Hard negative sampling contrast recommendation method based on graph generation diffusion model

Abstract

The application provides a hard negative sampling contrast recommendation method based on a graph generation diffusion model, including the following steps: encoding a user-item interaction graph through a graph convolutional neural network to obtain a node embedding vector, and then performing inner product on the node embedding vector to obtain a recommendation probability; model parameters of the graph convolutional neural network are obtained through the following training: S1, respectively generating contrast view 1 and contrast view 2 through an inner diffusion model view generator and a parameter topological denoising view generator; the inner diffusion model view generator comprises an inner diffusion model, and the parameter topological denoising view generator comprises a parameter topological denoising network; S2, performing contrast learning on the contrast view 1 and the contrast view 2. The application combines a signal alignment strategy to build a double-view generator contrast learning framework, aiming to improve the problems of insufficient model generation capacity and great data noise influence, so as to improve the performance of a recommendation system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of personalized recommendation, and particularly relates to a hard negative sampling contrast recommendation method based on a graph generated diffusion model. BACKGROUND

[0002] Existing recommendation systems are mainly based on user-item historical interaction graphs, and graph neural networks (GNN) are used to embed these data representations and optimize them to improve recommendation performance. With the popularity of online services, recommendation systems have become a key tool to solve the problem of information overload. By analyzing user behavior and needs, these systems can provide personalized product and content recommendations to users. From collaborative filtering to graph neural networks, the research of recommendation systems has made continuous progress. For example, PinSage, GCMC, NGCF, LightGCN and other models have shown excellent personalized recommendation results by capturing local and global information of user-item interaction graphs. In addition, in order to reduce the dependence on data labels, self-supervised learning is introduced into the recommendation system, such as SGL, SLRec and other models, which use the structure and patterns of data itself to create supervision signals, thereby improving the accuracy and relevance of the recommendation system.

[0003] Although existing technologies have made significant achievements in recommendation systems, there are still some challenges. First, the representation ability of the recommendation method is limited, and it is difficult to fully capture the complex relationship between users and items, which limits the performance of the recommendation system. Second, the problem of data noise is one of the key problems that need to be solved in the recommendation system. Due to the randomness of user interaction behavior and the limitations of data collection, there is a large amount of noisy data in the recommendation system, which may lead to inaccurate recommendation results. At the same time, the recommendation system in real scenarios is plagued by data sparsity, and this representation mechanism based on user-item historical interaction graphs cannot ensure the use of high-quality data to accurately predict user data. In addition, the dependence of the recommendation system on high-quality data is also a limitation. In real scenarios, high-quality data is often difficult to obtain, which further limits the effectiveness of the recommendation system in practical applications. Finally, the problem of model collapse in the training process is also a technical problem that needs to be solved in the field of recommendation systems. In particular, in self-supervised learning, how to determine an effective contrast view generation strategy to reduce the trial and error cost and how to avoid model collapse in the training process are important problems in the research of recommendation systems. In addition, single view generator in self-supervised contrast learning is also prone to model collapse risk, which further increases the complexity of technical challenges. SUMMARY

[0004] This invention aims to address at least the technical problems existing in the application of recommendation systems in real-world scenarios, such as poor user-item interaction graph representation due to data sparsity and noise, and the instability and limited generation capabilities of most models. In particular, it innovatively proposes a hard negative sampling comparative recommendation method based on a graph generation diffusion model.

[0005] To achieve the above-mentioned objectives of this invention, this invention provides a hard negative sampling comparison recommendation method based on a graph generation diffusion model, comprising the following steps:

[0006] A user-item interaction graph is constructed, where users and items are nodes, and their interactions (such as purchasing and rating) are edges. Then, the user-item interaction graph is encoded using a graph convolutional neural network to obtain user and item node embedding vectors. The inner product of the user and item node embedding vectors is then performed to obtain the recommendation probability. Finally, the top N items with the highest recommendation probability are recommended to the user.

[0007] The model parameters of the graph convolutional neural network are obtained through the following training:

[0008] S1, the node embedding vectors are used to generate comparison views through an inline diffusion model view generator and a parametric topology denoising view generator, respectively. Figure 1 and contrast Figure 2 The inline diffusion model view generator includes an inline diffusion model, and the parametric topology denoising view generator includes a parametric topology denoising network. By introducing the inline diffusion model (L-Diffusion) and the parametric topology denoising network (PTDNet) as view generators, the limited representation capability and data noise problems of recommendation methods can be improved.

[0009] S2 will compare the view Figure 1 and contrast Figure 2 Contrastive learning can alleviate the limitations of relying on high-quality data in recommendation systems, and the fact that the two contrastive views in contrastive learning come from different view generators can solve the problem of model crashes during training.

[0010] Preferably, the user-item interaction graph is encoded using a graph convolutional neural network to obtain node embedding vectors, including: improving the feature representations of user and item nodes by integrating multiple representation embedding propagation layers.

[0011] will u i and v j The representation embedding vectors obtained by traversing the graph neural network at layer l are defined as follows: and The target node information is propagated from the l-1 layer to the l layer, in order to obtain a high-quality node embedding representation, the node embedding of each propagation layer is summed, and the inner product between the final embedding representation of the user and the item is used to predict the preference degree of the user to the item in personalized recommendation, and the specific process of calculating the node embedding vector is as shown in formula (5):

[0012]

[0013] Wherein, And Respectively, u i And v j The representation embedding vector obtained by traversing the graph neural network at the l layer;

[0014] Indicates the preference score of the user to the item;

[0015] Respectively, the representation embedding vector obtained by traversing the graph neural network at the l layer and the representation embedding vector obtained by traversing the graph neural network at the l layer, which is the aggregation information of the user and the sampled anchor adjacent target node; and the aggregation information of the item and the sampled anchor adjacent target node;

[0016] Respectively, u i And v j The representation embedding vector obtained by traversing the graph neural network at the l-1 layer;

[0017] Respectively, the final node embedding vector of the user and the final node embedding vector of the item;

[0018] Respectively, u i And v j The representation embedding vector obtained by traversing the graph neural network at the l layer;

[0019] And Respectively, the information representation embedding vector of each user u i And the item v j ;

[0020] L represents the number of layers of the graph neural network;

[0021] The inner product of the user and item node embedding vectors is obtained, and the recommendation probability is represented as:

[0022]

[0023] Wherein, The transpose of .

[0024] Preferably, The calculation formula of is as follows:

[0025]

[0026] Wherein, E (u) , E (v) are the matrix embedding representations of users and items respectively;

[0027] , and respectively represent the aggregated information representations of users and items and the sampled anchor adjacent target nodes;

[0028] , and respectively represent the i-th row of the normalized adjacency matrix , and the j-th column of the normalized adjacency matrix ;

[0029] is the normalized adjacency matrix representation calculated by the adjacency matrix A of the user-item interaction graph, The calculation derivation of is as formula (4):

[0030]

[0031] Wherein, and respectively represent the diagonal matrix about users and items;

[0032] represents the element of the i-th row and the j-th column of the normalized adjacency matrix ;

[0033] A i,j represents the element of the i-th row and the j-th column of the adjacency matrix A of the user-item interaction graph;

[0034] L i , and L j are the sets of all neighbor nodes of users and items respectively; || is the absolute value symbol. The normalized matrix can better reflect the interaction signals between users and items, and can better transmit and iterate the aggregated information of the embedding layer.

[0035] Preferably, the in-line diffusion model view generator generates a contrast view for contrast learning. Figure 1 The method comprises the following steps:

[0036] S2-1, input the embedding representation vector e l of the user-item interaction into the VGAE encoder, and the process is as formula (6):

[0037]

[0038] where q φ (x|e) represents the probability distribution obtained by graph variational encoding;

[0039] N represents a Gaussian distribution;

[0040] x represents the embedded representation vector e l by the parameterized graph variational encoder;

[0041] μ φ (e) represents the Gaussian distribution mean inferred by the parameter set of the neural network;

[0042] σ φ (e) represents the Gaussian distribution variance inferred by the parameter set of the neural network;

[0043] e is obtained by formula (5), which is or

[0044] μ represents the mean of the Gaussian distribution, and the most likely position of the input data in the embedded vector space, σ represents the variance of the Gaussian distribution, and the variance between each dimension is independent, reflecting the dispersion around the mean data, and φ is the parameter set of the VGAE encoder,

[0045] S2-2, the VGAE encoder outputs a low-dimensional mapping x and inputs it into the inline diffusion model;

[0046] S2-2-1, forward process: in the forward propagation process, the inline diffusion model iteratively applies K times of adding noise steps, where K is a hyperparameter, and the embedded vector in the kth time of adding noise is represented as x k Each time the data is calculated by the iterative process as formula (7):

[0047]

[0048] where q(x k |x k-1 ) represents the probability distribution of the forward process;

[0049] N represents a Gaussian distribution;

[0050] x k is the embedded vector in the kth time of adding noise;

[0051] β k ∈(0,1) represents the size of the input noise;

[0052] S2-2-2, backward process: in the backward propagation process, the propagation target is to obtain the embedded representation x zRecover from noise in implicit vector space, reconstruct the original data, where k = 1, 2,..., K, specifically, the back propagation process is predicted by using a trainable deep neural network, and the propagation calculation process is as formula (8):

[0053] p(x k-1 |x k )=N(x k-1 ;W1(x k ,k),W2(x k ,k)) (8)

[0054] Where p(x k-1 |x k ) represents the reverse process probability distribution;

[0055] N represents a Gaussian distribution;

[0056] x k-1 is the noise representation of the embedded vector added at the k-1 time;

[0057] W1 and W2 represent the Gaussian parameters of the trainable neural network used to predict the Gaussian distribution;

[0058] S2-3, the low-dimensional embedded vector reconstructed by the forward and backward propagation processes of the inline diffusion model, is input into another MLP as a decoder, and the mean and standard deviation of the Gaussian distribution parsed in the encoding process are also input (i.e. formula 6 μ φ (e), ), to generate a new view.

[0059] On the basis of the diffusion model (Diffusion model), the widely used VGAE is introduced, which reduces the scale of adding noise in data noise, thereby avoiding the complete noise of user item interaction information while preserving the semantic relationship between nodes, thereby improving the problem of loss of user personalized information.

[0060] Preferably, the parameter topology denoising view generator generates a contrast view Figure 2 for contrast learning, and the parameter topology denoising view generator is represented as:

[0061] A l =A⊙Z l (10)

[0062] Where A l represents the subgraph adjacency matrix after transformation by the binary matrix Z l after l-layer graph neural network;

[0063] A represents the subgraph adjacency matrix;

[0064] Z ldenotes a binary matrix used to generate the subgraph after the l-th layer GNN processing;

[0065] denotes element-wise product, thus A l only contains Z l edges marked as 1.

[0066] Preferably, Z l is obtained by:

[0067] The sparsity neural network l0 regularization method is used to obtain A l To reduce the noisy edges, the number of non-zero edges in different GNN layers is directly penalized, as shown in equation (11):

[0068]

[0069] wherein, is an indicator function, and

[0070] l = 1 indicates that the calculation starts from the first layer;

[0071] (u, v) ∈ ε represents the set of user-item interaction edges of the input subgraph;

[0072] L represents the number of layers of the graph neural network;

[0073] ||·||0 represents the l0 norm;

[0074] Then, the graph attention mechanism (GAT) is selected as the denoising layer to learn parameters that can control whether to delete edges Taking a node u in the training subgraph as the center node, the neighbor nodes of the node u represent N u , the node u and its neighbor nodes v ∈ N u are traversed in the l-th layer of GNN, and as shown in equation (12):

[0075]

[0076] wherein, represents the quality score of the edge between the node u and the node v calculated by the l-layer graph neural network;

[0077] is an MLP model parameterized by θ l ; and

[0078] respectively represent the feature vector of the user node and the feature vector of the item node obtained by the l-layer graph neural network;

[0079] θl is a trainable parameter, containing the weight matrix and bias vector of each layer of the MLP;

[0080] by a binary Concrete distribution on the local parameters to obtain a The parameterized computation process is as shown in formula (13):

[0081] ∈ ~ Uniform(0, 1),

[0082] Wherein, ∈ ~ Uniform(0, 1) represents random sampling from a binary Concrete distribution;

[0083] ∈ represents a sample randomly drawn from a Concrete distribution;

[0084] Uniform(0, 1) represents a Concrete distribution;

[0085] represents the preliminary calculation result of the retention probability of the edge between node u and node v; the probability value tends to 0 or 1;

[0086] represents the quality score of the edge between node u and node v under a specific task;

[0087] τ ∈ R + represents a temperature coefficient;

[0088] σ(·) represents a sigmoid activation function;

[0089] The Hard Sigmoid function is used again to convert into a binary mask The conversion process is as shown in formula (14):

[0090]

[0091] Wherein, max() represents taking the maximum value;

[0092] min() represents taking the minimum value.

[0093] Preferably, the loss function of contrastive learning is represented as:

[0094]

[0095] Wherein, represents the contrastive loss function of the user;

[0096] represents the contrastive loss function of the item;

[0097] The calculation formula of is the same as that of The calculation formula of is:

[0098]

[0099] wherein, represents a target loss function;

[0100] u i and u i′ respectively represent a user in a user set and a negative sample user in the user set;

[0101] U represents a user node set;

[0102] represents a cosine similarity of a positive sample pair;

[0103] represents a cosine similarity of a negative sample pair;

[0104] The hyperparameter τ represents a temperature coefficient in softmax.

[0105] Preferably, the contrastive supervision loss optimized by the hard negative sample sampling is used to train the model:

[0106] First, the probability distribution of the hard negative sample pair (s, s - ) is calculated, so as to obtain e i :

[0107]

[0108] wherein, q(s, s - ) represents the probability distribution of the hard negative sample pair (s, s - );

[0109] represents an expected value of selecting a category c according to the category distribution ρ;

[0110] D c (s - |H(s, e i , τ)) represents the probability distribution of the negative sample in the category c, which is calculated by the given sample s, e i , and the temperature coefficient under the hard sampling strategy;

[0111] s - represents a negative sample;

[0112] e i represents an embedding representation of the corresponding sample;

[0113] τ represents a similarity threshold value;

[0114] H(s, e i , τ) represents the set of hard negative samples;

[0115] Then, the feature space similarity is calculated according to the embedding representation e i

[0116]

[0117] where h(s, s + ) represents the feature space similarity of positive samples;

[0118] e Τ is the transpose of e i

[0119] e is the embedding representation of all samples;

[0120] e + is the feature embedding representation of all positive samples;

[0121] represents the feature space similarity of a single negative sample;

[0122] e i is the transpose of e -

[0123] represents the feature embedding representation of a single negative sample;

[0124] Y represents the temperature coefficient, when the similarity is greater than the threshold value, i.e., h(s, s - ) > τ, and the two samples do not belong to the same probability distribution, the two samples are defined as hard negative samples;

[0125] Finally, the contrastive loss function based on hard negative samples is obtained:

[0126]

[0127] where, represents the contrastive loss function of hard negative samples;

[0128] represents the mathematical expectation of positive sample pairs and the mathematical expectation of negative sample pairs according to the distribution p;

[0129] k represents the number of negative samples;

[0130] represents the similarity between the sample and the negative sample;

[0131] represents the similarity between the sample and the positive sample.

[0132] ​Hard negative samples refer to those items that are very similar to positive samples but are actually negative samples. By designing hard negative samples, users can be better personalized, and the generalization ability of the model can be improved; by distinguishing hard negative samples, noise data remaining in the original data can be better dealt with, thereby improving the robustness of the recommendation system.

[0133] Preferably, in the contrast learning, in order to make the two generated contrast views Figure 1 and the contrast views Figure 2 In the training process, they can be aligned with each other and adapted to the CF task, and a BPR loss function is introduced to constrain the consistency of the two views:

[0134] For the inline diffusion model view generator, the BPR is calculated by using the embedding representation of the user-item interaction encoded by the VGAE encoder therein as shown in equation (22):

[0135]

[0136] wherein, represents the total loss function of the inline diffusion model view generator;

[0137] represents the KL divergence loss value;

[0138] represents the distribution loss value, which ensures that the node embedding distribution of the generated graph is similar to the node embedding distribution of the original graph;

[0139] represents the BPR loss function of the inline diffusion model view generator part;

[0140] For the parameter topology denoising view generator, the BPR is calculated by using the node embedding representation obtained thereby, and the loss function reconstruction is as shown in equation (23):

[0141]

[0142] wherein, represents the total loss function of the parameter topology denoising view generator;

[0143] represents the L0 regularization loss function;

[0144] represents the BPR (Bayesian personalized ranking) loss function of the parameter topology denoising view generator part;

[0145] The total loss function of the model is:

[0146]

[0147] wherein, a total loss function representing the inline diffusion model view generator;

[0148] a total loss function representing the parameter topology denoising view generator;

[0149] a hard negative sampling loss function;

[0150] a BPR loss function;

[0151] λ1 represents a hyperparameter for controlling the strength of the self-supervised signal;

[0152] a self-supervised loss function;

[0153] a regularization term;

[0154] λ2 is a hyperparameter for controlling the regularization strength.

[0155] Preferably, calculated by the following formula:

[0156]

[0157] where O represents all training data;

[0158] u, i, j represent a user, an item i, and an item j, respectively, i≠j;

[0159] the difference between the calculated positive and negative sample prediction scores is mapped to between 0 and 1 by a Sigmoid function, and then the negative logarithm is taken to obtain the final loss value;

[0160] σ represents a Sigmoid function;

[0161] respectively represent the prediction scores of the user for the positive sample item and the negative sample item.

[0162] In summary, due to the adoption of the above technical solutions, the present application combines a signal alignment strategy to build a dual-view generator contrast learning framework, aiming to improve the problems of insufficient model generation capability and large data noise influence, thereby improving the performance of the recommendation system.

[0163] Specific beneficial effects are:

[0164] (1) Construct a dual-view contrast framework to obtain high-quality graph enhanced training signals

[0165] To improve the similarity and difference of the contrast view group, the application introduces a diffusion model into the VGAE encoder, and constructs an inline diffusion model. At the same time, a parameter topology denoising model is introduced, which together with the inline diffusion model constitutes a double view contrast framework. This framework can more effectively capture the potential information in the user-item interaction graph and generate high-quality contrast views, thereby obtaining higher-quality graph-enhanced training signals. This helps to improve the representation ability of the recommendation system, enabling it to more comprehensively and accurately capture the complex relationship between users and items.

[0166] (2) A new hard negative sample sampling strategy for graph contrast learning is proposed to improve the quality of training signals

[0167] To further improve the quality of self-supervised learning training signals, the application proposes a new hard negative sample sampling strategy for graph contrast learning. Based on the effective sample selection mechanism of label information, this strategy can achieve more accurate sample selection. Combining this sampling strategy with the contrast loss function of graph generation learning training is conducive to learning the global information representation of the selected subgraph in user-item. This not only improves the quality of training signals, but also enhances the stability and robustness of the performance of the recommendation system when facing noisy data and sparse data.

[0168] (3) A graph contrast learning recommendation method GGDHSCL based on self-supervised learning is proposed

[0169] To comprehensively solve the above challenges, the application proposes a graph contrast learning recommendation method GGDHSCL based on self-supervised learning. This method fully utilizes the advantages of the double view contrast framework and the new hard negative sample sampling strategy, and effectively improves the performance of the recommendation system when facing noisy data and sparse data through self-supervised learning. At the same time, the GGDHSCL method also enhances the effectiveness of the collaborative filtering paradigm, enabling the recommendation system to more accurately predict user data and improve the accuracy and relevance of recommendations.

[0170] Additional aspects and advantages of the application will be partially given in the following description, partially will become apparent from the following description, or will be learned by practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0171] The above and / or additional aspects and advantages of the application will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:

[0172] Figure 1 is the overall framework schematic diagram of the GGDHSCL recommendation method of the application.

[0173] Figure 2 is the performance of the embodiment of the application under different sparsity levels of LastFM and Yelp data sets.

[0174] Figure 3 is the performance of the recommendation method affected by the noise disturbance of the embodiment of the application at different scales.

[0175] Figure 4 is the influence of the noise scale and diffusion step in the upper diffusion model of the Yelp data of the embodiment of the application.

[0176] Figure 5 is the hyperparameter analysis of the embodiment of the application on LastFM and Yelp. DETAILED DESCRIPTION

[0177] Embodiments of the application are described in detail below, examples of which are shown in the accompanying drawings, in which the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by reference to the accompanying drawings are exemplary and are only used to explain the application and cannot be understood as a limitation of the application.

[0178] The application proposes a hard negative sampling contrast recommendation method based on a graph generated diffusion model. The user-item interaction graph is encoded by a graph convolutional neural network, and then two different view generators are used to generate contrast views, realizing graph enhanced representation based on self-supervised signals and improving the performance of the recommendation system. The overall system architecture of the framework is shown in Figure 1 The two view generators, view generator 1 and view generator 2, work in parallel. View generator 1: first input the user-item interaction graph obtained by sampling, and obtain the embedding representation through a multi-layer graph convolutional neural network; then input the obtained embedding representation vector into the VGAE encoder to obtain a low-dimensional mapping, and at the same time obtain the mean vector and variance vector inferred by the neural network, which are used to describe the distribution of each node in the latent space. Then a diffusion model is designed in the implicit space: the forward process is to inject Gaussian noise into the low-dimensional embedding vector obtained by mapping through the principle of multiple small amounts until it obeys the Gaussian distribution; the reverse process is to reconstruct the low-dimensional embedding vector by using the variance mean and variance obtained by neural network analysis, and then input the reconstructed embedding vector into a two-layer multilayer perceptron to obtain a reconstructed graph structure. View generator 2: first use a multi-layer graph neural network to obtain the embedding representation of each node, and input it into a denoising network to obtain a new denoised graph structure. After obtaining the views generated by the two view generators, they are encoded by a graph convolutional neural network, and then the two encoded vectors are compared and learned, and at the same time a BPR loss is also calculated during the training of the two views to realize the function of signal alignment. In addition, a hard negative sample contrast loss is also calculated to enhance the self-supervised signal.

[0179] (1) Local graph collaborative information representation learning

[0180] Following a general collaborative filtering paradigm, it's necessary to learn the structural relationships between different sampled local user-item interaction subgraphs and the semantic relevance between each node. Subgraph segmentation is performed using the current user node as the center, and this node is also called the anchor point. Anchor points are selected through random sampling within the user node set. Aggregating the global information features of the subgraph structure requires traversing all nodes related to the anchor point in the subgraph, thus collecting high-order information features from the user-item interaction graph. Therefore, the interaction relationships between users and items are encoded, embedding the interaction graph into a d-dimensional latent vector space. Specifically, each user u will be generated... i and items v j Information representation embedding vector and (d represents the dimension of the representation embedding). The embedding representation matrix... and Defined as a matrix embedding representation of users and items (I and J represent the number of users and items in the subgraph structure, respectively). To capture and aggregate more comprehensive subgraph structure information, an information propagation layer for subgraph representation embedding is constructed as shown in Equation (3).

[0181]

[0182] Among them, E (u) E (v) These are matrix embedding representations of users and items, respectively;

[0183] These represent the aggregated information of users and items adjacent to the sampled anchor points, respectively.

[0184] Represent the normalized adjacency matrix respectively The i-th row of the normalized adjacency matrix The j-th column in the array.

[0185] It is a normalized adjacency matrix representation calculated from the adjacency matrix A of the user-item interaction graph. Specifically, The calculation derivation is shown in equation (4).

[0186]

[0187] in, and These are represented as diagonal matrices for users and items, respectively.

[0188] Represents the normalized adjacency matrix The element in the i-th row and j-th column;

[0189] A i,j An element of the adjacency matrix A representing the user-item interaction graph, in the i-th row and j-th column;

[0190] L i and L j are the sets of all neighbor nodes of users and items, respectively. The normalized matrix can better reflect the interaction signals between users and items, and can better transmit and iterate the aggregated information of the embedding layer.

[0191] In order to more effectively aggregate the semantic relationship feature information of the neighbor nodes of the sampled subgraph, the feature representation of the user and item nodes is improved by integrating multiple representation embedding propagation layers. The representation embedding vectors obtained by traversing the graph neural network at the l-th layer are defined as i and v j and The target node information is propagated from the l-1-th layer to the l-th layer. In order to obtain a high-quality node embedding representation, the node embeddings on each propagation layer are summed, and the inner product between the final user and item embedding representations is used to predict the preference degree of the user to the item in personalized recommendation. The embedding representation calculation process is as formula (5).

[0192]

[0193] wherein, and are the representation embedding vectors obtained by traversing the graph neural network at the l-th layer of u i and v j

[0194] respectively represent the representation embedding vectors obtained by traversing the graph neural network at the l-th layer of the aggregated information of the user and the sampled anchor adjacent target node and the aggregated information of the item and the sampled anchor adjacent target node;

[0195] respectively represent the representation embedding vectors obtained by traversing the graph neural network at the l-1-th layer of u i and v j

[0196] respectively represent the final node embedding vector of the user and the final node embedding vector of the item;

[0197] represents the preference score obtained by the inner product of the user and item embedding vectors;

[0198] respectively represent u i and v​​​j the representation embedding vectors obtained by the graph neural network of the l-th layer;

[0199] is the transpose of ;

[0200] and respectively represent the information representation embedding vectors of each user u i and item v j ;

[0201] L represents the number of layers of the graph neural network;

[0202] (2) Dual-view contrastive learning framework

[0203] The self-supervised graph contrastive learning recommendation system not only reduces the dependence on labels in the real data set and reduces the data construction cost, but also improves the sparsity problem of user behavior data always appearing in the real recommendation scene and the resistance to noise data. The additional high-quality training signal produced in the model training process improves the problem of data sparsity and insufficient model robustness. The existing contrastive recommendation system constructs the contrastive view by randomly deleting the connection edges and nodes of the graph or constructing a hypergraph to generate the contrastive view. The dual-view contrastive learning framework is selected from the same group of data by different methods or models. This view construction method can improve one problem, which is caused by the fact that the two view distributions generated by the same view generator are shared, resulting in insufficient accurate contrast enhancement and the risk of contrast model collapse. Therefore, two different view generators are selected to generate views, which can better avoid the above problems and risks, and understand and predict the true needs of users and understand the true preferences of user groups.

[0204] In the selection of view generator, an inline diffusion model and a parameter topology denoising model are selected as the generators of the two contrastive views. The graph generation learning model focuses on reconstructing the graph structure, and a new graph structure is generated by adding Gaussian noise to the graph; the graph denoising network model focuses on removing the noise data of the user-item interaction graph to form a low-noise contrastive view.

[0205] (2.1) Inline diffusion model view generator

[0206] In recent years, contrastive view generator based on graph generative model is very popular, which can generate different contrastive views by generative adversarial network (GAN), reconstruct graph structure by variational autoencoder (VAE), etc. Universal diffusion model has strong generative ability in graph generation task, but it needs to denoise the data until it becomes completely random noise, which will cause the loss of personalized information in user and item interaction. At the same time, although the graph variational autoencoder (VGAE) is used as a view generator, it has good performance in the recommendation system task, but it has limited representation ability in complex user interaction mode. Therefore, based on the diffusion model, the widely used VGAE is introduced, and when the diffusion model and VGAE are integrated, the size of the added noise in data denoising is reduced, thereby avoiding the complete noise of user and item interaction information while retaining the semantic relationship between nodes, thereby improving the problem of loss of personalized information of users.

[0207] The subgraph is encoded to obtain a graph representation embedding vector by a multi-layer graph convolutional neural network, and then the embedding vector is input into a multi-layer perceptron (MLP) to learn the hidden state variable of each node. Then the hidden state is used to estimate the mean and variance of the embedding vector, which constitutes a multivariate Gaussian distribution parameter. Compared with VAE, VGAE introduces Kullback-Leibler divergence (KL divergence) to reduce the risk of model overfitting. Specifically, the embedding representation vector e l is mapped to x by a parameterized graph variational encoder, and the mean and variance of the Gaussian distribution are learned. The graph variational encoding process is as shown in formula (6).

[0208]

[0209] wherein q φ (x|e) represents the probability distribution obtained by graph variational encoding;

[0210] N represents a Gaussian distribution;

[0211] x represents the embedding representation vector e l is mapped to x by a parameterized graph variational encoder;

[0212] μ φ (e) represents the Gaussian distribution mean inferred by the parameter set of the neural network;

[0213] σ φ (e) represents the Gaussian distribution variance inferred by the parameter set of the neural network;

[0214] e is obtained from formula (5), which is or

[0215] μ represents the mean of the Gaussian distribution, the most likely location of the input data to re-embed in the vector space, σ represents the variance of the Gaussian distribution, and the variance between dimensions is independent, reflecting the dispersion around the mean data, and φ is the parameter set of the VGAE encoder, e is obtained by formula (5), and is or In order to enlarge the distance between positive and negative samples in contrast learning, enhance the maximization of the similarity of positive sample pairs and the minimization of the similarity of negative sample pairs, and achieve the goal of graph contrast enhancement, a diffusion model is introduced to generate the denoised user-item interaction data after VGAE encoding. Based on the low-dimensional vector x mapped by the VGAE encoder, the forward and reverse processes of diffusion are designed in the implicit embedding space. In the forward diffusion process, a Gaussian noise increment is added to the original embedding vector x, and in order to improve the missing of interaction information between users and items, the size of the noise is reduced. On the contrary, the reverse process of diffusion uses a trainable deep neural network to eliminate noise and generate clean vector representation. Through the diffusion model, the features can be increased, and the discrimination of different features can be higher.

[0216] Forward process: in the forward propagation process, the inline diffusion model iteratively applies K times of noise addition steps, where K is a hyperparameter, and the embedding vector is represented as x k after adding noise for the k-th time. Each time the data is calculated through the iteration process as shown in formula (7).

[0217]

[0218] where q(x k |x k-1 ) represents the forward process probability distribution;

[0219] N represents the Gaussian distribution;

[0220] x k is the noise added to the embedding vector for the k-th time;

[0221] β k ∈(0,1) represents the size of the input noise, and the parameter is independent between dimensions.

[0222] Reverse process: in the backward propagation process, the propagation target is to recover the original data from the noise and reconstruct the embedding representation x z in the implicit vector space, where k = 1, 2,..., K. Specifically, the backward propagation process uses a trainable deep neural network to predict, and the propagation calculation process is as shown in formula (8).

[0223] p(x k-1 |x k ) = N(x k-1 ; W1(x k , k), W2(x k , k)) (8)

[0224] where p(x k-1 |x k ) denotes the reverse process probability distribution;

[0225] N denotes a Gaussian distribution;

[0226] x k-1 is the noisy representation of the embedding vector at the k-1th addition;

[0227] W1and W2denote the Gaussian parameters of the trainable neural network used to predict the Gaussian distribution. The low-dimensional embedding vector reconstructed by the forward and backward propagation processes of the inline diffusion model is input into another MLP serving as a decoder. The mean and standard deviation of the Gaussian distribution parsed in the encoding process are also input to generate a new view. Finally, the loss function is defined as (9).

[0228]

[0229] where denotes the KL divergence loss value between the node embedding distribution and the standard Gaussian distribution;

[0230] denotes the binary cross-entropy loss function;

[0231] denotes the loss function of the inline diffusion model;

[0232] μ denotes the mean of the Gaussian distribution;

[0233] σ denotes the variance of the Gaussian distribution;

[0234] p pos denotes the positive sample edge set;

[0235] p neg denotes the negative sample edge set;

[0236] N denotes the number of sampled samples.

[0237]

[0238] (2.2) Parameter topology denoising view generator

[0239] A high-quality contrastive view can improve the performance of the contrastive model, considering that the information propagation mechanism of the graph convolutional neural network is to enable each node and edge to effectively aggregate the local and global relationship information between nodes to update its own embedding representation. However, the low-quality graph with noisy edges will seriously affect the quality of the graph embedding and thus the performance of the model. Therefore, the goal of the second view generator in the dual-view generative contrastive framework is to build a parameterized topological view generator to reduce the noisy edge data in the graph structure through the graph attention mechanism, thereby achieving the effect of contrast enhancement.

[0240] In order to improve the quality of node embedding of each layer of GNN, a denoising network is proposed in GNN to filter the noisy edges in the graph, thereby achieving the effect of denoising the graph structure. The main idea of this model is to filter the noisy edges of the input model through the parameterized network, thereby achieving the goal of graph denoising. Specifically, the target task is to filter out the noisy edges in the input subgraph. Therefore, a binary matrix Z l ∈{0,1} J×J , and represents the edge between the two nodes u and v, and the element value of 0 indicates a noisy edge that should be removed. After the information is propagated in the GNN, the final subgraph adjacency matrix is as shown in equation (10).

[0241] A l =A⊙Z l (10)

[0242] Wherein, A l represents the subgraph adjacency matrix after the l-layer graph neural network and the transformation of the binary matrix Z l ;

[0243] A represents the subgraph adjacency matrix;

[0244] Z l represents a binary matrix used to generate the subgraph after the l-layer GNN processing.

[0245] ⊙ represents element product, so A l only contains the edges marked as 1 in Z l . In order to improve the probability of removing the noisy edges with high possibility in the model, the l0 regularization method of sparse neural network is used to reduce A l . The method to reduce the number of non-zero edges in different GNN layers is to directly punish the number of non-zero edges as shown in equation (11).

[0246]

[0247] Wherein, is an indicator function, and

[0248] l = 1 means starting from the first layer to calculate;

[0249] (u, v) e e represents the set of user-item interaction edges of the input subgraph;

[0250] L represents the number of layers of the graph neural network;

[0251] ||·||0 represents the l0 norm.

[0252] This regularization function is used to encourage the generation of sparse matrices on all layers of the parameterized topology denoising view generator, and then remove those possibly irrelevant or noisy edges by minimizing this regularization term. Due to the l0 norm combination and non-differentiability, this regularization term cannot be directly optimized using traditional gradient descent methods. However, each 0-1 element is obtained from the parameterized Bernoulli distribution, denoted as: Then the number of edges used can be re-regularized, denoted as: Then the method of reparameterization is introduced and the 0-1 element is optimized into a parameter and a deterministic function of independent random variables, so as to achieve the effect of helping the gradient optimization method to optimize the subgraph more effectively.

[0253] Then the graph attention mechanism (GAT) is selected as the denoising layer to learn the parameters that can control whether to delete the edge Take a node u in the training subgraph as the center node, then the neighbor nodes of the node represent N u . In the l-th GNN layer, node u and its neighbor nodes v e N u are calculated. As formula (12).

[0254]

[0255] where, represents the quality score of the edge between node u and node v calculated by the l-layer graph neural network;

[0256] is a parameterized MLP model; l

[0257] respectively represent the feature vectors of the user node and the item node obtained by the l-layer graph neural network.

[0258] l ​​is a trainable parameter containing the weight matrix and bias vector of each layer of the MLP. Then, the probability of retaining each edge is determined dynamically by a binary Concrete distribution and a Hard Sigmoid function according to dynamically. The probability of retaining each edge is determined by a binary Concrete distribution on the locally parameterized a The parameterized computation process is shown in equation (13).

[0259] ∈ ~ Uniform(0, 1),

[0260] where ∈ ~ Uniform(0, 1) means that a sample is randomly drawn from the binary Concrete distribution;

[0261] ∈ represents a sample randomly drawn from the Concrete distribution;

[0262] Uniform(0, 1) represents the Concrete distribution;

[0263] represents the preliminary calculation result of the probability of retaining the edge between node u and node v; the probability value tends to 0 or 1;

[0264] represents the quality score of the edge between node u and node v under a specific task;

[0265] τ ∈ R + represents the temperature coefficient;

[0266] σ(·) represents the sigmoid activation function.

[0267] The Hard Sigmoid function is used to convert into a binary mask The conversion process is shown in equation (14).

[0268]

[0269] After calculating the problem of equation (11) can be solved, thereby achieving the effect of denoising the parameterized network. According to equation (13), the can be derived to the probability of retaining the edge Then, the expected value of the probability of retaining each edge is calculated by L0 regularization loss, and the loss calculation process is shown in equation (15).

[0270]

[0271] wherein, represents that the cumulative distribution function probabilities less than 0 are mapped to 0 and 1 using the σ(·) mapping, resulting in the probability of edge preservation in the subgraph.

[0272]

[0273] (3) Model Optimization

[0274] (3.1) Contrastive Self-Supervised Loss Optimization

[0275] From the foregoing, it can be known that the entire model framework is selected to use a dual-view generator to generate a contrast view, and two different learnable view generators are applied to generate a contrast view. Based on the existing self-supervised collaborative filtering (CF) paradigm, the method allows nodes to automatically distinguish positive sample pairs and negative sample pairs. Specifically, the model considers the representation of the same node in different views as a positive sample pair (such as the representation of the embedding vector of the same user in two different views); while the representation of different nodes is considered as a negative sample pair (such as the embedding vectors of any two different users). The contrastive loss objective function is to maximize the consistency of positive sample pairs and minimize the consistency of negative sample pairs, and the target loss function is calculated as formula (16).

[0276]

[0277] wherein, represents the target loss function;

[0278] u i , u i′ represent a user in the user set and a negative sample user in the user set, respectively;

[0279] U represents a set of user nodes;

[0280] represents the cosine similarity of the positive sample pair;

[0281] represents the cosine similarity of the negative sample pair;

[0282] The hyperparameter τ represents the temperature coefficient in the softmax. The contrastive loss of the item is also calculated in the same way, therefore, the loss function of the self-supervised learning can be represented as

[0283] (3.2) Contrastive Supervised Loss Optimization with Hard Negative Sampling

[0284] The effectiveness of hard negative sample sampling strategy (HSCL) in contrastive learning and the practicability of label information in self-supervised learning, therefore, the HSCL strategy is introduced into the self-supervised recommendation framework. In the process of training the model in the contrastive learning framework, in order to improve the learning performance of the self-supervised learning recommendation algorithm, the HSCL is used to select positive and negative samples by fully combining the label information. Negative samples usually refer to items that have not been interacted by users. However, not all negative samples are equally helpful to the training model. Hard negative samples refer to those items that are very similar to positive samples but are actually negative samples. These samples are more difficult to distinguish, so they are more critical to the learning of the model during the training process. H-SCL selects hard negative samples by calculating the similarity between samples. If the similarity between a negative sample and an anchor sample is higher than a certain threshold, but they belong to different categories, then this negative sample is considered a hard negative sample. First, a sample seed set is constructed, and positive samples are randomly selected. If the label of the sample belongs to the current set, it is selected as a positive sample; otherwise, it is considered as a negative sample. A simple random probability sample selection strategy is designed to calculate the probability distribution of positive and negative samples in the sample set. Specifically, the positive sample (s, s + ) is independently selected from the same category distribution D c , and the category c is randomly selected according to the global category distribution p. The probability distribution of positive samples is as formula (17).

[0285]

[0286] where p(s, s + ) represents the probability distribution of positive samples (s, s + );

[0287] E[c] represents the expected value of selecting category c according to the category distribution p;

[0288] D c (s) represents the probability distribution of sample s in category c;

[0289] D c (s + ) represents the probability distribution of sample s+ in category c;

[0290] D c represents the probability distribution associated with category c.

[0291] The key point here is that for a given anchor sample s, its positive sample s + should come from the same category to ensure their similarity. This similarity is achieved by assuming that s and s + come from the same category distribution D cto ensure that the class c is randomly selected according to the distribution p of each class in the entire dataset. The negative sample selection is based on different negative probability distributions, and a helper function is designed to calculate the similarity between samples in the feature space, so as to optimize the process of the final loss function. Similar to unsupervised contrast learning, the negative sample is randomly selected in the input space as formula (18).

[0292]

[0293] where q(s,s - ) represents the probability distribution of the hard negative sample pair (s,s - );

[0294] represents the expected value of selecting the class c according to the class distribution p;

[0295] D c (s - |H(s,e i ,τ)) represents the probability distribution of the negative sample calculated by the given sample s, e i , temperature coefficient and hard sampling strategy in the class c;

[0296] s - represents the negative sample;

[0297] e i represents the embedding representation of the corresponding sample;

[0298] τ represents the similarity threshold;

[0299] H(s,e i ,τ) represents the set of hard negative samples, which consists of two parts: the sample s - and the anchor sample s belong to different classes; the sample s - is very close in the feature space. The feature space similarity calculation is formula (19).

[0300]

[0301] where h(s,s + ) represents the feature space similarity of the positive sample;

[0302] e Τ is the transpose of e i ;

[0303] e is the embedding representation of all samples;

[0304] e + is the feature embedding representation of all positive samples;

[0305] representing the feature space similarity of a single negative sample;

[0306] is the transpose of e i

[0307] e i representing the embedding representation of a corresponding sample;

[0308] representing the feature embedding representation of a single negative sample;

[0309] Y represents the temperature coefficient, when the similarity is greater than the threshold, i.e., h(s,s - ) > τ, and the two samples do not belong to the same probability distribution, the two samples are defined as hard negative samples. In constructing the contrastive loss function, e i is used to calculate the representation of positive samples and negative samples, and then calculate the loss, and the loss function form is as formula (20).

[0310]

[0311] wherein, represents the hard negative sample contrastive loss function;

[0312] represents the mathematical expectation of the positive sample pair according to the distribution p and the mathematical expectation of the negative sample pair;

[0313] k represents the number of negative samples;

[0314] represents the similarity of the sample and the negative sample;

[0315] represents the similarity of the sample and the positive sample;

[0316] by summing the similarity of all negative samples, i.e. is used to minimize the similarity of all negative samples.

[0317] (3.3) View generation optimization of signal alignment

[0318] In order to select two different generators to generate contrastive views on the contrastive view generator, a specific strategy needs to be designed to adjust and align the training signals of the two views to adapt to the CF (collaborative filtering) task to optimize the final effect. In order to achieve this optimization goal, BPR (Bayesian Personalized Ranking Loss) is selected to optimize the alignment of view training signals as formula (21).

[0319]

[0320] ​where O denotes all training data;

[0321] represents the difference between the positive and negative sample prediction scores calculated by the Sigmoid function to map it between 0 and 1, and then taking the negative logarithm to obtain the final loss value;

[0322] σ represents the Sigmoid function;

[0323] respectively represent the user's predicted score for the positive sample item (representing the interacted item) and the negative sample item (representing the non-interacted item) ;

[0324] In order to optimize the inline diffusion model view generator, the embedding representation of the user-item interaction encoded by the VGAE encoder therein is used to calculate the BPR as shown in equation (22).

[0325]

[0326] wherein, represents the total loss function of the inline diffusion model view generator;

[0327] represents the KL divergence loss value;

[0328] represents the distribution loss value, which ensures that the node embedding distribution of the generated graph is similar to the node embedding distribution of the original graph;

[0329] represents the BPR loss function of the inline diffusion model view generator part; is obtained by equation (21), in order to distinguish the diffusion model view and the denoising network view, so instead of represents.

[0330] represents the regularization term, which is calculated by the square of the Frobenius norm of the model parameter set, and λ2 is a hyperparameter used to control the regularization strength. The training signal of the optimized parameter topology denoising view generator can be used to calculate the BPR with the node embedding representation obtained by it, and the loss function reconstruction is shown in equation (23).

[0331]

[0332] wherein, represents the total loss function of the parameter topology denoising view generator;

[0333] represents the L0 regularization loss function;

[0334] BPR (Bayesian Personalized Ranking) loss function representing the parameter topology denoising view generator part; By formula (21), in order to distinguish the diffusion model view and the view of the denoising network, so But not Represented.

[0335] Finally, by combining multiple targets to train, maximize the user-item interaction prediction of all positive samples, while minimizing the user-item interaction prediction of all negative samples, and finally complete the model training by calculating the loss optimization as formula (24).

[0336]

[0337] Wherein, The total loss function of the inline diffusion model view generator is represented;

[0338] The total loss function of the parameter topology denoising view generator is represented;

[0339] The hard negative sampling loss function is represented;

[0340] The BPR loss function is represented;

[0341] λ1 represents a hyperparameter for controlling the strength of the self-supervised signal;

[0342] The self-supervised loss function is represented;

[0343] The regularization term is represented;

[0344] λ2 is a hyperparameter for controlling the regularization strength.

[0345] (4) Analysis of experimental results

[0346] In order to evaluate the performance and effectiveness of GGDHSCL, experiments are selected on three different real-world datasets and compared with various mainstream recommendation methods. Experiments are designed to verify the following research problems:

[0347] · Question 1: How does the proposed recommendation method perform compared to the current mainstream recommendation methods?

[0348] · Question 2: How does the key module of the proposed recommendation method contribute to the method on different datasets?

[0349] · Question 3: How does the proposed recommendation method perform on the problem of data sparsity?

[0350] • Question 4: How effective is the proposed recommendation method in mitigating the data noise problem?

[0351] • Question 5: How do the key hyperparameters affect the performance of the proposed recommendation method?

[0352] (4.1) Dataset Evaluation

[0353] To evaluate the performance of GGDHSCL, three public datasets from different real-world online platforms were selected to evaluate the performance of different recommendation tasks in different places, locations, and products. The datasets include: LastFM, Yelp, and BeerAdvocate. LastFM: This dataset contains label, musician, and social network listening information collected from a group of users collected from LastFM, which is mainly focused on music recommendation. Yelp: This mainstream dataset is collected from user ratings of commercial places in life from the Yelp platform. BeerAdvocate: This dataset comes from beer enthusiasts' comments on beer on the BeerAdvocate platform, targeting the beer recommendation field, diversifying the recommendation scenario. The statistical results of these datasets are shown in Table 1.

[0354] Table 1: Statistics of experimental datasets.

[0355] Dataset #Users #Items #Interactions Density LastFM 1,889 15,376 51,987 2.8e -3 ]]> Yelp 42,712 26,822 182,357 1.6e -4 ]]> BeerAdvocate 10,456 13,845 1,381,094 9.5e -3 ]]>

[0356] (4.2) Evaluation Metrics

[0357] To ensure the fairness of the experimental results, in the experiment, the ratio of 7:2:1 is used to divide the observed interactions of each dataset into training set, validation set and test set. The full rank evaluation scheme is used, for each test user, the positive items in the test set and all non-interaction items are tested and sorted together to infer the user's preference. Two representative indicators, Recall@N and NDCG@N, are used to evaluate the performance of the proposed GGDHSCL recommendation method. By default, the value of N is set to 20, which is used to evaluate Top-N recommendations. The calculation methods of Recall and NDCG are as follows:

[0358] 1) Recall: Recall reflects the proportion of relevant items that the recommendation system can successfully find. R(u) represents the Top-N recommendation list provided to the user according to the user's behavior on the training set; T(u) indicates the set of items that the user actually selects after the system recommends items to the user:

[0359]

[0360] 2) CG (Cumulative Gain): Cumulative Gain, which adds each recommendation result (relevance score) in the recommendation list. But there may be a list, high score to the bottom, low score to the highest.

[0361]

[0362] 3) DCG (Discounted Cumulative Gain): Discounted Cumulative Gain, which introduces the position factor on the basis of CG, and the recommendation effect of the recommendation result with lower ranking is "discounted".

[0363]

[0364] 4) NDCG (Normalized Discounted Cumulative Gain): Normalized Discounted Cumulative Gain, which evaluates the user recommendation list of the entire test set of the recommendation system as a whole, and normalizes the evaluation scores of the recommendation lists of different users. IDCG is the best recommendation list returned by the recommendation system for a specific user.

[0365]

[0366] (4.3) Comparison with baseline methods

[0367] Comparison of the performance of GGDHSCL with other 14 kinds of recommendation system baseline methods in Recall@20@40and NDCG@20@40

[0368] a) Traditional collaborative filtering recommendation methods

[0369] BiasMF: This is a method based on matrix decomposition, which converts users and items into vector representations in a latent space while considering their respective biases to reflect user preferences.

[0370] NCF: This is a method using neural networks, which uses a multi-layer neural network to encode non-linear features in user-item interactions.

[0371] AutoRec: This model uses a self-encoder architecture to learn embedding representations by reconstructing observed interaction data.

[0372] b) GNN-based recommendation methods

[0373] GCMC: This is a method using GCN, which introduces GCN for interaction matrix, and considers the problem of recommendation system matrix completion from the perspective of link prediction.

[0374] • PinSage: This is a GCN-based recommendation method that generates node embeddings that combine graph structure and node feature information through efficient random walks and graph convolutions, significantly improving recommendation quality.

[0375] • NGCF: This method explicitly incorporates collaborative signals into the embedding process by propagating embeddings on the user-item bipartite graph, effectively capturing high-order connectivity in the user-item graph and improving recommendation performance.

[0376] • STGCN: This method combines the advantages of graph convolutional encoders and graph autoencoders, improving the model's robustness when dealing with sparse data and cold start problems, and enhancing its performance in collaborative filtering tasks.

[0377] • LightGCN: This recommendation method uses linear propagation and weighted summation to learn user and item embeddings, simplifying the design of GCN, making it easy to implement and train, and showing significant performance improvement compared to advanced models like NGCF under the same experimental settings.

[0378] • GCCF: This is a GCN-based collaborative filtering that eliminates non-linear activation and introduces a residual network structure to alleviate the over-smoothing problem.

[0379] c) Recommendation methods based on self-supervised enhancement

[0380] • HCCF: By introducing a hypergraph-enhanced cross-view self-supervised contrastive learning architecture, it simultaneously captures local and global collaborative relationships, effectively addressing the over-smoothing problem of deep graph structures and the scarcity of supervision signals, significantly improving the representation quality and robustness of the recommendation system.

[0381] • SHT: This method is an innovative self-supervised hypergraph Transformer framework that improves the performance of the recommendation system by enhancing user representations and capturing global collaborative relationships, especially in handling data sparsity and noise.

[0382] • SLRec: A multi-task self-supervised learning framework for large-scale item recommendation, which addresses the label sparsity problem by learning the underlying relationships between item features and proposes a new data augmentation method that utilizes feature correlation.

[0383] • SGL: A graph self-supervised learning framework applied to user-item bipartite graph recommendation systems, which performs node and edge dropout on the input bipartite graph for data augmentation. The augmented graph can be considered as a sub-view of the original graph.

[0384] • NCL: This method is a neighborhood-enhanced contrastive learning method that significantly improves the performance of graph collaborative filtering recommendation systems by explicitly incorporating latent neighbors into the contrastive pairs and combining structural and semantic space neighbor information.

[0385] • AdaGCL: This is an adaptive graph contrastive learning framework that enhances the collaborative filtering paradigm through two trainable view generators to improve the robustness and generalization ability of recommendation systems.

[0386] Table 2: Comparison of recall@20@40 and NDCG@20@40 performance of 14 benchmark methods on LastFM, Yelp, and Beer datasets.

[0387]

[0388]

[0389] (4.4) Overall performance comparison (RQ1)

[0390] Table 2 presents the performance evaluation of GGDHSCL on Yelp, LastFM, and Beer three real datasets (Recall@20, NDCG@20, Recall@40, and NDCG@40) compared with 14 benchmark methods such as AdaGCL and SHT. From the data, the following observations are made:

[0391] • The evaluation results show that GGDHSCL outperforms all other baseline methods in both top-20 and top-40 settings, and significant performance improvements are observed. The excellent performance of GGDHSCL can be attributed to the effective performance of the graph contrastive learning framework in the user-item interaction graph data enhancement. The combination of the inline diffusion model and the parameter topology denoising model constructs a dual-view contrastive learning framework, and the view signal alignment optimization makes the view generator automatically adapt to the data features, ensuring that the view information generated by the view generator is rich and diverse. In addition, the introduction of hard negative sample contrastive loss optimization enhances the self-supervised contrastive learning signal, resulting in higher quality recommendation results. The above conclusions prove that the graph contrastive learning framework is effective and has certain interpretability in the recommendation system of the collaborative filtering paradigm, and the data enhancement view generation technology in contrastive learning is the core problem. High-quality data enhancement technology can effectively improve the performance of the recommendation method.

[0392] • From the results, it can be seen that GGDHSCL is better than other baseline methods in the recommendation task of the collaborative filtering paradigm based on self-supervised learning, and the performance gap of the CF model based on GNN exposes the problem of this method: it is difficult to solve the problem of noise in data embedding representation and model overfitting due to data sparsity. However, the recommendation data in real scenarios often has the problems of noise and data sparsity, and the improvement of introducing self-supervised signals is attributed to the data enhancement task to improve the representation ability of the model. GGDHSCL here shows two advantages. First, a double-view contrast framework is formed by constructing an in-line diffusion model view generator and a parameter topology denoising model view generator, which can effectively solve the problem of model collapse in graph contrast learning. Second, the two view generators are automatically adapted to create effective and reasonable information through signal alignment optimization loss, thereby avoiding the information loss and instability problems caused by data enhancement techniques such as random edge deletion and random mask nodes.

[0393] (4.5) Ablation Experiment (RQ2)

[0394] To further verify the performance of the method, an ablation experiment is conducted to further explore the effectiveness of each sub-module in the proposed GGDHSCL method. Table 3 shows the NDGC and Recall indicators of top-20 and top-40 on the LastFM and Yelp datasets for different modules.

[0395] Table 3: Ablation experiment results

[0396]

[0397] (4.5.1) Influence of in-line diffusion model The in-line diffusion model is embedded in the VGAE encoder as a generative view generator in the double-view generative contrast framework, which shows that it can also consider the representation ability of the unstable advantage in the generative task. In the ablation experiment, the variant w / o-DF uses only the VGAE encoding and decoding in the in-line diffusion model. The results show that the proposed GGDHSCL recommendation method has obvious improvement compared with w / o-DF, indicating that the in-line diffusion model has strong and stable generation ability for the generative recommendation task, thereby improving the performance of the recommendation system.

[0398] (4.5.2) The impact of the hard negative sampling strategy The proposed recommendation method performs well partly because the supervised contrast signal of the introduced hard negative samples enhances the training signal of self-supervised learning. In the ablation experiment, the variant w / o-HS discards the hard negative sampling strategy. The results show that the hard negative sampling strategy can effectively combine to enhance the self-supervised optimization loss, which is beneficial to enhance the recommendation system based on the GNN-based CF paradigm. In addition, the variant w / o-DH discards both the diffusion model in the inline diffusion model and the hard negative sampling strategy, while retaining the dual-view contrast framework. The results show that the combination of the diffusion model and the hard negative sampling strategy can effectively combat noise in the data and enhance the self-supervised signal to effectively make recommendations.

[0399] (4.5.3) The impact of the parameter topology denoising model To further study the reasons for the excellent performance of the proposed recommendation method, the impact of the denoising view in the dual-view generative contrast framework is considered. In the ablation experiment, the variant w / o-VG replaces the denoising view generator with the VGAE view generator in the dual-view framework. The results show that although data augmentation using VGAE still has good performance, it is difficult to solve the problem of data noise. The construction of the denoising view generator can effectively avoid this problem, thereby significantly improving the performance of the recommendation method.

[0400] (4.6) Data sparsity experiment (RQ3)

[0401] The performance of the proposed GGDHSCL recommendation method on data with different levels of sparsity is studied to verify the good robustness of the method to data sparsity. Specifically, by reducing the interaction information in the data set by different proportions (10%, 20%, 30%), the function of evaluating the sparsity robustness of the recommendation method is realized. The proposed method and other three mainstream methods, AdaGCL, SGL, and LightGCN, are compared and analyzed on the LastFM and Yelp data sets. In order to intuitively show the performance of different recommendation methods under different degrees of sparsity, four line graphs are used to present the influence of performance trends on sparse data in Figure 2

[0402] Figure 2 ​In summary, the proposed GGDHSCL recommendation method has good robustness in dealing with different sparsity degrees of user-item interaction relationships.

[0403] (4.7) Noise impact experiment (RQ4)

[0404] To better evaluate the impact of noise on the performance of the recommendation method and prove the good robustness of the proposed GGDHSCL recommendation method to data noise. In the specific experiment, 5%, 10%, 15%, 20%, and 25% of the interaction edges are replaced by random fake edges, and then the method is compared with other three baseline mainstream methods AdaGCL, SGL and LightGCN on LastFM and Yelp datasets. In order to clearly show the performance of different methods under different proportions of noise, four histograms are used to show the impact of noisy data on the performance decline trend. The NDCG and Recall performance results of the proposed GGDHSCL recommendation method under different proportions of noisy data are shown in Figs. 6 and 7, respectively. Figure 3 Figure 3 In summary, compared with other AdaGCL, SGL, LightGCN three methods, the proposed GGDHSCL method has the best performance in different proportions of noisy data, and the decline trend is more gentle, with stronger robustness. This observation is attributed to the proposed inline diffusion model as a generative contrast framework, which not only retains strong generative ability, but also has good ability to handle data noise; the denoising view in the proposed method's dual-view contrast framework is also crucial to the data noise problem. Therefore, the two view generators used in the method can generate contrast views with less noise and more task-related information. By observing the change trend of each recommendation method under two different datasets, because the Yelp dataset is more sparse, the impact of noise on all methods is more obvious. In summary, from the experimental results, it can be concluded that GGDHSCL is a robust recommendation method.

[0405] (4.8) Hyperparameter sensitivity analysis (RQ5)

[0406] ​To investigate the impact of different hyperparameters on the performance of recommendation methods Figure 4 and Figure 5 Experiments on the LastFM and Yelp datasets are presented. The GGDHSCL recommendation method has four important parameters, two of which are related to the diffusion model: the scale of the Gaussian noise injected during the forward propagation of the diffusion model and the number of time steps in the Markov chain of the diffusion model. Other parameters include the weights of the hard negative sample sampling strategy and the weights of the InfoNCE loss. Hyperparameter experiments were conducted on the Yelp dataset. By adjusting the scale of the Gaussian noise injected during the forward propagation of the diffusion model within the interval (0.0001, 0.0005, 0.001, 0.005, 0.01, 0.1), and controlling the diffusion step size to 5, a line graph was plotted as shown below. Figure 4 (a); Then, by controlling the injected noise scale to 0.005 and the diffusion step size within the range of (5, 10, 20, 50, 100), a histogram is plotted as follows. Figure 4 (b)

[0407] Figure 4 The results demonstrate performance on the Yelp dataset. When the diffusion step size is 5 and the injected Gaussian noise scale is 0.005, the proposed GGDHSCL recommendation method achieves optimal performance on the NDGC@40 and Recall@40 metrics. When the injected Gaussian noise scale is less than 0.005, the performance of the recommendation method increases with the increase of the noise scale. This is attributed to the fact that injecting higher-scale Gaussian noise is beneficial for disrupting the internal structure, thus making the structure generated by the view generator more conducive to widening the distance between negative sample pairs, enhancing the effect of contrastive learning, and thus improving recommendation performance. However, according to the optimal noise level principle in diffusion theory, there is an optimal noise level during propagation; exceeding this level introduces too much unnecessary complexity, causing performance degradation. This viewpoint explains the downward trend that occurs after the noise scale exceeds 0.005. With the increase of the diffusion step size, the performance of the proposed GGDHSCL recommendation method also shows a downward trend. This is attributed to the fact that an excessively large step size leads to the diffusion model undergoing excessive noise injection, making it difficult to recover a high-quality graph structure during backpropagation.

[0408] This study investigates the impact of the weight changes of the hard negative sampling strategy and the InfoNCE loss on the performance of the proposed GGDHSCL recommendation method. The method is evaluated on the NDGC@40 and Recall@40 metrics using the LastFM and Yelp datasets, respectively. Specifically, the H-SCL weights are searched in the interval (0.2, 0.4, 0.6, 0.8, 1.0), and the InfoNCE weights are searched in the interval (1, 0.1, 0.01, 0.001, 0.0001). The performance trends of the proposed recommendation method are shown below.Figure 5 are shown.

[0409] Figure 5 Figures 4(a) and 4(b) show the results of the impact of the H-SCL loss weight and the InfoNCE loss weight on the recommendation method for the LastFM and Yelp datasets, respectively. Figure 5 Figures 4(a) and 4(b) show the results of the impact of the H-SCL loss weight and the InfoNCE loss weight on the recommendation method for the LastFM and Yelp datasets, respectively. Figure 5 Figures 4(a) and 4(b) show the results of the impact of the H-SCL loss weight and the InfoNCE loss weight on the recommendation method for the LastFM and Yelp datasets, respectively.

[0410] In summary, this paper proposes an innovative hard negative sampling contrastive recommendation method based on graph generated diffusion model (GGDHSCL), which aims to address the challenges of existing recommendation systems in representation ability, data noise, and data sparsity. To achieve this goal, we introduce a dual-view contrastive framework, which includes two key components: an inline diffusion model and a parameter topology denoising model. The inline diffusion model serves as a generative view generator, capable of capturing the latent information in the user-item interaction graph and generating high-quality contrastive views. The parameter topology denoising model serves as a denoising view generator, further purifying the generated contrastive views and reducing the impact of data noise. To further enhance the effect of generated contrastive augmentation and mitigate the risk of model collapse, we introduce a signal alignment loss strategy that combines task-aware information to improve the quality of the lowest generation. This strategy makes the generated contrastive views more accurate and stable, helping to improve the performance of the recommendation system. In addition, we incorporate the H-SCL loss function to enhance the self-supervised signal, allowing the user-item interaction graph to propagate information more effectively. This improvement enables the graph-based self-supervised recommendation system to more accurately capture the relationships between users and items, thereby improving the accuracy and relevance of recommendations. To verify the rationality and effectiveness of the GGDHSCL method, we conduct extensive experiments on three real-world datasets, including LastFM. The experimental results show that, compared with 14 popular recommendation algorithms, GGDHSCL performs best in terms of Recall@20@40 and NDCG@20@40. In particular, on the BeerAdvocate dataset, GGDHSCL improves NDCG@40 by 3.6% and Recall@40 by 3.3%. This result fully demonstrates the effectiveness of GGDHSCL in addressing noisy data and sparse data. We also conduct four supplementary experiments to further verify the contribution of each module to the performance of the recommendation method, the robustness of noise and data sparsity perturbation experiments, and the hyperparameter sensitivity analysis experiments. These experimental results further demonstrate the rationality and effectiveness of the GGDHSCL method, providing strong support for the proposed recommendation method.

[0411] In summary, the GGDHSCL method effectively addresses the challenges faced by existing recommendation systems by introducing a dual-view contrastive framework, a signal alignment loss strategy, and an H-SCL loss function, thereby improving the performance of the recommendation system. Experimental results show that the GGDHSCL method performs best on multiple datasets and significantly improves the handling of noisy data and sparse data. Therefore, we can conclude that the GGDHSCL method is a reasonable and effective recommendation method.

[0412] While embodiments of the application have been shown and described, it is to be understood that the embodiments described are merely divergences of the principles and application of the present application and that numerous modifications, changes, substitutions, and alterations can be made thereto without departing from the spirit and scope of the present application, which is defined by the following claims and their equivalents.

Claims

1. A hard negative sampling contrast recommendation method based on graph generation diffusion model, characterized in that, The method comprises the following steps: A user-item interaction graph is constructed, in which users and items are nodes and interactions between them are edges; then, the user-item interaction graph is encoded by a graph convolutional neural network to obtain user and item node embedding vectors; then, the user and item node embedding vectors are subjected to inner product to obtain recommendation probabilities; finally, the top N items with the highest recommendation probabilities are recommended to the user; The model parameters of the graph convolutional neural network are obtained by training as follows: S1, the node embedding vectors are respectively generated into contrast view 1 and contrast view 2 by an in-line diffusion model view generator and a parameter topological denoising view generator; the in-line diffusion model view generator comprises an in-line diffusion model, and the parameter topological denoising view generator comprises a parameter topological denoising network; S2, contrast learning is performed on the contrast view 1 and the contrast view 2; The model is trained by using a contrast supervision loss optimization loss function with hard negative sample sampling: First, the probability distribution of hard negative sample pair (s, s - ) is calculated, thereby obtaining e i : where q(s,s - ) denotes the probability distribution of hard negative sample pair (s,s - ). E(c | p) represents the expected value of selecting a class c according to the class distribution p; D c (s - |H(s,e i ,τ)) represents the category c, given samples s and e i The probability distribution of negative samples calculated using a hard sampling strategy under τ; s - represents a negative sample; e i represents an embedding representation of the corresponding sample; τ represents a similarity threshold value; H(s, e i , τ) denotes a set of hard negative samples; Then, the embedding representation e of the corresponding sample is retrieved i Computing feature space similarity: where h(s, s + ) denotes the feature space similarity of positive samples; e Τ the transpose of e; e is an embedding representation of all samples; e + is a feature embedding representation for all positive samples; representing the feature space similarity of individual negative samples; is the transpose of e i is the transpose of e a feature embedding representation representing a single negative sample; Y represents a first temperature coefficient, when the similarity is greater than a threshold, i.e., h(s,s i - ) > τ, and the two samples do not belong to the same probability distribution, the two samples are defined as hard negative samples; Finally, a contrast loss function based on hard negative samples is obtained: wherein, represents the hard negative sample contrastive loss function; denotes the mathematical expectation of the positive sample pairs and the mathematical expectation of the negative sample pairs according to the distribution p; k represents the number of negative samples; represents the similarity of the sample to the negative sample; represents the similarity of the sample to the positive sample.

2. The hard negative sampling contrast recommendation method based on graph generated diffusion model according to claim 1, characterized in that, The user-item interaction graph is encoded by the graph convolutional neural network to obtain the node embedding vectors, comprising: the feature representation of the user and item nodes is improved by integrating multiple representation embedding propagation layers: u i and v j The representation embedding vectors obtained by the graph neural network of the l-th layer are defined as and The target node information is propagated from the (l-1)-th layer to the l-th layer. In order to obtain a high-quality node embedding representation, the node embeddings on each propagation layer are summed, and the inner product between the final obtained embedding representations of the user and the item is used to predict the preference degree of the user to the item in personalized recommendation. The specific process of calculating the node embedding vector is as shown in formula (5): wherein, and are u i and v j representation embedding vectors obtained by the graph neural network of the l-th layer. respectively represent the representation embedding vectors of the aggregated information of the user and the sampled anchor adjacent target node through the l-th layer of the graph neural network, and the representation embedding vectors of the aggregated information of the item and the sampled anchor adjacent target node through the l-th layer of the graph neural network. respectively, u i and v j representation embedding vectors obtained by traversing the graph neural network at the l-1 layer; respectively, u i and v j representation embedding vectors obtained by traversing the graph neural network of the l-th layer; and denote the information representation embedding vectors for each user u i and item v j respectively; L represents the number of layers of the graph neural network; The inner product of the user and item node embedding vectors is subjected to inner product to obtain the recommendation probability, which is represented as: wherein is the transpose of 3. The hard negative sampling contrast recommendation method based on graph generated diffusion model according to claim 2, characterized in that, n i (u) , n j (v) The calculation formula is as follows: where E (u) , E (v) are the matrix embedding representations of users and items, respectively. n i (u) , respectively represent the aggregated information of users and items and sampled anchor neighboring target nodes; respectively denote the i-th row of the normalized adjacency matrix the j-th column of the normalized adjacency matrix​ is a normalized adjacency matrix representation computed from the adjacency matrix A of the user-item interaction graph, The computation of d^ is derived as in equation (4): wherein, and are represented as diagonal matrices with respect to users and items, respectively; denotes the normalized adjacency matrix the element in the i-th row and j-th column A i,j An element of the adjacency matrix A representing a user-item interaction graph, in the i-th row and j-th column; L i and L j are the sets of all neighbor nodes of the user and item, respectively; || is an absolute value symbol.

4. The hard negative sampling contrast recommendation method based on graph generated diffusion model according to claim 2, characterized in that, The in-line diffusion model view generator generates the contrast view 1 for contrast learning, comprising the following steps: S2-1, the embedding representation e of the user item interaction is input into a VGAE encoder, and the process is as shown in formula (6): where q φ (x|e) denotes the probability distribution obtained by graph- variational encoding; N represents a Gaussian distribution; x represents that the embedding representation e of the user item interaction is mapped to a low dimension by a parameterized graph variational encoder; μ φ (e) represents a mean of a Gaussian distribution inferred by the parameter set of the neural network; σ φ (e) represents a variance of a Gaussian distribution inferred by the parameter set of the neural network; e From equation (5), we have or μ represents the mean of the Gaussian distribution, and the input data exists in the most possible position in the embedding vector space, σ represents the variance of the Gaussian distribution, and the variance between each dimension is independent, reflecting the dispersion around the mean data, and φ is a parameter set of the VGAE encoder, S2-2, the low-dimensional mapping x output by the VGAE encoder is input into the in-line diffusion model; S2-2-1, forward process: in the forward propagation process, the inline diffusion model iteratively applies K steps of adding noise, where K is a hyperparameter, and the embedding vector is denoted as x k Each data calculation is iterated as in equation (7): where q(x k |x k-1 ) represents the forward process probability distribution; N represents a Gaussian distribution; x k is the noise representation for the kth addition of the embedding vector; β k ∈(0,1) represents the magnitude of the input noise; S2-2-2, reverse process: In the reverse propagation process, the propagation goal is to add iterative over-noise embedding representation x k In the implicit vector space, the original data is reconstructed from the noise, where k = 1, 2,..., K, and the propagation calculation process is as formula (8): p(x k-1 |x k )=N(x k-1 ;W1(x k ,k),W2(x k ,k)) (8) where p(x k-1 |x k ) represents the reverse process probability distribution; N represents a Gaussian distribution; x k-1 is the noise representation for the k-1th embedding vector added; W1 and W2 represent Gaussian parameters of a trainable neural network for predicting a Gaussian distribution; S2-3, the low-dimensional embedding vector reconstructed by the forward and reverse propagation processes of the in-line diffusion model is input into another MLP as a decoder, and the mean and standard deviation of the Gaussian distribution analyzed in the encoding process are also input for decoding to generate a new view.

5. The hard negative sampling contrast recommendation method based on graph generated diffusion model according to claim 1, characterized in that, The parameter topological denoising view generator generates the contrast view 2 for contrast learning, which is represented as: A l = A O Z l (10) wherein A l represents the binary matrix Z l subgraph adjacency matrix after transformation; A represents an adjacency matrix; Z l denotes a binary matrix used to generate the subgraph after the l-th layer GNN processing; ⊙ represents element multiplication.

6. The hard negative sampling contrast recommendation method based on graph generated diffusion model according to claim 5, characterized in that, Z l By the following way: The sparsity neural network l0 regularization method is used to A l To reduce noisy edges, the number of non-zero edges in different GNN layers is directly penalized by a term as in equation (11): wherein is an indicator function, and l=1 represents that the calculation starts from the first layer; (u,v)∈ε represents a set of user item interaction edges of the input subgraph; L represents the number of layers of the graph neural network; ||·||0 represents the l0 norm; Next, a graph attention mechanism was chosen as the denoising layer to learn parameters that control whether or not edges are deleted. If a node u in the training subgraph is taken as the center node, then the neighbor nodes of this node are represented as N. u In the l-th layer of the GNN, node u and its neighbor nodes v∈N are traversed. u calculate As in equation (12): wherein, represents a quality score of the edge between node u and node v calculated under the graph neural network passing through l layers; is a parameterized MLP model l parameterized MLP model; respectively represent the feature vector of the user node and the feature vector of the item node obtained through the l-layer graph neural network; θ l is a trainable parameter containing the weight matrix and bias vector of each layer of the MLP; By a bivariate Concrete distribution in local parametrization gives a The parametric computation process is as formula (13): ∈ ~ Uniform(0, 1), wherein, ∈~Uniform(0,1) represents random sampling from a binary Concrete distribution; ∈ denotes a sample randomly drawn from the Concrete distribution; Uniform(0,1) denotes the Concrete distribution; a preliminary result of the calculation of the retention probability of the edge between node u and node v; the probability value tends to 0 or 1 ; denotes the quality score of the edge between node u and node v under a certain task; τ1∈R + denotes the second temperature coefficient; σ(·) denotes the sigmoid activation function; The Hard Sigmoid function is used again to convert into a binary mask The conversion process is as in equation (14): max() denotes the maximum value; min() denotes the minimum value.

7. The hard negative sampling contrast recommendation method based on graph generated diffusion model according to claim 1, characterized in that, The loss function of contrastive learning is represented as: wherein, represents the contrastive loss function for the user; The contrastive loss function representing the items; The calculation formula is the same as that of the first embodiment, The calculation formula is as follows: wherein, u i , u i′ respectively represent a user in the user set and a negative sample user in the user set; U denotes the set of user nodes; denotes the cosine similarity of the positive sample pair; denotes the cosine similarity of the negative sample pair; τ2 denotes the third temperature coefficient.

8. The hard negative sampling contrast recommendation method based on graph generated diffusion model according to claim 1, characterized in that, In contrastive learning, in order to make the two generated contrastive views 1 and contrastive views 2 align with each other in the training process and adapt to the CF task, the BPR loss function is introduced to constrain the consistency of the two views: For the inline diffusion model view generator, the BPR is calculated by the embedding representation of the user-item interaction encoded by the VGAE encoder in it as formula (22): wherein, represents the total loss function of the inline diffusion model view generator; denotes the KL divergence loss value; represents a distribution loss value, ensuring that the node embedding distribution of the generated graph is similar to the node embedding distribution of the original graph; BPR loss function representing the in-line diffusion model view generator part; For the parameter topology denoising view generator, the BPR is calculated by the node embedding representation obtained by it, and the loss function reconstruction is as formula (23): wherein, represents the total loss function of the parametric topological denoising view generator; denotes the L0 regularization loss function; BPR loss function representing the parameter topology denoising view generator part; The total loss function of the model is: wherein, represents the total loss function of the inline diffusion model view generator; denotes the total loss function of the parametric topological denoising view generator; represents the hard negative sampling loss function; denotes the BPR loss function; λ1 is a hyperparameter that controls the strength of the self-supervised signal; denotes a self-supervised loss function; denotes a regularization term; λ2 is a hyperparameter that controls the regularization strength.

9. The hard negative sampling contrast recommendation method based on graph generated diffusion model according to claim 8, characterized in that, Calculated by the following formula: O denotes all training data; u, i, j represent user, item i, item j, respectively, i≠j; represents the difference between the positive and negative sample prediction scores calculated by the Sigmoid function mapping to 0 and 1, and then taking the negative logarithm to obtain the final loss value; σ denotes the Sigmoid function; respectively represent the user's predicted score representation for the positive and negative sample items.

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