Semantic recommendation method based on credible relationship and article association

Abstract

The invention belongs to the technical field of recommendation systems, and relates to a semantic recommendation method based on credible relationship and article association, which comprises the following steps: acquiring a user purchase record R, a user comment text set S and an article comment text set I; inputting the record R and the sets S and I into a semantic feature extraction module to obtain a user enhanced comment vector set Tfinal and an article comment vector set TI; inputting the record R into a sequence embedding module to obtain a user sequence embedding vector set HU and an article sequence embedding vector set HI; splicing the set Tfinal with the HU to obtain a feature EU of the user; splicing the set TI and the set HI to obtain a feature EI of the article; the features EU and EI are fused; inputting the fused feature representation into a score prediction module to obtain a predicted score; calculating a loss function value L according to the predicted score, and updating model parameters according to L until a trained recommendation model is obtained; according to the method, the auxiliary comments are constructed according to the trust relationship among the users giving similar scores to the same project, prediction is performed according to the auxiliary comments, and the prediction accuracy is improved.

Description

Technical Field

[0001] The present invention belongs to the technical fields of deep learning and recommendation systems, and relates to a semantic recommendation method based on trust relationships and item associations. Background Art

[0002] In recent years, the emergence of advanced computer technologies such as cloud computing, big data, and artificial intelligence has changed personal life. In the era of increasing digital content, quickly and accurately screening a large amount of online data to retrieve relevant information is a major challenge for individuals. In this context, recommendation systems have become powerful tools to help users discover relevant and interesting content. Collaborative filtering (CF) is the mainstream algorithm used in recommendation systems, including user-based and item-based algorithms. The main idea behind CF is to use the similarity between users or items to reveal users' preferences for items. Matrix factorization technology is very effective in the field of collaborative filtering, and it solves the problems of high time complexity and limited scalability that are common in early collaborative filtering algorithms. Although CF algorithms have shown good performance in many applications, the data sparsity problem has always been a bottleneck hindering the further improvement of their performance. The problem of data sparsity occurs when the proportion of users with rated items is significantly lower than the total number of users. In practice, the rating data of users in the dataset is often very small, and most users and items have no rating records. Since sufficient information is required to guide the rating prediction model, the results of rating prediction are difficult to meet the needs of practice.

[0003] The rich semantic information contained in review texts, as well as the complex data analysis capabilities of deep learning, provide possible solutions to alleviate the data sparsity problem. In many recommendation systems, users often submit comments and integer ratings. Compared with rating statistics, these comments provide more extensive information. Users provide the detailed reasons for their evaluations in these text comments, providing useful insights for the model to evaluate the attributes of items. In addition, review texts usually reveal the emotional tendencies of users, and by analyzing words from an emotional perspective, users' preferences can be more precisely depicted.

[0004] However, existing review-based recommendation methods ignore the trust relationships between users and the similarities and correlations between items while depicting users' preferences and item characteristics. The comments of users with trust relationships are of great significance for constructing a comprehensive user profile, which may lead to incomplete and limited recommendation results. Summary of the Invention

[0005] To solve the above-mentioned problems in the prior art, the present invention adopts a semantic recommendation method based on trust relationships and item associations, including: obtaining user and item data, inputting the user and item data into a trained recommendation model to obtain a recommendation result; the recommendation model includes: a semantic feature extraction module, a sequence embedding module, and a score prediction module;

[0006] The training process of the recommendation model includes:

[0007] S1. Obtain a dataset of users and items; the dataset of users and items includes: user historical purchase records, user review text sets, and item review text sets;

[0008] S2. Input the user historical purchase records, user review text sets, and item review text sets into the semantic feature extraction module to obtain a set of user enhanced review feature vectors and a set of item review feature vectors;

[0009] S3. Input the user historical purchase records into the sequence embedding module to obtain a set of user sequence embedding vectors and a set of item sequence embedding vectors;

[0010] S4. Concatenate the set of user enhanced review feature vectors and the set of user sequence embedding vectors to obtain the feature representation E of the user U ; concatenate the set of item review feature vectors and the set of item sequence embedding vectors to obtain the feature representation E of the item I ; fuse the feature representation E of the user U and the feature representation E of the item I ;

[0011] S5. Input the fused feature representation into the score prediction module to obtain a predicted score;

[0012] S6. Calculate the loss function value according to the predicted score, update the parameters of the recommendation model according to the loss function value, and when the loss function value is the smallest, obtain the trained recommendation model.

[0013] Beneficial effects:

[0014] 1. The present invention uses the semantic feature extraction module to extract fine-grained semantic information of users and items from the user review text sets and item review text sets, and uses the sequence embedding module to capture the potential associations between items by analyzing the item co-occurrence patterns in the user historical purchase records, obtaining the embedding vectors of users and items, thereby mining from two perspectives of the depth and breadth of user preferences, and combining the semantic information of users and items and the embedding vectors of users and items, enhancing the recommendation effect; 2. The present invention constructs auxiliary reviews based on the trust relationship between users who give the same or similar scores to the same item and the target user, and helps to predict the score according to the auxiliary reviews, improving the prediction accuracy. Brief Description of the Drawings

[0015] Figure 1 It is a flowchart of a semantic recommendation method based on trust relationship and item association provided by an embodiment of the present invention;

[0016] Figure 2 It is a flowchart of an auxiliary comment selection method based on trust relationship provided by an embodiment of the present invention;

[0017] Figure 3 It is a framework diagram of the fusion of user comments and auxiliary comments provided by an embodiment of the present invention;

[0018] Figure 4 It is a framework diagram of a semantic recommendation method based on trust relationship and item association provided by an embodiment of the present invention; Detailed Description of the Invention

[0019] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0020] The embodiment of the present invention adopts a semantic recommendation method based on trust relationship and item association, as Figure 1 , Figure 4 shown, and specifically includes the following content: obtaining user and item data, inputting the user and item data into a trained recommendation model to obtain a recommendation result; the recommendation model includes: a semantic feature extraction module, a sequence embedding module, and a score prediction module;

[0021] The training process of the recommendation model includes:

[0022] S1. Obtaining a dataset of users and items; the dataset of users and items includes: user historical purchase records, user comment text sets, and item comment text sets;

[0023] The user historical purchase record R includes: user ID, item ID, and the score given by the user to the item;

[0024] The comment text set S of user u u ={S u1 ,..., S ui ,..., S uN}, where, represents the comment set of user u on item i, is the l-th comment text of user u on item i;

[0025] The set of item review texts I = {I1,..., I2,..., I N}, where represents the review set of item i, is the k-th review text of item i.

[0026] S2. Input the user's historical purchase records, the set of user review texts, and the set of item review texts into the semantic feature extraction module to obtain the set of user enhanced review feature vectors T final and the set of item review feature vectors T I ;

[0027] The processing of the semantic feature extraction module on the user's historical purchase records, the set of user review texts, and the set of item review texts includes:

[0028] S21. Construct a set of user auxiliary review texts based on the set of user review texts and the user's historical purchase records;

[0029] There is a trust relationship among users who give the same or similar scores to the same item, and the reviews of users with a trust relationship are of great significance for constructing a comprehensive user profile. Therefore, the auxiliary reviews provided by the trusted parties trusted by the user can be used to assist in score prediction.

[0030] Specifically, constructing the set of user auxiliary review texts includes:

[0031] S211. Extract the score r of each user u for each item i from the user's historical purchase records u，i ;

[0032] S212. Construct a candidate user set for each user u according to the scores of the users for the items;

[0033] As Figure 2 shown, constructing the candidate user set of user u according to the scores of the users for the items includes:

[0034] If there are users among the remaining users who give the same score r u，i to item i, then select the users who give the same score r u，i to item i as the candidate users of user u;

[0035] If there are no users among the remaining users who give the same score r u，i to item i and there are users who give a score r u，i +1 to item i, then select the users who give a score r u，i +1 to item i as the candidate users of user u;

[0036] If there are no users among the remaining users who give a score r to item iu，i and the rating r u，i users with a rating of +1 and there is a rating r given to item i u，i users with a rating of -1, then filter the users who give a rating r to item i u，i users with a rating of -1 as candidate users for user u;

[0037] Otherwise, select user u itself as the candidate user.

[0038] S213. Select a review text from the review text sets of the candidate users in the candidate user set of user u as the auxiliary review of user u.

[0039] When selecting the auxiliary review from the candidate user set, the priority of each review text can be comprehensively evaluated by combining the timeliness and quality of the review text and setting different weights for them; the timeliness of the review text is the degree of proximity between the review release time and the current time, ensuring that the review content can reflect the latest user experience; the quality of the review text is the text length of the review, and longer reviews usually contain more details and useful information. In this way, while ensuring the timeliness and effectiveness of the review content, reviews that are rich in information and detailed in expression can be preferentially selected, so as to provide a more reference-worthy auxiliary review for user u.

[0040] Specifically, selecting a review text from the candidate user set of user u as the auxiliary review of user u includes: calculating the timeliness score s of each review text in the review text sets of each user in the candidate user set of user u t and the length score s l , for the timeliness score s of each review text t and the length score s l are weighted and combined to obtain the comprehensive score S of each review text, and the review text with the highest comprehensive score is selected as the auxiliary review of user u.

[0041] Among them, is the timeliness weight, is the text length weight, The timeliness score can be calculated by the time difference between the current time and the review release time. The smaller the time difference, the higher the score; the text length score can be normalized by the number of characters or words in the review. The longer the length, the higher the score.

[0042] S22. Perform text embedding on the user review text set, the item review text set, and the user auxiliary review text set to obtain the user review feature vector set, the item review feature vector set, and the user auxiliary review feature vector set;

[0043] Performing text embedding on the user review text set includes:

[0044] For each user review text in the user review text set perform word segmentation to obtain the segmented review text t′ ui，l ; add a marker [CLS] at the beginning of the segmented review text t′ ui，l to obtain the review text [[CLS]; t′ ui，l , and use the pre-trained BERT model to convert the review text [[CLS]; t′ ui，l into a vector representation t mi，l = BERT([[CLS]; t′ ui，l ), to obtain the user review feature vector set T u ;

[0045] Similarly, perform text embedding on the item review text set and the user auxiliary review text set to obtain the item review feature vector set T I and the user auxiliary review feature vector set T c .

[0046] S23. Fuse the user review feature vector set and the user auxiliary review feature vector set to obtain the user enhanced review feature vector set.

[0047] To make full use of the information in the auxiliary review and further enhance the representation ability of the user review, introduce the cross-attention mechanism, and focus on the key information in the user review and the auxiliary review.

[0048] Specifically, as Figure 3 shown, the fusion of the user review feature vector set T u and the user auxiliary review feature vector set T c includes:

[0049] Calculate the cross-attention weight matrix A according to the user review feature vector set T u and the user auxiliary review feature vector set T c ;

[0050]

[0051] where W Q and W K are learnable query and key weight matrices, is the dimension of the user review feature vector.

[0052] Calculate the weighted representation T c→u = A(T c WV ); where, W V is a learnable value weight matrix;

[0053] Fuse the user comment feature vector set and the weighted representation T c→u to obtain an enhanced user comment feature vector set T' u = T u + T c→u ;

[0054] Calculate the weighted representation T of the user comment on the auxiliary comment according to the cross-attention weight matrix A and the user comment feature vector set u→c = A T (T u W V );

[0055] Fuse the user auxiliary comment feature vector set and the weighted representation T c→u to obtain an enhanced user auxiliary comment feature vector set T' c = T c + T u→c ;

[0056] Concatenate Concat the enhanced user comment feature vector set T u ' and the enhanced user auxiliary comment feature vector set T' c to obtain a user enhanced comment feature vector set T final = Concat(T' u , T' c ).

[0057] S3. Input the user's historical purchase record into the sequence embedding module to obtain a user sequence embedding vector set H U and an item sequence embedding vector set H I ;

[0058] The sequence embedding module is an Item2Vec model; the processing of the user's historical purchase record by the sequence embedding module includes:

[0059] S31. Construct a historical purchase item sequence I of each user u according to the user's historical purchase record u = {i1, i2,..., i T}, combine the historical purchase item sequences of each user to obtain a user sequence S U = {I1, I2,..., I U}; where, T is the number of items, and i t is the ID of the item of the t-th interaction in the historical purchase item sequence;

[0060] S32. The user sequence SU and the historical purchase item sequence I of each user u Input into the Item2Vec model to obtain a preliminary set of user sequence embedding vectors and a set of item sequence embedding vectors;

[0061] The Item2Vec model processes the historical purchase item sequence I of the user u including:

[0062] The objective function of the Item2Vec model is: where N t represents the context item set of item i t , and P(i j |i t ) is the observation probability, defined as follows:

[0063]

[0064] where V represents the set of all items, v t is the target embedding vector of i t , u t is the context embedding vector of i t , and j is the index of the item.

[0065] By using the Item2Vec model, each item in the sequence can be represented as a dense vector, which contains its semantic and context relevance to other items in the sequence; the set of item sequence embedding vectors is denoted as H I ={v1, v2,..., v U}, where the set of item sequence embedding vectors of user u is denoted as v u ={v1, v2,..., v T}.

[0066] Similarly, the Item2Vec model processes the user sequence S U to obtain a preliminary set of user sequence embedding vectors.

[0067] S33. Use the self-attention mechanism to process the preliminary set of user sequence embedding vectors to obtain the final set of user sequence embedding vectors H U .

[0068] Using only Item2Vec may not be sufficient to capture the changes in user behavior and interests. In particular, it may be necessary to distinguish between important and less important items in the sequence or to handle the long-term dependencies of the sequence. The attention mechanism (self-attention) can effectively weigh the importance of each segment of the input sequence when calculating the representation of the input sequence. By leveraging self-attention, the correlations between items in the sequence can be effectively understood, thereby enhancing the interpretability of the obtained embeddings.

[0069] Specifically, using the self-attention mechanism to process the initial set of user sequence embedding vectors respectively includes:

[0070] Multiply the embedding vector v of each user in the initial set of user sequence embedding vectors u ={v1, v2,..., v T} by the learnable weight matrices W q , W k and W v to project the vectors into different spaces.

[0071] Q = v1W q + v2W q + … + v T W q

[0072] K = v1W k + v2W k + … + v T W k

[0073] V = v1W v + v2W v + … + v T W v

[0074] where Q, K, and V are the query, key, and value matrices respectively, and T×d is the embedding dimension.

[0075] Calculate the attention weight of item i t as follows:

[0076]

[0077] where Q it is the t-th row of Q, is the scaling factor, and Softmax is used to normalize the scores so that their sum equals 1.

[0078] Apply an activation function to the attention weights to ensure that they have values higher than zero, obtaining the final attention weights :

[0079]

[0080] Obtain item i through the weighted sum of attention weights t 's updated representation: where j covers all items in the sequence, and h t is the feature of the t-th item in the final item sequence embedding vector.

[0081] S4. Concatenate the user-enhanced comment feature vector set with the user sequence embedding vector to obtain the user's feature representation E U ; Concatenate the item comment feature vector set with the item sequence embedding vector to obtain the item's feature representation E I ; Concatenate the user's feature representation E U and the item's feature representation E I to perform fusion to obtain the fused feature representation E P = E U ⊙ E I ; where ⊙ represents the element-wise product operation;

[0082] S5. Input the fused feature representation into the rating prediction module to obtain the predicted rating;

[0083] The rating prediction module includes: a fusion module, a residual network, and a multi-layer perceptron; the fusion module includes a fully connected layer and a head self-attention layer; the processing of the fused feature representation by the rating prediction module includes:

[0084] S51. Input the fused feature representation into the fully connected layer; this layer converts the input into a new representation space;

[0085] The output representation of the fully connected layer (FC) is: F P = σ(W f E P + b f ); where W f is the weight, b f is the bias, and σ is the activation function.

[0086] S52. Input the output of the fully connected layer into the multi-head self-attention layer;

[0087] The multi-head attention layer (Multi-head attention) can effectively capture the complex relationships between the input subspaces. The multi-head self-attention layer combines a scaling factor to adjust the value of the inner product. The formula is as follows: [n1,..., n i ,..., n h = split(F P ); split(Fp ) represents the process of splitting the output of the fully connected layer to obtain the input of the i-th subspace, where n i is the i-th sub-part, and h is the number of attention heads.

[0088] The self-attention layer calculates the attention weights for each sub-part of the input. Specifically, the following formula is used to calculate the output of the i-th subspace:

[0089] Q i = n i W i Q

[0090] K i = n i W i K

[0091] V i = n i W i V

[0092] [[ID=3-six]]where Q[[ID=3-seven]] i [[ID=3-eight]]、K[[ID=3-nine]] i 、V i are the query, key, and value matrices for the i-th head, and W i Q 、W i K 、W i V are the weight matrices for the i-th head.

[0093] The attention scores for each subspace are calculated as follows: where Head i represents the attention score for the i-th subspace.

[0094] All subspaces are concatenated, and the final multi-head attention output is obtained through a linear transformation: MultiHead(Q, K, V) = concat(Head1,..., Head h )W O ; where W O ∈R d×d [[ID=6-nine]]represents the output weight matrix of the multi-head self-attention layer.

[0095] S53. Input the output of the multi-head self-attention layer and the fused feature representation into the residual network;

[0096] The residual network consists of several residual blocks, and each residual block includes a pointwise two-layer feed-forward network.

[0097] X = concat(E P, MultiHead)

[0098] X1 = residual_Connect(E P , X)

[0099] MultiHead represents the output of multi - head attention, residual_Connect represents residual connection, X represents the concatenated features, and X1 ∈ R T×d represents the output of the residual network.

[0100] S54. Input the output of the residual network into a multi - layer perceptron to obtain the predicted score.

[0101] The final result of the residual network is then fed into a multi - layer perceptron, which consists of several fully - connected layers with non - linear activation functions. The output of the last layer is then used to predict the score.

[0102] z l = σ(W l z l-1 + b l )

[0103]

[0104] where z l represents the output of the l - th layer perceptron, z0 = X1, L is the number of layers of the perceptron, W l is the weight of the l - th layer perceptron, b l is the bias of the l - th layer perceptron, represents the output of the last layer perceptron, that is, the predicted score.

[0105] S6. Calculate the value of the loss function according to the predicted score, update the parameters of the recommendation model according to the value of the loss function, and when the value of the loss function is the smallest, obtain the trained recommendation model.

[0106] To optimize the parameters of the model, an optimizer is used. This optimizer combines the advantages of momentum technology and the RMSProp algorithm and dynamically adjusts the learning rate during training. The squared loss function is used as the loss function:[[]] where Γ represents the dataset of users and items, is the predicted score of user u for item i, r ui is the true score of user u for item i.

[0107] The above-mentioned embodiments have further elaborated on the purpose, technical solutions, and advantages of the present invention. It should be understood that the above-mentioned embodiments are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made to the present invention within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A semantic recommendation method based on trust relationships and item associations, characterized in that, Including: Obtain data of users and items, input the data of users and items into a trained recommendation model, and obtain a recommendation result; The recommendation model includes: a semantic feature extraction module, a sequence embedding module, and a score prediction module; The training process of the recommendation model includes: S1. Obtain a dataset of users and items; the dataset of users and items includes: user historical purchase records, a set of user review texts, and a set of item review texts; S2. Input the user historical purchase records, the set of user review texts, and the set of item review texts into the semantic feature extraction module to obtain a set of user enhanced review feature vectors and a set of item review feature vectors; S3. Input the user historical purchase records into the sequence embedding module to obtain a set of user sequence embedding vectors and a set of item sequence embedding vectors; S4. Concatenate the user enhanced comment feature vector set and the user sequence embedding vector set to obtain the feature representation E of the user U ; concatenate the item comment feature vector set and the item sequence embedding vector set to obtain the feature representation E of the item I ; the feature representation E of the user U and the feature representation E of the item I are fused; S5. Input the fused feature representation into the score prediction module to obtain a predicted score; S6. Calculate the value of the loss function according to the predicted score, update the parameters of the recommendation model according to the value of the loss function, and when the value of the loss function is the smallest, obtain a trained recommendation model.

2. The semantic recommendation method based on trust relationship and item association according to claim 1, characterized in that, The processing of the semantic feature extraction module on the user historical purchase records, the set of user review texts, and the set of item review texts includes: S21. Construct a set of user auxiliary review texts according to the set of user review texts and the user historical purchase records; S22. Perform text embedding on the set of user review texts, the set of item review texts, and the set of user auxiliary review texts to obtain a set of user review feature vectors, a set of item review feature vectors, and a set of user auxiliary review feature vectors; S23. Fuse the set of user review feature vectors and the set of user auxiliary review feature vectors to obtain a set of user enhanced review feature vectors.

3. The semantic recommendation method based on trust relationship and item association according to claim 2, characterized in that The user historical purchase records include: user ID, item ID, and the score of the user for the item; constructing a set of user auxiliary review texts includes: S211. Extract the rating r of each item i by each user u from the user's historical purchase records u,i ; S212. Construct a candidate user set for each user u according to the score of the user for the item; S213. Select review texts from the set of review texts of the candidate users in the candidate user set of user u as the auxiliary review texts of user u.

4. The semantic recommendation method based on trust relationship and item association according to claim 3, characterized in that, Constructing a candidate user set for user u includes: If there are users among the remaining users who give the same rating r to item i u,i then screen out the users who give the same rating r u,i to item i as the candidate users of user u; If there is no user among the remaining users who gives the same rating r to item i and there is a user who gives a rating r u,i +1 to item i, then the users who give a rating r u,i +1 to item i are selected as candidate users for user u; u,i ​ If there is no user among the remaining users who gives a rating of r u,i and a rating of r u,i +1, and there is a user who gives a rating of r u,i -1 to item i, then select the users who give a rating of r u,i -1 to item i as the candidate users of user u; Otherwise, select user u itself as a candidate user.

5. The semantic recommendation method based on trust relationship and item association according to claim 3, characterized in that, Selecting review texts from the set of review texts of the candidate users in the candidate user set of user u as the auxiliary review of user u includes: calculating the timeliness score and length score of each review text in the set of review texts of the candidate users in the candidate user set of user u, performing weighted combination on the timeliness score and length score of each review text to obtain the comprehensive score of each review text, and selecting the review text with the highest comprehensive score as the auxiliary review of user u.

6. The semantic recommendation method based on trust relationship and item association according to claim 5, wherein The timeliness score of the review text is the time difference between the current time and the publication time of the review text.

7. A semantic recommendation method based on trust relationships and item associations according to claim 2, wherein Fusing the user comment feature vector set and the user auxiliary comment feature vector set includes: calculating the cross-attention weight matrix A based on the user comment feature vector set and the user auxiliary comment feature vector set; calculating the weighted representation T of the auxiliary comment on the user comment based on the cross-attention weight matrix A and the user auxiliary comment feature vector set c→u , fusing the user comment feature vector set and the weighted representation T c→u to obtain the enhanced user comment feature vector set T u '; calculating the weighted representation T of the user comment on the auxiliary comment based on the cross-attention weight matrix A and the user comment feature vector set u→c , fusing the user auxiliary comment feature vector set and the weighted representation T cvu to obtain the enhanced user auxiliary comment feature vector set T c '; concatenating the enhanced user comment feature vector set T u ' and the enhanced user auxiliary comment feature vector set T c ' to obtain the user enhanced comment feature vector set.

8. A semantic recommendation method based on trust relationship and item association according to claim 1, characterized in that The sequence embedding module processes the user's historical purchase records, including: constructing the historical purchase item sequence for each user based on the user's historical purchase records, combining the historical purchase item sequences of each user to obtain the user sequence; inputting the user sequence and the historical purchase item sequence of each user into the sequence embedding module respectively to obtain the user sequence embedding vector set and the item sequence embedding vector set; using the self-attention mechanism to process the user sequence embedding vector set to obtain the final user sequence embedding vector set.

9. A semantic recommendation method based on trust relationship and item association according to claim 1, characterized in that The rating prediction module includes: a fully connected layer, a multi-head self-attention layer, a residual network, and a multi-layer perceptron; the rating prediction module processes the fused feature representation, including: inputting the fused feature representation into the fully connected layer, inputting the output of the fully connected layer into the multi-head self-attention layer, inputting the output of the multi-head self-attention layer and the fused feature representation into the residual network, and inputting the output of the residual network into the multi-layer perceptron to obtain the predicted rating.

10. A semantic recommendation method based on a trusted relationship and item association according to claim 1, characterized in that The loss function value L is: Among them, Γ represents the dataset of users and commodities, is the predicted score of user u for commodity i, r ui is the true score of user u for commodity i.

Images