Distributed robust graph recommendation method and device for recommendation system

Abstract

The invention discloses a distributed robust graph recommendation method and device for a recommendation system. The graph recommendation method comprises the steps that a user-article interaction graph is constructed, and node embedding and graph embedding are initialized; applying disturbance to the initial neighborhood distribution through a graph edge adding strategy to generate neighborhood distribution after disturbance; constructing a distribution robust optimization objective function based on Renyi divergence, and calculating worst distribution in the uncertainty set; performing graph neural network aggregation operation by using the ratio of the worst distribution to the disturbance distribution to generate final node embedding; and based on the final node embedding, calculating a recommendation loss function and updating model parameters. According to the method, distribution robust optimization is introduced into aggregation operation of a graph neural network through a graph regularization perspective, so that the problem of vulnerability of an existing graph-based recommendation system in the face of distribution drift is solved, a graph edge adding strategy is provided for the problem of data sparsity of the recommendation system, and a graph edge is obtained by adding slight disturbance to graph initial distribution. And the potential distribution range is expanded.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of recommendation system, in particular to a distribution robust graph recommendation method and device for recommendation system. BACKGROUND

[0002] The success of machine learning models often relies on the independent and identically distributed (IID) assumption, which states that the test data and the observed training data come from the same distribution. However, this assumption often fails in real-world scenarios, leading to performance degradation. Distribution Robust Optimization (DRO) has been proven to effectively alleviate this problem. The core idea of DRO is to extend the model optimization beyond the observed training distribution, but to consider a broader family of potential distributions that include perturbations. Specifically, the goal of DRO is to minimize the worst-case expected loss over a set of potential distributions Q. This means that DRO not only focuses on the performance under the training data distribution, but also tries to ensure that the model maintains good performance under a variety of possible distributions. In this way, DRO can improve the robustness of the model, ensuring that it can still work effectively when faced with distribution changes, thereby enhancing the reliability and stability of the model in real-world applications.

[0003] GNN-based recommendation systems: In recent years, Graph Neural Networks (GNNs) have attracted widespread attention in the field of recommendation systems (RS). GNN-based recommendation methods generally follow the following typical process: Constructing graph: Construct a graph structure based on the historical interactions of users in the training data.

[0004] Using multi-layer GNN: Apply a multi-layer GNN on the constructed graph to extract embedding representations of users and items.

[0005] Generating recommendations: Generate recommendation results based on the similarity between embeddings.

[0006] Since GNNs can capture high-order collaborative signals, GNN-based methods have achieved state-of-the-art performance in collaborative recommendation tasks. These methods can more effectively capture user preferences by modeling the complex relationships between users and items, thereby providing more accurate recommendations. As a representative GNN-based recommendation method, LightGCN learns user / item representations by following the general message passing mechanism of GNNs. However, it removes feature transformations and nonlinear activations because these operations tend to increase the risk of overfitting without necessarily improving performance.

[0007] Existing methods for OOD problems in GNN-based recommendation (the problem of inconsistency between the data distribution encountered by the recommendation system in the test phase and the training phase): InvCF: This method effectively alleviates the impact of popular item distribution changes by introducing an auxiliary classifier. This classifier generates recommendations based on the popularity of items.

[0008] InvPref and HIRL: These two methods automatically identify elements that remain invariant in different environments by dividing the dataset into multiple environments and assigning an environment variable to each interaction.

[0009] Causal Learning: COR: Utilizes causal graph modeling and counterfactual reasoning to handle the impact of OOD interactions.

[0010] CausPref: Uses a differentiable causal graph learning method to obtain invariant user preferences.

[0011] Noise Interaction Handling: Some research attempts to handle noisy interactions in recommendations, which is also considered a general OOD problem.

[0012] BOD: Applies a double-layer optimization to determine the weight of each interaction to offset the impact of noisy interactions.

[0013] Application of DRO in Recommendation Systems: S-DRO: Utilizes DRO to enhance the fairness of user experience.

[0014] RobFair: Also uses the DRO method to improve the fairness of recommendations.

[0015] DROS: Addresses the issue of changing data distribution over time in sequence recommendations using DRO.

[0016] BSL: Combines DRO to solve Softmax loss, thereby enhancing the robustness of the model to noisy positive samples.

[0017] Although these methods address the OOD problem to some extent, they are not specifically designed for GNN-based recommendation systems, and therefore do not effectively address the impact of distribution changes on the structure of the graph model itself. This means that: Vulnerability of graph structure: Distribution changes can lead to changes in the graph structure, affecting the effectiveness of information transmission and aggregation.

[0018] Lack of specificity: Existing methods are generally applicable, not specifically tailored to the needs of GNN models, and are not customized for graph neural network (GNN) based methods. Therefore, distribution drift is still deeply rooted in the constructed graph, causing the learned embeddings and recommendation results to be distorted.

[0019] DRO Research in GNN These studies explore the application of DRO in GNNs, but have the following limitations: Noise handling: These methods mainly focus on the distribution changes caused by noise in node embeddings, rather than the distribution changes in the topology of the graph that we are interested in.

[0020] Unique challenges of recommendation systems: Existing DRO methods do not consider the unique characteristics of recommendation datasets, so they may face challenges when applied to recommendation systems. SUMMARY

[0021] A distribution-robust graph recommendation method, device, electronic equipment and storage medium for a recommendation system are provided in the present embodiment to solve the above technical problems.

[0022] In a first aspect, the present embodiment provides a distribution-robust graph recommendation method for a recommendation system, which comprises: Constructing a user-item interaction graph, initializing node embeddings and graph embeddings; Applying perturbation to the initial neighborhood distribution through a graph edge addition strategy to generate a perturbed neighborhood distribution wherein, is the initial neighborhood distribution of node is the addition distribution determined from the candidate node set by minimizing the similarity function, is the perturbation coefficient; Based on the Renyi divergence, a distribution-robust optimization objective function is constructed, and the worst distribution in the uncertainty set is calculated; The ratio of the worst distribution to the perturbed distribution is used for graph neural network aggregation operation to generate the final node embedding; Based on the final node embedding, the recommendation loss function is calculated and the model parameters are updated.

[0023] Optionally, the similarity function is minimized as follows: ; wherein, is the embedding of node is the degree of node is the model parameter, is the embedding of node is the degree of node

[0024] Optionally, the execution of the graph edge addition strategy comprises: Randomly sampling a candidate node subset for each node ​​​​​​Selecting nodes in a candidate subset such that minimizing; constructing a distribution based on the selected nodes and fused with the initial distribution weighted.

[0025] Optionally, the worst distribution in the uncertainty set is calculated The formula is as follows: ; ; wherein, is the coefficient used to fit the neighborhood of the worst distribution, denotes the neighborhood distribution, is a hyperparameter, is the introduced Lagrange multiplier.

[0026] Optionally, the setting of the Renyi divergence parameter γ satisfies: Under the independent and identically distributed setting, γ∈{1.05, 1.06, …, 1.35}; Under the distribution offset setting, γ∈{1.5, 2.0, …, 7.0}.

[0027] Optionally, the perturbation coefficient The value range is {0.1, 0.2, 0.3, 0.4, 0.5}.

[0028] Optionally, the graph neural network aggregation operation adopts a multi-layer propagation structure: ; ; wherein, , is an adjacency matrix, is a degree matrix, is the ratio of the worst distribution and the neighborhood distribution is the embedding calculated out in the first layer.

[0029] Compared with the prior art, the beneficial effects of the distribution robust graph recommendation method for a recommendation system of the present application are as follows: ​This invention introduces Distributed Robust Optimization (DRO) into the aggregation operation of Graph Neural Networks (GNNs) from the perspective of graph regularization, providing an innovative method for recommender systems. This method can better address the problem of data distribution drift, enhance the robustness of graph models, alleviate the vulnerability of existing graph-based recommender systems to distribution changes, provide a new perspective for enhancing the robustness of graph-based recommender systems, and open up new directions for future research and applications.

[0030] This invention addresses the problem of data sparsity in recommender systems by proposing a graph edge addition strategy. By adding a slight perturbation to the initial distribution of the graph, the potential distribution range of the DRO is expanded. This allows for the use of initial non-neighbor nodes to train better robust embeddings, alleviating the inherent defects of DRO in sparse recommender datasets, expanding the range of the potential distribution, and utilizing the rich information of non-neighbor nodes.

[0031] This invention employs Rényi divergence constraints within the DRO framework. Since Rényi divergence can be viewed as a generalization of KL divergence and worst-case regret divergence, it fully combines the advantageous structures of both, improving the recommendation performance of the model. It effectively inherits and enhances the advantageous characteristics of Softmax Loss and Cosine Contrastive Loss, while mitigating their shortcomings of sensitivity to false negatives and low data utilization.

[0032] Although this invention involves a complex optimization process, its implementation is relatively simple and efficient. This makes it highly operable in practical applications and can effectively improve the performance and robustness of recommendation systems.

[0033] Secondly, embodiments of the present invention provide a split-bar graph recommendation device for a recommendation system, comprising: The graph construction module builds a user-item interaction graph and initializes node embedding and graph embedding. The perturbation module applies a perturbation to the initial neighborhood distribution using a graph edge addition strategy, generating a perturbed neighborhood distribution. ,in, For nodes The initial neighborhood distribution, The distribution of additions determined from the candidate node set by minimizing the similarity function. The disturbance coefficient; The distribution calculation module constructs a sub-Bruker optimization objective function based on Renyi divergence to calculate the worst distribution in an uncertain set. The generation module uses the ratio of the worst distribution to the perturbation distribution to perform graph neural network aggregation operations to generate the final node embeddings; The update module calculates the recommendation loss function based on the final node embedding and updates the model parameters.

[0034] In a third aspect, an electronic device is provided, comprising a processor, a communication interface, a memory and a bus, wherein the processor, the communication interface and the memory communicate with each other through the bus, and the processor can invoke a logical instruction in the memory to execute steps of the method provided in the first aspect.

[0035] In a fourth aspect, a non-transitory computer-readable storage medium is provided, which stores a computer program, and the computer program is executed by a processor to implement steps of the distributed robust graph recommendation method for a recommendation system according to the first aspect.

[0036] Compared with the prior art, the distributed robust graph recommendation device for a recommendation system, the electronic device and the storage medium have the same beneficial effects as the distributed robust graph recommendation method for a recommendation system according to the first aspect, and thus will not be described here. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort based on these drawings.

[0038] Figure 1 The flow chart of the distributed robust graph recommendation method for a recommendation system in the embodiments of the present application; Figure 2 The structural block diagram of the distributed robust graph recommendation device for a recommendation system in the embodiments of the present application; Figure 3 The structural block diagram of the electronic device in the embodiments of the present application. DETAILED DESCRIPTION

[0039] In order to more clearly understand the purposes, technical solutions and advantages of the present application, the present application will be described and illustrated in the following with reference to the drawings and embodiments.

[0040] Unless otherwise defined, technical terms and scientific terms used in the present application shall have the same meaning as those commonly understood by a person of ordinary skill in the art to which the present application belongs. The terms "one", "a", "an", "the", "these", and similar terms in the present application do not mean "only one" or "exactly one", but can mean "one or more". The terms "include", "contain", "have", and any variant thereof in the present application are intended to cover the non-exclusive inclusion; for example, a process, method, and system, product or device containing a series of steps or modules (units) are not limited to the listed steps or modules (units), but can include steps or modules (units) not listed, or can include other steps or modules (units) inherent to the process, method, product or device. The terms "connect", "connected", "coupled" and the like in the present application are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The term "multiple" in the present application means two or more. The term "and / or" describes the association relationship of the associated objects, which means that there can be three relationships, for example, "A and / or B" can mean that A exists alone, A and B exist together, and B exists alone. Generally, the character " / " means that the objects before and after are "or" relationship. The terms "first", "second", "third" and the like in the present application are only used to distinguish similar objects, and do not represent a specific order of the objects.

[0041] A distributed robust graph recommendation method for a recommendation system is provided in the embodiments of the present application, Figure 1 The flow chart of the distributed robust graph recommendation method for the recommendation system of the present application is shown in Figure 1 The flow chart includes the following steps: S100, constructing a user-item interaction graph, initializing node embedding and graph embedding; In the embodiment, the node embedding and hyperparameters are initialized, and before starting the model training, the node embedding size is set to 32, the propagation layer number is set to 3 layers, the batch size is set to 1024 during training, the learning rate is selected in , and the optimizer uses Adam.

[0042] The parameter of L2 regularization is selected in , the parameter of GEA is selected in , and the hyperparameter of DRO is selected, the learning rate is adjusted in , the SGD optimizer is used, under the IID setting, let , under the OOD setting, let , and additionally set .

[0043] S200, applying disturbance to the initial neighborhood distribution through a graph edge addition strategy to generate a disturbed neighborhood distribution wherein, is the initial neighborhood distribution of node , is an addition distribution determined from a candidate node set by minimizing a similarity function, is a disturbance coefficient; minimizing the similarity function: ; wherein, is the embedding of node , is the degree of node , is a model parameter, is the embedding of node , is the degree of node .

[0044] The execution of the graph edge addition strategy includes: randomly sampling each node to form a candidate node subset; selecting a node in the candidate subset such that is minimized; constructing based on the selected node and weightedly fusing with the initial distribution.

[0045] Specifically, the graph edge addition GEA module: for each node , its initial neighborhood distribution is , a part of the nodes are randomly formed into a candidate set, and the traversal operation is only performed on this subset to find a point such that is minimized, and such a point is found as , , thus obtaining the neighborhood distribution after slight disturbance of the original graph .

[0046] S300, constructing a distribution robust optimization objective function based on Renyi divergence, and calculating the worst distribution in the uncertain set; calculating the worst distribution in the uncertain set The formula is as follows: ; ; wherein, is used to fit the neighborhood a coefficient of the worst distribution, denotes the neighborhood distribution, is a hyperparameter, is the introduced Lagrange multiplier.

[0047] Specifically, in combination with the above, it can be proved that the simple aggregation process of LightGCN is equivalent to optimizing the graph smoothing regular term of the following formula using the gradient descent method: ; ; Here, is the neighborhood node distribution of the point , is the model parameter, and the embedding of the node is denoted by .

[0048] Using the Renyi divergence to make DRO on this optimization target, it can be proved that it is equivalent to optimizing the following formula: ; ; Here, is a hyperparameter, is the introduced Lagrange multiplier.

[0049] Using the above conclusion on the perturbed distribution , the worst distribution in the uncertainty set of DRO under the Renyi divergence for the optimization target of the graph smoothing regular term is obtained: ; It should be noted that, ; is a coefficient used to fit the neighborhood worst distribution. Since is a proportional relationship, and is known to be expected to be 1, according to and the calculated in the previous calculation, the worst distribution in the uncertainty set of DRO under the Renyi divergence is calculated for each .

[0050] S400, using the ratio of the worst distribution to the perturbed distribution to perform a graph neural network aggregation operation to generate a final node embedding; The graph neural network aggregation operation adopts a multi-layer propagation structure: ; ; wherein,​ , It is an adjacency matrix. It is a degree matrix. worst distribution and neighborhood distribution The ratio, To calculate the first Layer embedding.

[0051] Specifically, let the worst distribution and neighborhood distribution The ratio is ,but That is the formula above. The value can also be calculated using the above formula, and at the same time... Calculate the adjacency matrix degree matrix Standardized adjacency matrix .

[0052] The feature propagation process of LightGCN is performed according to... Calculate the first Layer embedding The 0th layer For checkpoint embedding.

[0053] The final embedding is calculated based on the embedding at each layer of the feature propagation process. .

[0054] S500 calculates the recommendation loss function based on the final node embedding and updates the model parameters.

[0055] Specifically, small batches of positive and negative sample pairs are sampled, based on the embedding... Calculate BPRloss and parameters The corresponding loss.

[0056] ; BPRloss is used to update model parameters. The above formula corresponds to the parameter. The loss is used to update each node. corresponding In practice, multiple samplings are performed, the loss is calculated, and the model parameters are adjusted based on the loss gradient. and Alternate updates. The above process is repeated multiple times during training until the model converges or reaches a specified number of steps.

[0057] The inference part is similar to the training part but more simplified. It removes edges from the training process and adds a GEA module, directly using the original graph neighborhood distribution. and not DRO-optimized, i.e., directly neighborhood-based fitting and also feature propagation, predicting the outcome from the final embedding.

[0058] The present application proposes a new GNN-based recommendation method, which introduces distributionally robust optimization (DRO) into the aggregation operation of graph neural networks (GNN) from the perspective of graph regularization, to solve the vulnerability of existing graph-based recommendation systems when facing distribution drift, and proposes a graph edge addition strategy to address the data sparsity problem of recommendation systems, which expands the potential distribution range by adding slight perturbations to the initial distribution of the graph.

[0059] In addition, the present application adopts Rényi divergence constraints within the DRO framework, effectively inheriting and enhancing the advantageous properties of Softmax Loss and Cosine Contrastive Loss, while alleviating their shortcomings.

[0060] The present application introduces distributionally robust optimization (DRO) into the aggregation operation of graph neural networks (GNN) from the perspective of graph regularization, providing an innovative method for recommendation systems that can better address data distribution drift issues, enhance the robustness of graph models, and alleviate the vulnerability of existing graph-based recommendation systems when facing distribution changes, providing a new perspective for enhancing the robustness of graph-based recommendation systems and opening up new directions for future research and application.

[0061] The present application proposes a graph edge addition strategy to address the data sparsity problem of recommendation systems, which expands the potential distribution range of DRO by adding slight perturbations to the initial distribution of the graph, allowing the use of initial non-neighbor nodes to train better robust embeddings, alleviating the inherent shortcomings of DRO in sparse recommendation data sets, expanding the range of potential distributions, and utilizing the rich information of non-neighbor nodes.

[0062] The present application adopts Rényi divergence constraints within the DRO framework, as Rényi divergence can be considered a generalization of KL divergence and worst-case regret divergence, fully combining the advantageous structures of both, improving the recommendation performance of the model, effectively inheriting and enhancing the advantageous properties of Softmax Loss and Cosine Contrastive Loss, while alleviating their sensitivity to false negatives and low data utilization.

[0063] The present application, although involving complex optimization processes, is relatively simple and efficient to implement. This makes it highly operable in practical applications, effectively improving the performance and robustness of recommendation systems.

[0064] The embodiment of the present application also provides a distributed robust graph recommendation device for a recommendation system, which is used to realize the above-mentioned method embodiment, and details are not repeated. The terms "module", "unit", "sub-unit" and the like used below can be a combination of software and / or hardware that realizes a predetermined function. Although the device described in the following embodiment is preferably realized in software, hardware or a combination of software and hardware is also possible and is conceived.

[0065] As shown in Figure 2 , Figure 2 is a structural block diagram of a distributed robust graph recommendation device for a recommendation system in the present application, which comprises: a graph construction module 101, which constructs a user-item interaction graph, initializes node embedding and graph embedding; a perturbation processing module 102, which applies perturbation to an initial neighborhood distribution through a graph edge addition strategy to generate a perturbed neighborhood distribution , wherein, is the initial neighborhood distribution of a node , is an addition distribution determined from a candidate node set by minimizing a similarity function, is a perturbation coefficient; a distribution calculation module 103, which constructs a distribution robust optimization objective function based on Renyi divergence and calculates a worst distribution in an uncertainty set; a generation module 104, which performs graph neural network aggregation operation using a ratio of the worst distribution to the perturbed distribution to generate a final node embedding; an update module 105, which calculates a recommendation loss function based on the final node embedding and updates model parameters.

[0066] Figure 3 As shown in Figure 3 , the structural block diagram of an electronic device provided by the embodiment of the present application, the electronic device can include: a processor 610, a communications interface 620, a memory 630 and a communications bus 640, wherein the processor 610, the communications interface 620, the memory 630 complete mutual communication through the communications bus 640. The processor 610 can call the logic instructions in the memory 630 to execute the following method: constructing a user-item interaction graph, initializing node embedding and graph embedding; applying perturbation to an initial neighborhood distribution through a graph edge addition strategy to generate a perturbed neighborhood distribution , wherein, is the initial neighborhood distribution of a node , To determine the added distribution from the candidate node set by minimizing the similarity function, To perturb the coefficient; Based on the Renyi divergence, a distribution robust optimization objective function is constructed, and the worst distribution in the uncertainty set is calculated; The ratio of the worst distribution and the perturbation distribution is used for graph neural network aggregation operation to generate the final node embedding; Based on the final node embedding, a recommendation loss function is calculated and the model parameters are updated.

[0067] In addition, the logical instructions in the memory 630 described above can be implemented in the form of a software function unit and sold or used as an independent product, which can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts that contribute to the prior art or parts of the technical solutions can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the method described in various embodiments of the present application. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0068] The embodiments of the present application also provide a non-transitory computer readable storage medium having a computer program stored thereon, which is executed by a processor to implement the method provided by each of the above embodiments.

[0069] From the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software and the necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such understanding, the above technical solutions essentially or the parts that contribute to the prior art can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including a plurality of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute the method of each embodiment or some parts of the embodiment.

[0070] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the present application, but not to limit the same; and although the present application has been described in detail with reference to the foregoing embodiments, it should be appreciated by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features thereof can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A distributed robust graph recommendation method for a recommendation system, characterized in that, The distribution robust graph recommendation method for the recommendation system comprises the following steps: A user-item interaction graph is constructed, and node embedding and graph embedding are initialized; The initial neighborhood distribution is disturbed by adding edges to the graph to generate a disturbed neighborhood distribution wherein, is the initial neighborhood distribution of a node is the initial neighborhood distribution of a node is an adding distribution determined from a candidate node set by minimizing a similarity function, is a disturbance coefficient; A distribution robust optimization objective function is constructed based on Renyi divergence, and a worst distribution in an uncertainty set is calculated; A graph neural network aggregation operation is performed using a ratio of the worst distribution to a perturbed distribution to generate final node embedding; A recommendation loss function is calculated based on the final node embedding, and model parameters are updated.

2. The distributed robust method for a recommendation system according to claim 1, wherein, A similarity function is minimized: ； wherein is the embedding of node , is the degree of node , is the model parameter, is the embedding of node , is the degree of node .

3. The method for recommending system of claim 2, wherein, The execution of the graph edge addition strategy comprises the following steps: For each node Randomly sampling forms a candidate node subset; Selecting nodes in a candidate subset Causing Minimizing; Based on the selected nodes to construct And the initial distribution weighted fusion.

4. The method of claim 1, wherein, Computing a worst distribution in an uncertain set The formula is as follows: ； ； where, is the coefficient of the worst distribution, is the coefficient of the worst distribution, represents the neighborhood distribution, is the hyperparameter, is the introduced Lagrange multiplier.

5. The method for recommending system of claim 4, wherein, The setting of the Renyi divergence parameter γ satisfies: In an independent and identically distributed setting, γ∈{1.5, 2.0, …, 7.0}. 1.05，1.06，…，1.35}； In a distribution shift setting, γ∈{1.5, 2.0, …, 7.0}.

6. The method for recommending system of claim 1, wherein, The perturbation coefficient The value range of the perturbation coefficient is {0.1, 0.2, 0.3, 0.4, 0.5}.

7. The method for recommending system of claim 1, wherein, The graph neural network aggregation operation adopts a multi-layer propagation structure: ； ； wherein, , is an adjacency matrix, is a degree matrix, is the worst distribution and neighborhood distribution ratio, is to compute the embedding of the layer.

8. A distributed robust graph recommendation apparatus for a recommendation system, characterized in that, It comprises the following steps: A graph construction module constructs a user-item interaction graph, initializes node embedding and graph embedding; The disturbance processing module generates a disturbed neighborhood distribution by applying disturbance to the initial neighborhood distribution through an edge adding strategy wherein, is the initial neighborhood distribution of the node is the initial neighborhood distribution of the node is an adding distribution determined from the candidate node set by minimizing a similarity function, is a disturbance coefficient; A distribution calculation module constructs a distribution robust optimization objective function based on Renyi divergence, and calculates a worst distribution in an uncertainty set; A generation module performs a graph neural network aggregation operation using a ratio of the worst distribution to a perturbed distribution to generate final node embedding; An update module calculates a recommendation loss function based on the final node embedding, and updates model parameters.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the distribution robust graph recommendation method for the recommendation system according to any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by the processor to implement the steps of the distribution robust graph recommendation method for the recommendation system according to any one of claims 1 to 7.

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