θ d These represent the parameters of the recommender and the discriminator, respectively. The specific adjustments to the MAML model are as follows:

[0060] For local updates, the focus is on optimizing the parameters of the discriminator, as shown in the following formula:

[0061]

[0062] In the above formula, This represents the personalized model parameters of the discriminator, fine-tuned for each user, where d represents the discriminator. β is a learnable hyperparameter used as the learning rate for updating local parameters. L is the prediction loss of the entire model on the support set.

[0063] Finally, the overall loss is updated using the following formula:

[0064]

[0065] In the above formula, This represents the personalized model parameters of the recommender, which are fine-tuned for each user. 'r' represents the recommender. R This represents the prediction loss of the recommendation model on the support set.

[0066] In terms of global updates, both the parameters of the discriminator and the parameters of the recommender are considered, so the formula needs to include two parts, as shown in the following formula.

[0067]

[0068] In the above formula, β represents the learning rate, which can be continuously learned through training, and L represents the loss function of the entire MFCN model.

[0069] S52: The loss function of MFCN consists of two parts: the loss of the recommender and the loss of the discriminator. Therefore, the overall loss function is shown in the following formula.

[0070]

[0071] This invention proposes a fair recommendation method based on meta-learning and feature enhancement, starting from the perspective of user preferences, modeling user interaction and item attributes separately, using fusion feature enhancement technology to fuse and enhance these two modules, and employing generative adversarial learning for fairness judgment. Compared with existing technologies, the advantages of this invention are:

[0072] 1. Compared with traditional sequence recommendation, this invention is a session-based sequence recommendation that takes into account the combination of user interaction information and item information, mines the user's potential preferences, and improves the accuracy of recommendations.

[0073] 2. Compared with traditional sequence recommendation, this invention incorporates generative adversarial learning to capture sensitive information of users and group recommendation information respectively, thereby enabling the recommender to generate information that ensures fairness to users.

[0074] 3. By adopting a meta-learning strategy and using the MAML algorithm to train the parameters of the entire model, the model can be efficiently adapted to small sample tasks.

[0075] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural changes made using the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention. Attached Figure Description

[0076] Figure 1 This is a flowchart illustrating a fair recommendation method based on meta-learning and feature enhancement in an embodiment of the present invention.

[0077] Figure 2 This is a schematic diagram of the fusion feature enhancement module in an embodiment of the present invention.

[0078] Figure 3 This is a flowchart of the recommendation model in an embodiment of the present invention.

[0079] Figure 4 This is a flowchart of the meta-learning process in an embodiment of the present invention. Detailed Implementation

[0080] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0081] 1. Training dataset

[0082] This invention uses the Movielens-1M dataset as an example. The Movielens dataset contains not only user ratings of movies but also movie metadata (such as title, category, etc.), which is very useful for understanding and improving recommendation algorithms. The Movielens dataset contains numerous versions, each with a different amount of data. Movielens-1M contains 1,000,000 reviews from 6,000 users on 4,000 movies, with ratings ranging from 1 to 5 stars. This dataset is an extended version of the ml-100k dataset. To verify the model's effectiveness, movies appearing less than 5 times in the Movielens dataset were filtered out, and 70%, 10%, and 20% were used as the support set, query set, and validation set, respectively; the last item in each session was used as the true value predicted by the model. Furthermore, sessions containing only one movie in the training and testing sets were also removed. After preprocessing, the support set, query set, and validation set contained 697,927, 106,782, and 195,291 records, respectively.

[0083] 2. Embedding and representing user data and movie data.

[0084] Step 1: Initialize the user and movie data in the training set. First, initialize the movie data. Since movies have attribute information, the movie embedding representation is represented by the attribute information, as follows:

[0085] ai = {at1, at2, ..., at} s}

[0086] Step Two: Since the user has viewed a limited number of movies, a self-attention mechanism is used to obtain the user's movie preferences. Movie attribute preferences are used to represent the user's embedded representation. Because different movie attributes are often heterogeneous and have varying impacts on the user's preference decisions, this invention employs an attention mechanism to obtain the preference weights for different attributes. The attention network γi for movie i is calculated as follows:

[0087] γi = softmax(w f ai+b f )

[0088] Therefore, user u iThe embedding representation of {l1, l2, ..., l T}, where l i Let T represent the information for the i-th movie that the user has interacted with, and T be the total number of movies the user has interacted with. Introduce an attention mechanism for the movie information l. i The following formula can be used to calculate it.

[0089] l i =γiai

[0090] 3. Computational Fusion Enhanced Embedded Representation

[0091] Step 1: Obtain the fusion enhancement code. Using the user embedding representation and the movie embedding representation as inputs to this module, first, the user embedding representation is obtained. The user interaction code is then obtained and input into the Gaussian mixture model. The final value of the Gaussian mixture model is a probability, and the user's preference distribution can be obtained through the Gaussian mixture model. For example... Figure 2 The formula for the first part is as follows:

[0092]

[0093] In the formula, S represents the number of single Gaussian distributions, s is the formal parameter, l is the feature vector of the item attribute, and β s The mixed weights represent the probability of being selected from a Gaussian distribution, g(l|μ) s , ∑ s ) represents the component Gaussian density, where each component density is a bivariate Gaussian function, in form:

[0094]

[0095] Where μ s Let ∑ be the average eigenvector. s For covariance, use the average eigenvector, covariance matrix, and the mixing weight β of each mixture component. s Parameterizing the Gaussian mixture model Used to represent these parameters,

[0096] For a specific user u i Given a set of users' historical movie interaction attributes, where T is the total number of movies a user has interacted with, and user u... i The embedding is represented as {l1, l2, ..., l... T}, that is u i ={l1, ..., l T The likelihood of the GMM is given by the following formula:

[0097]

[0098] Step Two: Next, the feature attributes of the movies are acquired and fed into a graph convolutional neural network. In this network, the correlation between movies is modeled using a graph G = (V, E), where V represents each movie itself, and E represents the weighted edges between movies, indicating the similarity between two movies with the same attributes. G is represented by an adjacency matrix A, where A... i，j =sim(x i x j In the movie dataset, graph convolution is defined as:

[0099]

[0100] Where I is the identity matrix, included to capture the film's own characteristic properties. The D matrix is... The degree matrix is ​​Wβ, which is the weight matrix of the β-th layer in the GCN, and Hβ is the output of the β-th layer.

[0101] Specifically, H0 = X, In the formula, X is the initial vertex feature matrix, and Z is the final output of the GCN. Indicates the number of layers in the GCN.

[0102] Step 3: Then, these two blocks are passed through a fully connected neural network to obtain a fused and enhanced embedding representation, as shown in the following formula:

[0103]

[0104] 4. Calculate the model's predicted values ​​and losses.

[0105] Step 1: Feed the fusion-enhanced embedding along with the movie data to be recommended into the MLP. The MLP contains many fully connected neural networks, which can improve recommendation accuracy. The specific formula is as follows:

[0106]

[0107] Step 2: Where Fi is user u i The fusion feature enhancement representation is given by , where ai is the embedded representation of movie i. f represents the recommendation model. The loss function of this recommendation model is expressed as follows:

[0108]

[0109] 5. Improve individual and group fairness.

[0110] Step 1: Conduct research on individual fairness and group fairness. Figure 1The two polygons on the left represent the discriminator in generative adversarial learning. Their main function is to obtain user age information and group recommendation metrics. Individual fairness primarily targets user age, while group fairness primarily targets recommendation accuracy within the same group. Firstly, regarding individual fairness, a fully connected neural network is used to capture user age, and its loss function is as follows:

[0111]

[0112] In this formula, a u That is, the user's age, g is the discriminator used to predict the user's age, and E is the user's age. g Additional information.

[0113] Step Two: The formula for similar group fairness is as follows:

[0114]

[0115] In this formula, 'a' u E represents the type of recommendation. h Additional information. The loss function for the entire discriminator is as follows:

[0116]

[0117] Among them, the hyperparameters λ and ξ are mainly used to balance these two types of losses, while l D This will be combined with the recommendation loss function l R For co-training, this design uses two hyperparameters to more flexibly control the loss function.

[0118] 6. Use meta-learning to train and update the model parameters.

[0119] Step 1: Train the entire model using meta-learning. First, use the support set to perform local updates on the entire model, focusing on optimizing the parameters of the discriminator. The formula is shown below:

[0120]

[0121] In the above formula, This represents the personalized model parameters of the discriminator, fine-tuned for each user, where d represents the discriminator. β is a learnable hyperparameter used as the learning rate for updating local parameters. L is the prediction loss of the entire model on the support set.

[0122] Finally, the overall loss is updated using the following formula:

[0123]

[0124] In the above formula, This represents the personalized model parameters of the recommender, which are fine-tuned for each user. 'r' represents the recommender. R This represents the prediction loss of the recommendation model on the support set.

[0125] Step 2: In terms of global updates, both the parameters of the discriminator and the parameters of the recommender are considered. Therefore, the formula needs to include two parts, as shown in the following formula.

[0126]

[0127] In the above formula, β represents the learning rate, which can be continuously learned through training, and L represents the loss function of the entire MFCN model. The loss function L on the movie dataset is expressed as:

[0128]

Claims

1. A fair recommendation method based on meta-learning and feature enhancement, characterized in that, Includes the following steps: S1: Split the dataset into a support set and a query set, and initialize user attributes and project attributes; S2: Use GMM and graph neural network to model the user interaction attribute representation and the item attribute representation respectively to obtain the learned fusion feature-enhanced representation embedding; S3: The combined value to be predicted is embedded into the input MLP by fusing the enhanced feature representation, and the prediction score is obtained through multi-layer neural network operations; S4: By leveraging the idea of ​​generative adversarial learning, we can capture sensitive user information and group information through the network; S5: Construct loss functions separately, use the meta-learning MAML algorithm to train and tune the entire model, and perform joint optimization; The specific steps of S4 are as follows: S41: The input to the individual fairness discriminator is the user's fused feature enhanced embedding representation, and the output is the user's sensitive attributes. The goal is to maximize the difference between the two to achieve the purpose of privacy protection. Therefore, the loss function of the individual fairness discriminator is as follows: in This represents the discriminator, which is the component used to obtain sensitive user information. This represents the user's sensitive information, which has many categories. It is the user Embedded representation, This represents the loss function of the discriminator, which, unlike traditional adversarial games, also incorporates external information. To achieve better performance. The loss function for each fairness level is shown in the following equation: In the above formula In the function, since the discriminator needs to take into account the generation of the recommender, therefore... use , Initialization: Here, r and d represent the parameters of the recommender and discriminator, respectively, and c represents the user's sensitive information category. This represents the probability that the sensitive information of user u is predicted by the discriminator to be of class c; when When the value is 1, it means that this is a real class; S42: The input to the group fairness discriminator is the output of the recommender, and the output is sensitive information about the group. The goal is to maximize the difference between the two to achieve similar recommendation results. Therefore, the loss function of the group fairness discriminator is as follows: in For discriminator, This is external information; the project embeddings are considered as supplementary information in this paper. Project data often contains sensitive information. Multi-task learning is performed using representation-level and prediction-level adversarial learning, as shown in the following formula: Among them, hyperparameters and Primarily used to balance these two types of losses, while This will be combined with the recommendation loss function. Co-training uses two hyperparameters to more flexibly control the loss function.

2. The fair recommendation method based on meta-learning and feature enhancement according to claim 1, characterized in that, The specific steps of S1 are as follows: S11: Divide the dataset into a support set and a query set to meet the needs of small sample testing; S12: Initialize the user embedding representation and the item embedding representation. First, initialize the item embedding representation, which can be derived from the item's attribute vector. This indicates that, because projects often have multiple different attributes, therefore , To indicate the project number One attribute, This represents the number of attributes included in the project, and uses an attention mechanism to obtain the preference weights for different attributes. Attention network The following formula can be used for calculation: in, and All are learnable parameter matrices. Set user The embedding is represented as ,in The first time a user has interacted Individual project feature information, The project information, which incorporates an attention mechanism, represents the total number of items a user has interacted with. Calculated using the following formula: 。 3. The fair recommendation method based on meta-learning and feature enhancement according to claim 1, characterized in that, The specific steps of S2 are as follows: S21: Construct user interaction code, model it using a Gaussian mixture model, and generate the corresponding user interaction code. The Gaussian mixture model is... The weighted set of component Gaussian densities is as follows: In the formula, This indicates the number of simple Gaussian distributions. Formal parameters, The feature vector of the project attributes. The mixed weights represent the probability of being selected from a Gaussian distribution. The component Gaussian density is a bivariate Gaussian function, in the form of: in The average eigenvector, For covariance, use the average eigenvector, covariance matrix, and mixing weights of each mixture component. Parameterizing the Gaussian mixture model Used to represent these parameters, For a specific user Given a set of users' historical interaction item attribute information, The number of all items the user has interacted with. The embedding is represented as ,Right now The likelihood of GMM is given by the following formula: The expectation-maximization algorithm is used to estimate the parameters for the user. After constructing the GMM, the preference information for a given project , Provided user For the project Preferences; S22: Construct project-related coding; the relationships between projects are illustrated using a graph. Modeling is performed, in which It represents each project, and These are weighted edges, representing the similarity between two items with the same attributes, expressed using an adjacency matrix. express ,in ; Graph Convolutional Networks (GCNs) are defined on adjacency graphs. They allow the extraction and aggregation of neighborhood information for each vertex. Graph convolution is defined as: ,in It is an identity matrix. The purpose of including an identity matrix is ​​to capture the project's own attribute characteristics. A matrix is The degree matrix, It is the first in GCN The weight matrix of the layer, at the same time It is the first The output of the layer, Specifically , In the formula The initial vertex feature matrix, This is the final output of GCN, where Indicates the number of layers in the GCN; S23: After modeling the user interaction code and project-related code, perform joint output and use MLP to fuse the outputs of these two modules, as shown in the following formula: in This represents the output of the fusion feature enhancement layer, which consists of two connected modules. The function is intended for use in connecting two modules.

4. The fair recommendation method based on meta-learning and feature enhancement according to claim 1, characterized in that, The specific steps of S3 are as follows: S31: In order to capture user preference information, the input of the prediction layer includes the output of the fusion feature enhancement module and the item embedding representation. These two embedding representations are concatenated and fed into a fully connected layer for the final calculation of user preferences for items. Where Fi represents user u i Enhanced fusion features indicate that For the embedded representation of project i, This represents a recommendation model; In the entire recommendation model, the mean absolute error (MAE) is used as the loss function. The mean absolute error loss is calculated as the average of the sum of the absolute differences between the actual and predicted values. Therefore, the overall loss of the recommendation model is shown in the following formula: In the above formula, Represents the Initialized recommendation model ,exist In this context, r represents the recommender, and m represents the total number of items. This represents the user's predicted rating of the item, while That is the actual rating information.

5. The fair recommendation method based on meta-learning and feature enhancement according to claim 1, characterized in that, The specific steps of S5 are as follows: S51: The meta-learning MAML algorithm is used for parameter training and updating. The MAML algorithm mainly optimizes the parameters of the entire recommendation model and the discriminant model. The model parameters consist of two parts. These represent the parameters of the recommender and the discriminator, respectively. The specific adjustments to the MAML model are as follows: For local updates, the focus is on optimizing the parameters of the discriminator, as shown in the following formula: In the above formula, This represents the personalized model parameters of the discriminator, fine-tuned for each user, where d represents the discriminator. These are learnable hyperparameters, the learning rate used to update local parameters, and L is the prediction loss of the entire model on the support set. Finally, the overall loss is updated using the following formula: In the above formula, This represents the personalized model parameters of the recommender, which are fine-tuned for each user. 'r' represents the recommender. This represents the prediction loss of the recommendation model on the support set; For global updates, both the parameters of the discriminator and the recommender are considered, therefore the formula needs to include two parts, as shown in the following equation: In the above formula, represents the learning rate, which can learn continuously through training; L represents the loss function of the entire MFCN model. S52: The loss function of MFCN consists of two parts: the loss of the recommender and the loss of the discriminator. Therefore, the overall loss function is as follows: In the above formula, This represents the loss function of the recommendation model. This represents the loss function of the discriminator model, and the overall loss L of the model is the integration of these two modules.

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