A commodity prediction method integrating commodity association relationships

Abstract

The present invention discloses a commodity prediction method integrating commodity association relationships, which belongs to the technical field of commodity personalized prediction system, and includes the following steps: establishing a user-commodity bipartite graph through the historical interaction records of users on commodities; establishing a commodity-commodity isomorphism graph according to the historical interaction sequences of users on commodities; constructing a twin-tower model for feature learning using a graph convolutional neural network and a graph embedding algorithm; initializing the features of the twin-tower model; training the twin-tower model using an improved BPR loss function to obtain a low-dimensional dense embedding representation of user and commodity nodes after training; calculating the scores of users and test set commodities according to the trained user and commodity embedding representations, and sorting them according to the scores, so as to recommend commodities to users. The present invention can solve the problems of scarcity of user-commodity interaction information and different lengths of interaction sequences in data sets, and improve the accuracy of personalized prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of commodity personalized prediction systems, and in particular to a commodity prediction method integrating commodity association relationships. Background Art

[0002] In recent years, with the advent of the 5G era and the popularization of mobile smart terminals such as mobile phones, the scale of online shopping has continued to expand. As a result, the data generated has grown exponentially, and these data contain rich information. Whether it is merchants or users, it is difficult to obtain key and effective information in the face of huge amounts of data. Therefore, how to quickly and effectively mine valuable information from these data is of great significance to both. As an important means to solve "information overload", the prediction system can predict the products that users may be interested in in the future from massive data through corresponding prediction methods. Therefore, improving the accuracy of the prediction method is the key to the prediction system.

[0003] At present, the prediction system based on heterogeneous graph convolution has achieved good results in the field of product prediction. The system mainly realizes product prediction by constructing a bipartite graph based on user-product. For example, the collaborative filtering recommendation algorithm NGCF based on graph convolution learns the embedded representation of users and products by designing a neural network method that recursively propagates on the graph. Subsequently, LightGCN further optimized and streamlined the model based on NGCF, and concluded through extensive ablation experiments that the network structure, feature transformation and nonlinear activation using symbols to represent user nodes and product nodes did not contribute to the effectiveness of NGCF, but instead reduced the performance of the model. In LightGCN, the author constructed a user-product bipartite graph for representation learning. Specifically, after associating each user (product) with an ID embedding, the embedded representation is propagated on the user-product interaction graph to improve them. The embedding information of different propagation layers is then combined with the weighted sum to obtain the final prediction embedding information.

[0004] However, most current technologies conduct experiments based on the bipartite graph of users and products, and the interaction between users and products is severely data-scarce, that is, among a large number of products, each user has only interacted with a small number of products. Therefore, simply using the user-product relationship for modeling can easily fail to obtain accurate user and product embedding representations due to data scarcity, resulting in insufficient prediction accuracy. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a commodity prediction method that integrates commodity association relationships, which can solve the problems of scarcity of user-commodity interaction information and varying lengths of interaction sequences in the data set, improve the accuracy of personalized predictions, and utilize the user's historical interaction sequence with commodities to construct a commodity-commodity network based on the user-commodity bipartite graph. At the same time, the synchronous distillation method is used in the model training process to improve the model accuracy.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A commodity prediction method integrating commodity association relationships comprises the following steps:

[0008] S1. Establish a user-product bipartite graph through the historical interaction records of users on products;

[0009] S2. Establish a product-product isomorphism graph based on the user's historical interaction sequence with the product;

[0010] S3, constructing a dual-tower model for feature learning based on graph convolutional neural network and graph embedding algorithm;

[0011] S4, initializing the features of the twin tower model;

[0012] S5. Use the improved BPR loss function to train the dual-tower model to obtain low-dimensional dense embedding representations of user and product nodes after training;

[0013] S6. Calculate the scores of users and test set items based on the trained user and item embedding representations, and sort them according to the scores to recommend items to users.

[0014] A further improvement of the technical solution of the present invention is that in S1, the user-product bipartite graph is constructed through each user's historical interaction sequence with the product, and if there is an interaction between the user and a product, an edge is established between the two.

[0015] A further improvement of the technical solution of the present invention is that in S2, the construction of the product-product isomorphism graph is constructed through the historical interaction sequence of each user with the product. If the time interval between two consecutive products in the user's historical interaction sequence with the product is less than the time threshold Δt, there is an edge between the two in the product-product isomorphism graph, and the weight of the edge is the sum of the number of product pairs that meet the above time condition after traversing the historical interaction sequences of all users.

[0016] A further improvement of the technical solution of the present invention is that: in S3, the left side of the dual-tower model is a graph convolution structure based on a user-product bipartite graph, and the right side is a graph embedding structure based on a product-product isomorphic network; the graph convolution neural network adopts a neighbor aggregation method, and the graph embedding structure is constructed using a second-order similarity construction method.

[0017] A further improvement of the technical solution of the present invention is that the second-order similarity construction method specifically includes the following steps:

[0018] B1. Assume that there is an edge e=(i1,i2) between commodity nodes i1 and i2, and the vector of i1(i2) as the central node is The vector as the context node is The probability of generating context node i2 with i1 as the center node is defined as follows:

[0019]

[0020] Where |V| represents the number of nodes in the network, so the distribution probability of other context nodes of node i1 can be expressed as p2(·|i1);

[0021] B2. There is also an empirical distribution probability between commodity nodes i1 and i2 as follows:

[0022]

[0023] in, is the weight of edge e=(i1,i2), N(i1) represents the set of context nodes when i1 is the center node, that is, the set of neighbor nodes of node i1;

[0024] B3. Make the conditional distribution close to the empirical distribution, introduce KL divergence to characterize the distance between the conditional distribution and the empirical distribution, and use the node degree d j To represent the weight of the node in the network, the objective function of the second-order similarity training model is as follows:

[0025]

[0026] B4. By eliminating the ineffective parameters, we can simplify the formula to obtain the following formula, and then minimize the formula to obtain a low-dimensional dense product embedding representation:

[0027]

[0028] A further improvement of the technical solution of the present invention is that the improved BPR loss function adopts a synchronous distillation method based on the traditional BPR loss function, so that the left model and the right model with independent weights learn from each other, so as to achieve the purpose of further optimizing the model.

[0029] A further improvement of the technical solution of the present invention is that the improved BPR loss function is as follows:

[0030]

[0031] Among them, D1={(u,i + ,i - )|(u,i + )∈R + ,(u,i - )∈R -}, R + Indicates that the paired positive training samples are interactive behaviors between users and products, R - Indicates that the paired negative training samples are the users and products that do not have actual interaction behavior; D2 = {(u l ,i l+ )∈R l+}, which means the set of positive sample user-item embedding data pairs obtained by the left model structure, and is a positive sample; similarly, D3 = {(u r ,i r+ )∈R r+} represents the set of positive sample user-item embedding data pairs obtained by the model structure on the right. represents the score of the positive sample of the user on the left side, Indicates the score of the positive sample of the model structure user on the right, through The structures on both sides learn from each other during the back propagation process; σ represents the Sigmoid function, λ||Θ|| 2 is the regularization term, where λ is an adjustable parameter of the regularization term, ||·|| 2 is the two-norm, which prevents overfitting by adjusting the parameter size; Θ in this loss function is actually the initial representation vector of the user and the product, that is, in

[0032] A further improvement of the technical solution of the present invention is that S6 specifically includes the following steps:

[0033] S6.1 The embedding connection layer concatenates the two sets of user embedding representations and product embedding representations obtained from the dual-tower model structure to obtain the final user and product embedding matrix representation, as shown in the following formula:

[0034]

[0035]

[0036] S6.2 calculates the similarity score between the user and the product;

[0037] User i With product i j The similarity score between them is as follows:

[0038]

[0039] in, and Represents user u i With product i j Final embedding representation;

[0040] S6.3 For each user, select the top k items after ranking the scores of all items in the test set for recommendation.

[0041] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0042] 1. The present invention proposes to deeply explore the association relationship between commodities by constructing a commodity-commodity network, so as to more accurately extract the user's preference information for commodities, thereby improving the prediction accuracy.

[0043] 2. The present invention targets the dual-tower model structure and draws on the characteristics of mutual learning between the two models in synchronous distillation. It introduces the difference between the positive sample scores of the left structure and the positive sample scores of the right structure into the BPR loss function, so that the left and right models can effectively learn from each other during the back propagation process.

[0044] 3. The present invention conducts a large number of comparative experiments on three public data sets of Amazon. The results show that the prediction model proposed in the present invention has a certain effect on improving the commodity prediction effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a schematic diagram of the model matching process in the present invention;

[0046] Figure 2 It is the overall model diagram of the present invention;

[0047] Figure 3 is the statistics of model parameters in the present invention;

[0048] Figure 4 is a schematic diagram of a basic collaborative filtering model in the present invention;

[0049] Figure 5 This is a comparison experiment of the number of iterative layers in the present invention;

[0050] Figure 6 This is a schematic diagram of the first-order similarity in the present invention.

[0051] Figure 7It is a schematic diagram of the second-order similarity in the present invention;

[0052] Figure 8 This is a comparison experiment between the first-order similarity and the second-order similarity in the present invention;

[0053] Fig. 9 It is a comparative experiment of different dimensions in the present invention;

[0054] Fig.10 It is a line chart of results of different dimensions in the present invention;

[0055] Fig.11 Schematic diagram of the double tower model sorting algorithm proposed by the present invention;

[0056] Fig.12 The final experimental results of the present invention. DETAILED DESCRIPTION

[0057] The present invention is further described in detail below with reference to the accompanying drawings and embodiments:

[0058] like Figure 1 As shown, a commodity prediction method integrating commodity association relationships includes the following steps:

[0059] S1. Establish a user-product bipartite graph through the historical interaction records of users on products;

[0060] The construction of the user-item bipartite graph is based on the historical interaction sequence of each user with the item. If a user interacts with a certain item, an edge is established between the two. The user interaction sequence is recorded as Among them, U is the user set, user u i The interaction sequence can be written as Based on the user interaction sequence D, construct the user-item bipartite graph G ui =(V ui ,E ui ), where the node set V ui ={U∪I} includes the user set U={u} and the commodity set I={i}, indicating that there is interaction between the user node and the commodity node.

[0061] S2. Establish a product-product isomorphism graph based on the user's historical interaction sequence with the product;

[0062] The product-product isomorphism graph is constructed by constructing the historical interaction sequence of each user on the product. If the time interval between two consecutive products in a user's historical interaction sequence is less than the time threshold Δt, there is an edge between the two in the product-product isomorphism graph. The weight of the edge is the sum of the number of product pairs that meet the above time conditions after traversing the historical interaction sequences of all users. Given the user interaction sequence D, construct the product-product network G.ii =(V ii ,E ii ), where V ii = {I} represents the product set; if the historical interaction product of user u (u∈U) With goods The time difference between adjacent commodities and behaviors in the time series In the commodity With goods Establish an edge relationship, denoted as E ii .

[0063] S3, constructing a dual-tower model for feature learning based on graph convolutional neural network and graph embedding algorithm;

[0064] like Figure 2 As shown in Figure 2, the “double tower” model is denoted as the BiInf model. The left side of the double tower model is a graph convolution structure based on the user-product bipartite graph, and the right side is a graph embedding structure based on the product-product isomorphic network. The model parameters are as follows: Figure 3 As shown; the twin tower model is improved based on the collaborative filtering model. The basic model is as follows Figure 4 shown.

[0065] The graph convolution structure based on the user-product bipartite graph includes bipartite graph construction and embedding propagation layer, and builds a GCN-like propagation architecture in the embedding propagation layer. The graph convolution operation is performed through an iterative method, and finally each node aggregates the neighbor node features. The number of iteration layers is used as an adjustable parameter for experiments. The experimental results are shown in Figure 5 As shown in the figure, the graph convolutional neural network adopts the neighbor aggregation method, abandoning the nonlinear transformation and weight parameters in the traditional graph neural network; the graph embedding algorithm adopts the first-order similarity and second-order similarity construction methods respectively, fully considering the local structural characteristics of the network.

[0066] First, we construct a user-product bipartite graph based on the interaction between users and products. Then, we obtain the embedded representation of user ID and product ID through the embedding layer, and build a GCN-like propagation architecture in the embedding propagation layer. We perform graph convolution operations through iterations, and finally make each node aggregate neighbor node features. The user node aggregation method and the product node aggregation method are shown in the following formula. Specifically, taking user node u as an example, the u node in the k+1th layer of graph convolution aggregates the features of the kth layer of neighbor nodes:

[0067]

[0068]

[0069] Among them, N u represents the neighbor set of user u, N irepresents the neighbor set of product i, represents the feature representation of user u at the k+1th layer, Represents the feature representation of the k-th layer of products.

[0070] In the process of node feature aggregation, the introduction of symmetric normalization terms can effectively prevent the excessive increase of embedding scale during graph convolution. The final embedding representation of users and products obtained from the left side is as follows. The final representation is the weighted sum of the embedding representations of each convolution layer. The embedding representation of users and products obtained by the model structure on the left side is denoted as and

[0071]

[0072]

[0073] in, is an adjustable weight parameter.

[0074] The right side shows the graph embedding structure based on the commodity-commodity isomorphic network. The commodity-commodity isomorphic graph is constructed, and the initial embedding representation of the commodity nodes is obtained through the embedding layer. Then the first-order similarity and second-order similarity are used to train the model. The first-order similarity takes into account that two nodes in the network are directly connected neighbor nodes. Figure 6 As shown in , it means that the relationship between the node pairs is closer and there should be a higher similarity. Based on the graph embedding structure of the commodity-commodity isomorphic network, first, according to the commodity-commodity isomorphic graph constructed by S2, the initial embedding representation of the commodity node is obtained through the embedding layer; then, the graph embedding model is used for training.

[0075] The first-order similarity mainly represents the local similarity structure in the network. The construction of the first-order similarity training model specifically includes the following steps:

[0076] A1. Assume that there is an edge e = (i1, i2) between commodity nodes i1 and i2 in the commodity-commodity isomorphic graph, and the embedding representations of i1 and i2 are and

[0077] A2. Define the probability of co-occurrence between product i1 and product i2 as follows:

[0078]

[0079] A3. Define the empirical distribution between commodity i1 and commodity i2 as follows:

[0080]

[0081] in, represents the weight of edge e=(i1,i2), and W is the sum of the weights of all edges in the graph;

[0082] A4. The goal of the first-order similarity training model is to make the co-occurrence probability as close to the empirical distribution as possible, that is, to minimize the following formula:

[0083]

[0084] Where d represents the distance between the two distributions, and the co-occurrence probability is the probability that two products are interacted with by a certain user.

[0085] A5. In order to characterize the distance between distributions, KL divergence is introduced, so O1 can be simplified to the following formula, and a low-dimensional dense commodity node embedding representation is obtained by minimizing the objective formula:

[0086]

[0087] After building a commodity-commodity network, the relationship between two directly connected nodes is close, but it fails to fully reflect the structural information of the network. Here, the neighbors of a node are used as the context information of the current node. Assuming that two nodes have more common neighbors, that is, the two nodes have more similar context information, then the relationship between the two nodes is closer, such as Figure 7 As shown in the figure. In the actual commodity-commodity network, there are sequential interactions between two directly connected commodity nodes, such as being purchased, clicked, and collected. If only the relationship between two connected commodities is considered, more structural information of the network is ignored. On this basis, the second-order similarity aggregates the information of neighboring nodes and considers the structural information of nodes, that is, the context information of nodes, when calculating the node embedding representation.

[0088] The second-order similarity focuses on the overall structure of the network. The training model construction specifically includes the following steps:

[0089] B1. Assume that there is an edge e=(i1,i2) between commodity nodes i1 and i2, and the vector of i1(i2) as the central node is The vector as the context node is The probability of generating context node i2 with i1 as the center node is defined as follows:

[0090]

[0091] Where |V| represents the number of nodes in the network, so the distribution probability of other context nodes of node i1 can be expressed as p2(·|i1);

[0092] B2. There is also an empirical distribution probability between commodity nodes i1 and i2 as follows:

[0093]

[0094] in, is the weight of edge e=(i1,i2), N(i1) represents the set of context nodes when i1 is the center node, that is, the set of neighbor nodes of node i1;

[0095] B3, using the same method as the first-order similarity, the conditional distribution is close to the empirical distribution, KL divergence is introduced to characterize the distance between the conditional distribution and the empirical distribution, and the node degree d is used j To represent the weight of the node in the network, the objective function of the second-order similarity training model can be obtained as follows:

[0096]

[0097] B4. Finally, the following formula is obtained by eliminating irrelevant parameters and minimizing the formula to obtain a low-dimensional dense product embedding representation:

[0098]

[0099] After obtaining the embedded representation of the product node through the first-order similarity or second-order similarity, the average of all the embedded representations of the products interacted by the user is taken as the embedded representation of the user node, as shown in the following formula:

[0100]

[0101] Among them, S(u j ) represents user u j A collection of historical interactive products.

[0102] Finally, the embedding representations of users and products are obtained from the tower structure on the left, which are recorded as The first-order similarity and second-order similarity calculation results are compared. Figure 8 As shown, it can be seen that the modeling effect is better using second-order similarity, so the graph embedding algorithm uses the second-order similarity construction method.

[0103] S4, initializing the features of the twin tower model;

[0104] Feature initialization is to give all user IDs and product IDs an initial embedding representation of a certain dimension. All users and products in the twin tower model are numbered as nodes, and the embedding representation of each node is initialized. At the same time, the initialization dimension can be adjusted through the evaluation index as an adjustable parameter. The experimental results of different dimensional parameters are shown in the figure below. Fig. 9 , Fig.10 shown.

[0105] S5. Use the improved BPR loss function to train the dual-tower model to obtain low-dimensional dense embedding representations of user and product nodes after training;

[0106] The experiment uses the Bayesian Personalized Ranking (BPR) loss, which is widely used in recommendation systems. This loss function is a personalized ranking algorithm based on Bayesian posterior optimization. The core is to model the user's relative preferences and finally calculate the items that the user may be interested in based on the user's preferences. The improved BPR loss function, based on the traditional BPR loss function, uses the synchronous distillation method to allow the left model and the right model with independent weights to learn from each other, so as to achieve the purpose of further optimizing the model. The improved BPR loss function is as follows:

[0107]

[0108] Among them, D1={(u,i + ,i - )|(u,i + )∈R + ,(u,i - )∈R -}, R + Indicates that the paired positive training samples are interactive behaviors between users and products, R - Indicates that the paired negative training samples are the users and products that do not have actual interaction behavior; D2 = {(u l ,i l+ )∈R l+}, which means the set of positive sample user-item embedding data pairs obtained by the left model structure, and is a positive sample; similarly, D3 = {(u r ,i r+ )∈R r+} represents the set of positive sample user-item embedding data pairs obtained by the model structure on the right. represents the score of the positive sample of the user on the left side, Indicates the score of the positive sample of the model structure user on the right, through The structures on both sides learn from each other during the back propagation process; σ represents the Sigmoid function, λ||Θ|| 2 is the regularization term, where λ is an adjustable parameter of the regularization term, ||·|| 2 is the two-norm, which prevents overfitting by adjusting the parameter size; Θ in this loss function is actually the initial representation vector of the user and the product, that is, in

[0109] Therefore, the trainable parameters in this model are the initial vector representations of users and products, and the stochastic gradient descent method is used to optimize the model.

[0110] S6. Calculate the scores of the user and the items in the test set based on the trained user and item embedding representations, and sort them according to the scores to recommend items to the user.

[0111] The low-dimensional dense embedding representation of users and products obtained by model training for the dual-tower model is used to calculate the scores of users and products in the test set. Sort by score and select the top k products to recommend to the user.

[0112] The widely used Amazon dataset and Last.fm music dataset were used for the experiment. The Amazon dataset uses Vedio partitioned products and Automatic partitioned products. The above datasets all include user ID, product ID, and interaction timestamp information. For each user, the products they purchased are sorted by time, with the first 80% of the time as the training set and the last 20% as the test set. The statistical results of the dataset are shown in Table 1.

[0113] Table 1 Dataset statistics

[0114]

[0115] The bottom layer of the dual-tower model structure is the embedding connection layer and the recommendation prediction layer. The embedding connection layer concatenates the two sets of user embedding representations and product embedding representations obtained from the dual-tower model structure to obtain the final user and product embedding matrix representation, and calculates the similarity score between users and products through the recommendation prediction layer, and recommends users based on the score. The overall model flow chart is shown below: Fig.11 As shown, the specific steps include:

[0116] S6.1 The embedding connection layer concatenates the two sets of user embedding representations and product embedding representations obtained from the dual-tower model structure to obtain the final user and product embedding matrix representation, as shown in the following formula:

[0117]

[0118]

[0119] S6.2 calculates the similarity score between the user and the product;

[0120] As user u i With product i j For example, the similarity score between the two is as follows:

[0121]

[0122] in, and Represents user u i With product i j Final embedding representation;

[0123] S6.3 For each user, select the first k items after ranking the scores of all items in the test set for recommendation. The final result is shown as follows Fig.12 shown.

[0124] In summary, the problem of scarce user-item interaction information and varying lengths of interaction sequences in the data set can be solved, the accuracy of personalized prediction can be improved, and the item-item network is constructed based on the user-item bipartite graph using the user's historical interaction sequence with the item. At the same time, the synchronous distillation method is used in the model training process to improve the model accuracy.

Claims

1. A commodity prediction method integrating commodity association relationships, characterized in that: The following steps are involved: S1. Establish a user-product bipartite graph through the historical interaction records of users on products; S2. Establish a product-product isomorphism graph based on the user's historical interaction sequence with the product; S3, using graph convolutional neural network and graph embedding algorithm to build a dual-tower model for feature learning; In S3, the left side of the dual-tower model is a graph convolution structure based on a user-product bipartite graph, and the right side is a graph embedding structure based on a product-product isomorphic network; the graph convolution neural network adopts a neighbor aggregation method, and the graph embedding structure is constructed using a second-order similarity construction method; S4, initializing the features of the twin tower model; S5. Use the improved BPR loss function to train the dual-tower model to obtain low-dimensional dense embedding representations of user and product nodes after training; The improved BPR loss function is as follows: Among them, D1={(u,i + ,i - )|(u,i + )∈R + ,(u,i - )∈R - }, R + Indicates that the paired positive training samples are interactive behaviors between users and products, R - Indicates that the paired negative training samples mean that there is no actual interaction between the user and the product; D2={(u l ,i l+ )∈R l+ }, which means the set of positive sample user-item input data pairs obtained by the left model structure, and is a positive sample; similarly, D3 = {(u r ,i r+ )∈R r+ } represents the set of positive sample user-item embedding data pairs obtained by the model structure on the right. represents the score of the positive sample of the user on the left side, Indicates the score of the positive sample of the model structure user on the right, through The structures on both sides learn from each other during the back propagation process; σ represents the Sigmoid function, λ||Θ|| 2 is the regularization term, where λ is an adjustable parameter of the regularization term, ||·|| 2 is the two-norm, which prevents overfitting by adjusting the parameter size; Θ in this loss function is actually the initial representation vector of the user and the product, that is, in S6. Calculate the scores of users and test set items based on the trained user and item embedding representations, and sort them according to the scores to recommend items to users.

2. A commodity prediction method integrating commodity association relationships according to claim 1, characterized in that: In S1, the user-item bipartite graph is constructed through each user's historical interaction sequence with a product. If a user interacts with a product, an edge is established between the two.

3. The commodity prediction method integrating commodity association relationships according to claim 1, characterized in that: In S2, the product-product isomorphism graph is constructed by constructing the historical interaction sequence of each user with respect to the product. If the time interval between two consecutive products in the historical interaction sequence of the user with respect to the product is less than the time threshold Δt, there is an edge between the two in the product-product isomorphism graph, and the weight of the edge is the sum of the number of product pairs that meet the above time condition after traversing the historical interaction sequences of all users.

4. The commodity prediction method integrating commodity association relationships according to claim 1, characterized in that: The second-order similarity construction method specifically comprises the following steps: B1. Assume that there is an edge e=(i1,i2) between commodity nodes i1 and i2, and the vector of i1(i2) as the central node is The vector as the context node is The probability of generating context node i2 with i1 as the center node is defined as follows: Where |V| represents the number of nodes in the network, so the distribution probability of other context nodes of node i1 can be expressed as p2(·|i1); B2. There is also an empirical distribution probability between commodity nodes i1 and i2 as follows: in, is the weight of edge e=(i1,i2), N(i1) represents the set of context nodes when i1 is the center node, that is, the set of neighbor nodes of node i1; B3. Make the conditional distribution close to the empirical distribution, introduce KL divergence to characterize the distance between the conditional distribution and the empirical distribution, and use the node degree d j To represent the weight of the node in the network, the objective function of the second-order similarity training model is as follows: B4. By eliminating the ineffective parameters, we can simplify the formula to obtain the following formula, and then minimize the formula to obtain a low-dimensional dense product embedding representation:

5. The commodity prediction method integrating commodity association relationships according to claim 1, characterized in that: The improved BPR loss function is based on the traditional BPR loss function and adopts a synchronous distillation method to allow the left model and the right model with independent weights to learn from each other, so as to achieve the purpose of further optimizing the model.

6. The commodity prediction method integrating commodity association relationships according to claim 1, characterized in that: S6 specifically includes the following steps: S6.1 The embedding connection layer concatenates the two sets of user embedding representations and product embedding representations obtained from the dual-tower model structure to obtain the final user and product embedding matrix representation, as shown in the following formula: S6.2 calculates the similarity score between the user and the product; User i With product i j The similarity score between them is as follows: in, and Represents user u i With product i j Final embedding representation; S6.3 For each user, select the top k items after ranking the scores of all items in the test set for recommendation.

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