An information recommendation method based on graph convolution neural collaborative filtering

Abstract

The present invention provides an information recommendation method based on graph convolution neural collaborative filtering, comprising the following steps: S1: Collect user behavior data and the attribute content of users and items; S2: If the collected behavior is explicit scoring, construct a user-user graph according to the scoring information of users for items, calculate the similarity between users and users, items and items to construct a user-user graph, an item-item graph; If the collected behavior information is only implicit interaction information such as browsing and clicking, construct a user-item graph: S3: Perform graph convolution operation on the constructed relationship graph to obtain the feature vectors of the nodes of users and items; S4: Fully connect the feature vectors of the nodes of users and items with the attribute features of users and items respectively; S5: Use the obtained feature vectors of the nodes of users and items as the input layer of the neural collaborative filtering algorithm framework, so as to make predictions and perform information recommendation according to the prediction results.

Description

Technical Field

[0001] The present invention relates to the technical field of information recommendation, and particularly to an information recommendation method based on graph convolutional neural collaborative filtering. Background Art

[0002] According to the 45th Statistical Report on the Development of China's Internet Network, as of March 2020, the scale of China's netizens has reached 904 million, and the Internet penetration rate has reached 64.5%. The user scale and usage rate of various Internet applications are in a continuous growth mode. As the Internet gradually integrates into people's daily lives, traditional search engines can no longer meet people's needs. In order to quickly and accurately predict users' preferences, the recommendation system plays a very important role in helping users find the items they like in the vast amount of data. However, the recommendation system still faces some problems at present.

[0003] (1) At present, the recommendation of the recommendation system mainly focuses on collecting users' rating data. However, some users are reluctant to leave ratings due to concerns about privacy leakage or unwillingness to waste their time, resulting in data sparsity.

[0004] (2) The traditional matrix factorization collaborative filtering algorithm uses a simple inner product method to calculate the complex features of users and items in a low-dimensional space, and cannot deeply learn the relationship between the features of users and items.

[0005] (3) Traditional recommendation methods do not consider users' attributes, items' attributes, the interaction relationship between users, and the interaction relationship between items enough. Summary of the Invention

[0006] In order to overcome the above problems existing in the prior art, the purpose of the present invention is to provide an information recommendation method based on graph convolutional neural collaborative filtering, which uses a convolutional network model to process, uses the interaction logs of users and items, models the intensity of the interaction behavior between users as the edges in the relationship representation, further obtains an interaction relationship graph, superimposes spectral graph convolution on the graph to generate user and item node feature vectors, and in order to improve the generalization ability of the model, combines the own attribute features of users and items to obtain the feature vectors of users and items, and uses the neural collaborative filtering algorithm (NCF) to map the feature vectors of users and items to a very high-dimensional space, and obtains more accurate predictions by obtaining more information from the features.

[0007] The purpose of the present invention is to provide an information recommendation method based on graph convolutional neural collaborative filtering, including the following steps:

[0008] S1: Collect user behavior data and the attribute content of users and items;

[0009] S2: If the collected behavior is explicit scoring, construct a user-user graph based on the scoring information of the user for the item, calculate the similarity between users and between items and items to construct a user-user graph and an item-item graph; if the collected behavior information only includes implicit interaction information such as browsing and clicking, construct a user-item graph;

[0010] S3: Perform graph convolution operations on the constructed relational graph to obtain the feature vectors of the nodes of users and items;

[0011] S4: Fully connect the feature vectors of the nodes of users and items with the attribute features of users and items respectively;

[0012] S5: Use the obtained feature vectors of the nodes of users and items as the input layer of the neural collaborative filtering algorithm framework, so as to make predictions and perform information recommendation according to the prediction results.

[0013] Preferably, the user behavior data in S1 includes browsing, purchase and scoring information; the browsing, purchase and scoring information includes the age, gender and occupation of the user; the category of the item; the score of the user for the item within the range of 1-5; and the purchase, browsing times and click times in the user's browsing behavior.

[0014] Preferably, before implementing S2, it further includes the step of data preprocessing, where the preprocessing includes: converting the 'F' and 'M' in the gender field to 0 and 1; dividing the age into paragraphs, including the following: 1: "less than 18 years old"; 18: "18-24"; 25: "25-34"; 35: "35-44"; 45: "45-49"; 50: "50-55"; 56: "56+"; converting the Age field to 7 consecutive numbers 0-6; and assigning a multi-value attribute to the item category field and using Multi-Hot encoding.

[0015] Preferably, the step S3 includes:

[0016] S31, construct a user-user graph;

[0017] S32, construct an item-item graph;

[0018] S33, construct a user-item graph.

[0019] S34, construct a degree matrix.

[0020] Preferably, the step S31 includes:

[0021] S311, calculate the user-user similarity: use the Person correlation coefficient to measure user u i and user u iThe similarity relationship sim(u i , u j ), where is the set of items jointly rated by users u i and u j ;

[0022] S312. Construct the adjacency matrix A u of the user;

[0023] The step S311 includes:

[0024] S3111. Calculate the average score u u of each user u using the ratings of each user:

[0025]

[0026] S3112. Calculate the Pearson correlation coefficient between users u i and u j as follows:

[0027]

[0028] In the step S312, the adjacency matrix A u is a symmetric matrix with diagonal elements of 0. The element e(u i , u j ) in the matrix represents the edge weight between each pair of users, which is the user u i and u j , that is, sim(u i , u j )

[0029]

[0030] The step S312 uses an adjusted cosine function to define the similarity between item i and item j, including:

[0031] S3121. Mean centering: The rating of item j by user u:

[0032] s uj = r uj - μ u (4):

[0033] S3122. Calculate the similarity between item i and item j

[0034]

[0035] Preferably, the step S32 includes:

[0036] S321. Define the item-item similarity;

[0037] S322. Construct the adjacency matrix A of the items v ; The adjacency matrix A of the items v is a symmetric matrix with diagonal elements being 0.

[0038] The e(v i , v j ) in the matrix represents the weight on the edge between item i and item j, that is, sim(i, j), where

[0039]

[0040] Preferably, the step S33 includes:

[0041] S331. When the user has explicit rating information, the user-item rating matrix R ∈ R M×N (M represents the number of users, N represents the number of items), R ∈ {1, 2, 3, 4, 5}; Construct a user-item interaction graph, i.e., a (0, 1) matrix, for each level of rating. That is, when r = 1, if user i has rated item j, then r ij = 1, otherwise r ij = 0;

[0042]

[0043] S332. When the user only has implicit behavior, there is only information on the user's browsing and purchasing behavior of the items, without explicit ratings. Among them, R ∈ {0, 1} M×N , R represents whether there is an interaction between the user and the item. Therefore, there is only one user-item interaction graph. That is, if user i has had interaction information with item j, then r ij = 1, otherwise r ij = 0, and the adjacency matrix A implicit is as follows:

[0044]

[0045] Preferably, the step S34 includes: Calculate the degree matrix D through the adjacency matrix A. The degree matrix D is a diagonal matrix, and the matrix element is the sum of the corresponding row and column in the adjacency matrix A, that is, D ii = ΣjA ij

[0046]

[0047] Calculate the degree matrix D using the user adjacency matrix A u through formula (9), and calculate the degree matrix D using the item adjacency matrix A u , and calculate the degree matrix D using the item adjacency matrix A v ​v ; in the explicit case, utilize the adjacency matrix A of user-item ratings r Calculate r degree matrices D r ; utilize the adjacency matrix A of implicit behavior implict Calculate the degree matrix D implicit .

[0048] Preferably, the step S3 includes:

[0049] S31, regularization:

[0050] In the graph convolution operation, multiply the Laplacian matrix by the eigenvector, perform a regularization operation on the Laplacian matrix, and obtain a symmetric and normalized Laplacian matrix, that is:

[0051]

[0052] The above formula (10) only contains the information of neighbor nodes. In order to include the information of the node itself, a unit matrix I needs to be added to this formula N , that is:

[0053]

[0054] S32: Perform convolution operation:

[0055] Use X to represent the feature vector matrix of user / item nodes on the relationship graph, and Θ as the convolution parameter. Then the single-layer convolution operation on the relationship graph G can be expressed as:

[0056]

[0057] The update of the hidden layer when multiple convolutional layers are stacked is:

[0058]

[0059] where the input X of the latter layer is the output H of the upper layer t , and the corresponding convolutional layer parameter for each layer is Wt.

[0060] Preferably, the step S4 includes:

[0061] S41, use a fully connected layer to combine the user and item node feature vectors obtained by graph convolution with the attribute feature vectors of users and items respectively;

[0062] S42, use a fully connected layer to connect these two different pieces of information:

[0063] Z = σ(W[Z node , Z attribute +b) (14)

[0064] Preferably, a neural network-based matrix factorization framework NCF is used to implement S5 in combination with GMF and MLP, where GMF is a traditional matrix factorization layer, and its output calculation is shown in the following formula (15):

[0065]

[0066] where p i represents the feature vector of user i, q j represents the feature vector of item j, and ⊙ represents the operation symbol of element-wise multiplication of vectors;

[0067] where MLP is a multi-layer perceptron, and relu is used as the activation function between MLP layers. The calculation is as follows:

[0068]

[0069] Finally, the latent vectors learned by GMF and MLP are fully connected, and the output is transformed into a vector between 0 and 1 using logistic.

[0070]

[0071] Advantages of the present invention:

[0072] (1) When there is a lack of explicit user rating information, implicit interaction information can be used for prediction and recommendation.

[0073] (2) Based on the recommendation model for predicting ratings of user and item features, the improvement is made by adding user interaction behaviors and the relationship expression between items, mining the deep-level relationship graphs between users and users, and between items and items beyond user ratings, enhancing the robustness and personalized adaptation ability of the recommendation model.

[0074] (3) The existing Nonlinear Neural Collaborative Filtering (NCF) maps the feature vectors of users and items to a very high-dimensional space to make accurate predictions. However, the auxiliary information is not considered in the recommendation process of the model. The present invention uses a graph convolutional model to fuse the auxiliary information and rating information into the node feature vectors of users and items. At the same time, the attribute content of users and items is also added as auxiliary information, and the node feature vectors of users and items after graph convolution are combined as the input of NCF, improving the generalization ability of the model and enhancing the accuracy of the recommendation system. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Att Figure 1 is a schematic diagram of the process of the recommendation system according to an embodiment of the present invention;

[0076] AttFigure 2 Schematic diagram of the explicit recommendation sub - graph process according to an embodiment of the present invention;

[0077] Appendix Figure 3 Schematic diagram of the implicit recommendation sub - graph process according to an embodiment of the present invention;

[0078] Appendix Figure 4 NCF framework diagram according to an embodiment of the present invention. Detailed implementation manners

[0079] The following will describe the detailed implementation manners of the present invention in conjunction with the accompanying drawings, but it is not used to limit the protection scope of the present invention.

[0080] Refer to Figure 1 The information recommendation method based on graph convolution neural collaborative filtering in the shown embodiment includes the following steps:

[0081] S1: Collect user behavior data (including information such as browsing, purchasing, and rating) and the attribute content of users and items;

[0082] S2: If the collected behavior is explicit rating, construct a user - user graph according to the rating information of users for items, calculate the similarity between users and users, and between items and items to construct a user - user graph and an item - item graph; if the collected behavior information is only implicit interaction information such as browsing and clicking, construct a user - item graph;

[0083] S3: Perform graph convolution operations on the constructed relationship graph to obtain the feature vectors of the nodes of users and items;

[0084] S4: Fully connect the feature vectors of the nodes of users and items with the attribute features of users and items respectively;

[0085] S5: Use the obtained feature vectors of the nodes of users and items as the input layer of the neural collaborative filtering algorithm framework, and then make predictions, and perform information recommendation according to the prediction results.

[0086] The specific implementation process of this embodiment includes:

[0087] I. The collected user browsing records and the attribute features of user items

[0088] Users: Age, gender, occupation

[0089] Items: Category

[0090] User ratings for items: 1 - 5

[0091] User browsing behaviors: Purchasing, browsing times, clicking times, etc.

[0092] II. Data pre - processing

[0093] Gender field: Need to convert 'F' and 'M' to 0 and 1

[0094] Age: There are several ways to divide age into paragraphs:

[0095] 1: "Under 18 years old"

[0096] 18: 18-24

[0097] 25: 25-34

[0098] 35: 35-44

[0099] 45: 45-49

[0100] 50: 50-55

[0101] 56: 56+

[0102] Age field: Convert to 7 consecutive numbers 0-6

[0103] Item category field: multi-value attribute, using Multi-Hot encoding

[0104] 3. Build a relationship diagram

[0105] 1. Build a User-User Graph

[0106] 1. User-user similarity

[0107] In this embodiment, the Person correlation coefficient (Pearson correlation coefficient) can be used to measure the user u i and user u j The similarity relationship sim(u i ,u j ),in Is user u i and u j The set of items that are rated jointly by two or more people.

[0108] The first step is to use the ratings of each user u to calculate the average score of each user u u :

[0109]

[0110] The second step is to calculate user u i and u j The Pearson correlation coefficient between them is as follows:

[0111]

[0112] 2. Construct the user's adjacency matrix Au

[0113] A u is a symmetric matrix with diagonal elements being 0, and the element e(u i , u j ) in the matrix represents the edge weight between each pair of users, that is, sim(u i and u j ), namely sim(u i , u j )

[0114]

[0115] (II) Constructing the item-item graph

[0116] 1. Defining the item-item similarity

[0117] In this embodiment, the adjusted cosine function is used to define the similarity between item i and item j.

[0118] The first step: Mean centering: The rating of user u for item j:

[0119] s uj = r uj - μ u (4)

[0120] The second step: Calculating the similarity between item i and item j

[0121]

[0122] 2. Constructing the adjacency matrix A of items v

[0123] A v is a symmetric matrix with diagonal elements being 0, and e(v i , v j ) in the matrix represents the weight on the edge between item i and item j, that is, sim(i, j), where

[0124]

[0125] (III) Constructing the user-item graph

[0126] 1. As Figure 2 shown, when the user has explicit rating information

[0127] the user-item rating matrix R ∈ R M×N (M represents the number of users, N represents the number of items), R ∈ {1, 2, 3, 4, 5}

[0128] Construct a user-item interaction graph, i.e., a (0, 1) matrix, for each level of rating. That is, when r = 1, if user i has rated item j, then r ij = 1; otherwise, r ij = 0.

[0129]

[0130] 2. When there is no explicit rating from the user

[0131] As Figure 3 shown, when there is only implicit behavior, there is only information on user behavior such as browsing and purchasing of items, without explicit ratings. Among them, R ∈ {0, 1} M×N , where R represents whether there is an interaction between the user and the item. Therefore, there is only one user-item interaction graph. That is, if user i has had interaction information with item j, then r ij = 1; otherwise, r ij = 0. The adjacency matrix A implicit is as follows.

[0132]

[0133] (IV) Construct the degree matrix

[0134] The degree matrix D can be calculated through the adjacency matrix A. It is a diagonal matrix, and the matrix elements are the sum of the corresponding rows and columns in the adjacency matrix A, i.e., D ii = ∑jA ij

[0135]

[0136] Therefore, through formula (9), the degree matrix D is calculated using the user adjacency matrix A u , the degree matrix D can be calculated using the item adjacency matrix A u ; the degree matrix D can be calculated using the adjacency matrix A of user-item ratings v ; r degree matrices D can be calculated using the adjacency matrix A of implicit behavior v ; (explicit) using the adjacency matrix A of implicit behavior r r , the degree matrix D can be calculated(explicit) Using the adjacency matrix A of implicit behavior implict , the degree matrix D can be calculated implicit .

[0137] IV. Graph Convolution

[0138] (I) Regularization

[0139] In graph convolution operations, the Laplacian matrix needs to be multiplied by the eigenvector. To avoid changing the distribution of the features, a regularization operation needs to be performed on the Laplacian matrix to obtain a symmetric and normalized Laplacian matrix, i.e.:

[0140]

[0141] Equation (10) above only contains the information of neighbor nodes. To include the information of the node itself, an identity matrix I needs to be added to this equation. N , that is:

[0142]

[0143] (2) Convolution operation

[0144] Using X to represent the feature vector matrix of user / item nodes on the relational graph, and Θ as the convolution parameter, then the single-layer convolution operation on the relational graph G can be expressed as:

[0145]

[0146] When multiple convolution layers are stacked, the update of the hidden layer is:

[0147]

[0148] where the input X of the latter layer is the output H of the upper layer. t , and the corresponding convolution layer parameter for each layer is Wt.

[0149] V. User and item feature vectors

[0150] Method: Use a fully connected layer to combine the user and item node feature vectors obtained from graph convolution with the attribute feature vectors of users and items respectively;

[0151] Use a fully connected layer to combine these two different types of information.

[0152] Z = σ(W[Z node , Z attribute +b) (14)

[0153] VI. Prediction

[0154] As Figure 4 shown, this embodiment uses a neural network-based matrix factorization framework NCF, combining GMF and MLP.

[0155] (1) GMF is a traditional matrix factorization layer, and its output calculation is as follows:

[0156]

[0157] where p i represents the feature vector of user i, q j represents the feature vector of item j, and ⊙ represents the operation symbol of element-wise multiplication of vectors.

[0158] The MLP is a multi-layer perceptron (the relu function is used as the activation function between MLP layers).

[0159]

[0160] Finally, the latent vectors learned by the two are fully connected, and the output is transformed into a vector between 0 and 1 using logistic.

[0161]

[0162] Adopt the method of this embodiment:

[0163] (1) When there is a lack of explicit user rating information, implicit interaction information can be used for prediction and recommendation.

[0164] (2) Improve the recommendation model based on the user and the recommendation model for predicting item features, add user interaction behaviors and the relationship expression between items, mine the deep-level relationship graphs between users and between items beyond user ratings, and enhance the robustness and personalized adaptation ability of the recommendation model.

[0165] (3) The existing non-linear neural collaborative filtering (NCF) maps the feature vectors of users and items to a very high-dimensional space to make accurate predictions. However, auxiliary information is not considered in the recommendation process of the model. The present invention uses a graph convolutional model to fuse the auxiliary information and rating information into the node feature vectors of users and items. At the same time, the attribute content of users and items is also added as auxiliary information, and the node feature vectors of users and items after graph convolution are combined as the input of NCF, improving the generalization ability of the model and the accuracy of the recommendation system.

[0166] The technical solutions provided by the embodiments of the present invention have been introduced in detail above. Specific examples are used in this article to elaborate on the principles and implementation manners of the embodiments of the present invention. The descriptions of the above embodiments are only applicable to help understand the principles of the embodiments of the present invention; at the same time, those of ordinary skill in the art will have changes in the specific implementation manners and application scopes according to the embodiments of the present invention. In summary, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. An information recommendation method based on graph convolutional neural collaborative filtering, characterized in that It includes the following steps: S1: Collect user behavior data and the attribute content of users and items; S2: If the collected behavior is explicit scoring, construct a user-item graph based on the scoring information of users for items, calculate the similarity between users and users, and between items and items to construct a user-user graph and an item-item graph; if the collected behavior information is only implicit interaction information such as browsing and clicking, construct a user-item graph; S3: Perform graph convolution operation on the constructed relationship graph to obtain the feature vectors of the nodes of users and items; S4: Fully connect the feature vectors of the nodes of users and items with the attribute features of users and items respectively; S5: Use the obtained feature vectors of the nodes of users and items as the input layer of the neural collaborative filtering algorithm framework to perform prediction, and make information recommendations according to the prediction results.

2. The information recommendation method based on graph convolutional neural collaborative filtering according to claim 1, characterized in that: The user behavior data in S1 includes browsing, purchase, and scoring information; the browsing, purchase, and scoring information includes the age, gender, and occupation of users; the category of items; the score of users for items within the range of 1-5; and the purchase, browsing times, and click times in the user's browsing behavior.

3. An information recommendation method based on graph convolutional neural collaborative filtering according to claim 1, characterized in that: Before implementing S2, it also includes the step: data preprocessing, where the preprocessing includes: converting 'F' and 'M' in the gender field to 0 and 1; dividing the age into paragraphs, including the following: 1: "less than 18 years old"; 18: "18-24"; 25: "25-34"; 35: "35-44"; 45: "45-49"; 50: "50-55"; 56: "56+"; converting the Age field to 7 consecutive numbers from 0 to 6; and endowing the item category field with multi-value attributes and using Multi-Hot encoding.

4. The information recommendation method based on graph convolutional neural collaborative filtering according to claim 1, characterized in that The step S3 includes: S31, construct a user-user graph; S32, construct an item-item graph; S33, construct a user-item graph; S34, construct a degree matrix.

5. The information recommendation method based on graph convolutional neural collaborative filtering according to claim 4, wherein The step S31 includes: S311, Calculate the user-user similarity: Use the Person correlation coefficient to measure the similarity relationship sim(u i and user u j ), where i u j ) between, and is the set of items jointly rated by user u i and u j ; S312, construct the adjacency matrix A of the user u ; The step S311 includes: S3111, calculate the average score $\overline{u}$ of each user $u$ using the ratings of each user $u$ u : S3112, calculate the user u i and u j The Pearson correlation coefficient between them is as follows: The adjacent matrix A in the step S312 u is a symmetric matrix with diagonal elements being 0, and the element e(u i , u j ) in the matrix represents the edge weight between each pair of users u i and u j , that is, sim(u i , u j ) The step S312 uses an adjusted cosine function to define the similarity between item i and item j, including: S3121, mean centering: the score of user u for item j: s uj = r uj - μ u (4); S3122, calculate the similarity between item i and item j 6. The information recommendation method based on graph convolutional neural collaborative filtering according to claim 4, characterized in that The step S32 includes: S321, define item-item similarity; S322, construct the adjacency matrix A of the items v ; the adjacency matrix A of the items v is a symmetric matrix with diagonal elements being 0, e(v i , v j ) in the matrix represents the weight on the edge between item i and item j, that is, sim(i, j), where 7. The information recommendation method based on graph convolutional neural collaborative filtering according to claim 4, characterized in that The step S33 includes: S331. When the user has explicit rating information, the user-item rating matrix $R \in \mathbb{R}$ M×N (where $M$ represents the number of users and $N$ represents the number of items), $R \in \{1, 2, 3, 4, 5\}$; construct a user-item interaction graph, i.e., a $(0, 1)$ matrix, for each level of rating. That is, when $r = 1$, if user $i$ has rated item $j$, then $r$ ij $= 1$, otherwise $r$ ij $= 0$. S332, when the user only has implicit behavior, there is only information on the user's browsing and purchasing behavior of goods, without explicit ratings, where R ∈ {0, 1} M×N , R represents whether there is an interaction between the user and the item. Therefore, it only contains a user-item interaction graph, that is, if user i has interacted with item j, then r ij = 1, otherwise r ij = 0, the adjacency matrix A implicit is as follows: 。 8. An information recommendation method for neural collaborative filtering based on graph convolution according to claim 4, characterized in that The step S34 includes: a degree matrix D can be calculated through the adjacency matrix A, which is a diagonal matrix, and the matrix element is the sum of the corresponding row and column in the adjacency matrix A, that is, D ii = ∑jA ij ; Calculate the degree matrix D using the user adjacency matrix A through formula (9). u Calculate the out-degree matrix D using the item adjacency matrix A u ; In the explicit case, calculate r degree matrices D using the adjacency matrix A of user-item ratings v ; Calculate the degree matrix D using the adjacency matrix A of implicit behavior v ; r ; Calculate r degree matrices D r ; Calculate the degree matrix D using the adjacency matrix A of implicit behavior implict ; implicit .

9. The information recommendation method based on graph convolutional neural collaborative filtering according to claim 1, wherein The step S3 includes: S31, regularization: In the graph convolution operation, multiply the Laplacian matrix by the feature vector, perform regularization operation on the Laplacian matrix to obtain a symmetric and normalized Laplacian matrix, that is: Only the information of neighbor nodes is included in the above formula (10). To include the information of the node itself, an identity matrix I needs to be added to this formula N , that is: S32: perform convolution operation: Use X to represent the feature vector matrix of user / item nodes on the relationship graph, and Θ as the convolution parameter. Then the single-layer convolution operation on the relationship graph G can be expressed as: The update of the hidden layer when multiple convolution layers are stacked is: where the input X of the latter layer is the output H of the upper layer t , and the corresponding convolutional layer parameter for each layer is Wt.

10. The information recommendation method based on graph convolutional neural collaborative filtering according to claim 1, wherein The step S4 includes: S41, use a fully connected layer to combine the feature vectors of user and item nodes obtained by graph convolution with the attribute feature vectors of users and items respectively; S42, use a fully connected layer to connect these two different pieces of information: Z = σ(W[Z node , Z attribute + b) (14) Use a neural network-based matrix factorization framework NCF to implement the S5 by combining GMF and MLP, where GMF is a traditional matrix factorization layer and its output calculation is as shown in the following formula (15): where p i represents the feature vector of user i, q j represents the feature vector of item j, represents the operation symbol for multiplying vector elements; where MLP is a multi-layer perceptron, and relu is used as the activation function between MLP layers, and the calculation is as follows: Finally, fully connect the latent vectors learned by the GMF and MLP, and use logistic for the output to convert the output vector of the last layer to between 0 and 1.

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